{"exportedAt":"2026-10-16T20:40:13.574Z","totalPuzzles":1414,"puzzles":[{"id":"4qJrNJh6tP","ctcId":17,"ctcDifficulty":"HARD","title":"Round The Houses","author":"Tallcat","rules":"Normal sudoku rules apply. Connect some cells in the grid to form an orthogonally connected loop that must pass through every cage in the grid exactly once. The cage totals given are the sum of the digits on the loop in each cage (at least one cell in each cage is not visited by the loop). Digits may not repeat in cages.","solution":"592786143138294576467315982854127369913648257726953814679831425241579638385462791","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The cage totals given are the sum of the digits on the loop in each cage (at least one cell in each cage is not visited by the loop).","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Connect some cells in the grid to form an orthogonally connected loop that must pass through every cage in the grid exactly once.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"H2qm8BLDHh","ctcId":43,"ctcDifficulty":"MEDIUM","title":"Dustpan","author":"Qodec","rules":"Normal sudoku rules apply. Cells marked with a circle show the number of digits with the same parity as that circled digit in that cell's 3x3 neighbourhood (including the digit in the cell itself). (Eg if r1c1 is a 1, all 3 cells surrounding it must be even.) Digits cannot appear in the same relative position within different 3x3 box regions. (Eg r1c1 and r4c4 cannot contain the same digit as they both represent the top left cell of their 3x3 boxes.)","solution":"378592641651374829924681375215867934796243518843159762189726453462935187537418296","constraints":["custom","disjoint-groups"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells marked with a circle show the number of digits with the same parity as that circled digit in that cell's 3x3 neighbourhood (including the digit in the cell itself).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"dL2mfgFDn8","ctcId":44,"ctcDifficulty":"MEDIUM","title":"Tallmath","author":"Qodec","rules":"Normal sudoku rules apply. The sum of the digits on a line is equal to the sum of the two digits in the circles that are connected by that line. Digits may be repeated on line-circle combinations.","solution":"278349651139765824564182973896471532357928146412536789943817265725694318681253497","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits on a line is equal to the sum of the two digits in the circles that are connected by that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"76mPFr6pLm","ctcId":56,"ctcDifficulty":"EASY","title":"Diagonal Sudoku","author":"Tom Collyer","rules":"Normal sudoku rules apply. Digits may not repeat along either marked diagonal.","solution":"786351249134279658295468731372984516648715923951632487563147892427893165819526374","constraints":["diagonal"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"J4mGJq6brH","ctcId":58,"ctcDifficulty":"EASY","title":"Between 1 and 9 Sudoku","author":"Tom Collyer","rules":"Normal sudoku rules apply. A clue outside the grid gives the sum of the digits between 1 and 9 in that row or column.","solution":"385794261726183594149625738268439157537812946914567823673958412851246379492371685","constraints":["sandwich"],"constraintFacts":[{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"P7NmpD3P9p","ctcId":59,"ctcDifficulty":"EASY","title":"Thermo Sudoku","author":"Tom Collyer","rules":"Normal sudoku rules apply. Digits increase along a thermo from bulb to tip.","solution":"948627135267531984531948276692854317753169428814273569375482691186395742429716853","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"8kw6qfv8ku","ctcId":60,"ctcDifficulty":null,"title":"Elbow Joint","author":"Arachno","rules":"Each row, column, and 3x3 region contains the digits 1 through 9. Digits increase from the bulb end of a thermometer.","solution":"617235498824169573935874216469317825572698341381542967743981652156423789298756134","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"2qstow5gy2","ctcId":61,"ctcDifficulty":"HARD","title":"Fault Lines","author":"SeveNateNine","rules":"Sudoku: Place the digits 1-9 in each cell of the grid such that no digit repeats in any row, column or box.\n\nYin-Yang: Chose two colors with which to color each cell in the grid such that all cells of either color are orthogonally connected to each other, and no 2x2 area may be entirely one color.\n\nArrows: A circled cell will contain a digit equal to the sum of each connected arrow.\n\nColoring: Identical digits which see each other by a bishops move (diagonally) must be the same color.\n\nCaged cells must be the same color.","rulesClarified":"Normal sudoku rules apply: place the digits 1-9 so that no digit repeats in any row, column or box.\n\nYin-Yang: colour every cell with one of two colours, so that the cells of each colour are all orthogonally connected to each other. No 2x2 area may be one colour throughout.\n\nArrows: a circled cell contains a digit equal to the sum of the digits along each arrow that starts at that circle. The circled cell is not part of the sum. A circled cell with two arrows must satisfy both sums.\n\nColouring: two identical digits on the same diagonal, at any distance along it, must be the same colour.\n\nCaged cells must be the same colour.","solution":"213867954658924173794531286945716832372498561186352749431285697827649315569173428","constraints":["arrow","custom","yin-yang"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Coloring: Identical digits which see each other by a bishops move (diagonally) must be the same color. Caged cells must be the same color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"r1jg7q3rbs","ctcId":62,"ctcDifficulty":null,"title":"Odds And Ends","author":"Ul-Rhymm","rules":"Normal sudoku rules apply ie place the digits 1 to 9 exactly once each in every row, column, and 3x3 region. Each pink line contains a set of non-repeating consecutive digits in any order. In cages, digits do not repeat and sum to the number in the top left corner. Cages marked with an “O” sum to an odd number.","solution":"831926754596478123742531698963147285175283469284659317359762841618394572427815936","constraints":["cage","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"bo3con7363","ctcId":63,"ctcDifficulty":null,"title":"Maze Of Lies","author":"Egregious Error","rules":"Normal sudouku rules may apply. You find yourself in a maze of regions connected by doors. Each region is made of rooms connected by passageways.\nYou enconter some helpful people along your travels through the rooms. Here's what they have to say:\n\nStephanie\nSome rules apply to the whole maze. Others apply to regions.\nSome people tell only lies. Some only tell the truth.\nAll true statements about region specific rules apply to different regions.\n\nDaniel\nEveryone lies all the time. In particular Stephanie lies all the time. Only listen to me.\nI'm pretty sure Stephanie didn't even tell you the truth about what you're supposed to do here.\nSome rooms contain a digit from 1-8 while other are empty.\nRooms in the same column or row containing the same digit must be further apart than the value of that digit.\nRooms containing the same digit can not touch diagonally.\nMaurice is a liar.\n\nMaurice\nAll rooms contain a digit from 1-9 such that no digit is repeated in a row, column, or region.\nOnly one digit is still visible, a five. In fact, once you know the rules of the regions you will be able to immediately place 2 more fives in the grid. Please help us find all the missing digits.\n\nPatrick\nMaurice and Helen are both telling the truth.\nThere is a region with a single door to the West in which orthogonally connected rooms not separated by a wall must contain digits at least 4 apart.\nThere is a region in which orthogonally connected rooms not separated by a wall must contain digits that differ by a power of 2.\nThere is a region in which orthogonally connected rooms not separated by a wall must contain digits that are non-consecutive.\n\nCaroline\nIn one region with only 2 doors the largest and smallest digits on the shortest path between the doors are next to the doors.\nIn another region with only 2 doors the digits on the shortest path between the doors strictly increase from one door to the other.\nIn yet another region with only 2 doors along the shortest path between the doors the digit next to one of the doors is equal to the sum of the remaining digits.\nBy the way, Annabelle is a liar.\n\nVladimir\nPatrick is a liar.\nThere is a region with a single door to the South in which all numbers formed by reading the digits from North to South or West to East from wall to wall (or door) are perfect squares.\nAnother region read this way contains prime numbers.\nA third region read this way contains multiples of 7.\n\nHelen\nExactly one of Jessica and Annabelle is a liar.\nOne region of the maze is an exact clone of another, but may be rotated.\n\nAnnabelle\nIn one region with only 2 doors the digits on the shortest path between the doors alternate between odd and even.\nIn another region with only 2 doors the digits on the shortest path between the doors form a prime number when read in one direction.\nIn yet another region with only 2 doors the product of the digits on the shortest path between doors is a perfect square.\nBy the way, Caroline is a liar.\n\nJessica\nThere are either 3 or 4 liars here.\nThere is a region with a single door to the North in which orthogonally connected rooms not separated by a wall must not both contain prime numbers.\nThere is another region with a single door to the East in which orthogonally connected rooms not separated by a wall contain digits that either have a difference of 1 or one is double the other (or both!)\n\nSee the full adventures at https://www.two-pi-noir.agency/puzzles/maze_of_lies","solution":"814569723952137648371248965695324871486712359723856194569481237137695482248973516","constraints":["clone","custom"],"constraintFacts":[{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c43"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Rooms in the same column or row containing the same digit must be further apart than the value of that digit. Rooms containing the same digit can not touch diagonally. All rooms contain a digit from 1-9 such that no digit is repeated in a row, column, or region. There is a region with a single door to the West in which orthogonally connected rooms not separated by a wall must contain digits at least 4 apart.","evidence":"rules","lessonPolicy":"open","sectionIds":["c18","c19","c22","c28"]}]},{"id":"fx2o4cl240","ctcId":67,"ctcDifficulty":"MEDIUM","title":"Don't Repeat Yourself","author":"DedaKosta","rules":"Normal sudoku rules apply. Each unique clue type listed below cannot contain more than one instance of each of the digits 1-9. Clue types: a) Digits separated by a white dot are consecutive; b) digits separated by a black dot are in a 1:2 ratio, ie. one digit is double the other; c) digits in cages sum to the total in the upper left corner, if given; d) digits on a pink line form a set of consecutive digits IN ORDER. Eg 123 and 321 are valid length-3 lines but 132 is not; e) digits outside the grid give the sum of the digits on the diagonal pointed to by the arrow; f) each segment on a blue line sums to the same total. Box borders separate a line into segments. The grid is covered in fog. Placing correct digit in a cell may reveal some of the fog, possibly revealing more clues.","solution":"596317482418629537372548169641295873789136245253784916164953728835472691927861354","fogLight":"","constraints":["cage","custom","fog","kropki","little-killer","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each unique clue type listed below cannot contain more than one instance of each of the digits 1-9. Clue types: a) Digits separated by a white dot are consecutive; b) digits separated by a black dot are in a 1:2 ratio, ie. one digit is double the other; c) digits in cages sum to the total in the upper left corner, if given; d) digits on a pink line form a set of consecutive digits IN ORDER.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"Ln8JDNTH8r","ctcId":197,"ctcDifficulty":"HARD","title":"Exclusion","author":"Phistomefel","rules":"Normal sudoku rules apply. Digits increase along a thermometer starting from the bulb end. The digits on a purple line form a non-repeating, consecutive set. These digits can appear in any order.","solution":"729453186154689273368172954417598632593726418682314597871245369235967841946831725","constraints":["renban","thermometer"],"constraintFacts":[{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qnBRLpQQ4H","ctcId":210,"ctcDifficulty":"MEDIUM","title":"Leapfrog","author":"jovi_al and echoes","rules":"Normal Sudoku rules apply. Digits in marked cages must not repeat, and must sum to the total given in the top left corner of the cage.","solution":"746218953825973641319645872567132498932486715184759326651394287473821569298567134","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"PnnNbp7GHR","ctcId":272,"ctcDifficulty":"HARD","title":"Even Lighting","author":"Jay Dyer","rules":"Normal sudoku rules apply. Some cells (to be located by the solver) are doublers, and have a value equal to double their digit. The even-valued cells (including doublers) form a single orthogonally connected area. Every even-valued cell must see at least one doubler in a straight line horizontally or vertically (odd-valued cells block the view). Doublers must not see each other. The values of cells in a cage sum to the total in the corner of the cage (if given). Digits may not repeat in a cage (though values may repeat).","solution":"691783524842591637357642918915836472238475196476129853184257369763914285529368741","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The values of cells in a cage sum to the total in the corner of the cage (if given).","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Some cells (to be located by the solver) are doublers, and have a value equal to double their digit. The even-valued cells (including doublers) form a single orthogonally connected area. Every even-valued cell must see at least one doubler in a straight line horizontally or vertically (odd-valued cells block the view). Doublers must not see each other. Digits may not repeat in a cage (though values may repeat).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7"]}]},{"id":"h9q22bptmF","ctcId":273,"ctcDifficulty":"HARD","title":"Blackout","author":"Jay Dyer","rules":"Normal sudoku rules apply. Cells are initially covered in fog, and placing correct digits will clear the fog around those digits. Mark nine cells such that there is one marked cell in each row, column and 3x3 box. The digit in the first cell of a row, column or 3x3 box gives the position of the marked cell in that row, column or 3x3 box. Each digit appears in exactly one marked cell. Adjacent digits on a green line differ by at least 5.\n\nEg if r5c3 was a marked cell then r5c1 would be a 3 (marked cell is 3rd position in its row); r1c3 would be a 5 (marked cell is 5th position in its column); and r4c1 would be a 6 (marked cell is the 6th position in normal reading order of its 3x3 box).","rulesClarified":"Normal sudoku rules apply.\n\nCells start covered in fog. Placing a correct digit clears the fog around it.\n\nMark nine cells so that each row, each column and each 3x3 box contains exactly one marked cell.\n\nThe digit in the first cell of a row, column or box gives the position of that group's marked cell, counted from 1. The first cell of a row is its leftmost cell, the first cell of a column is its topmost cell, and the first cell of a 3x3 box is its top-left cell. Position in a box is counted in normal reading order: left to right, then top to bottom.\n\nEach digit from 1 to 9 appears in exactly one marked cell.\n\nAdjacent digits on a green line differ by at least 5.\n\nExample: if r5c3 is a marked cell, then r5c1 holds 3 (it is third in row 5), r1c3 holds 5 (it is fifth in column 3), and r4c1 holds 6 (it is sixth in reading order in its box).","solution":"147963528859472136623518974291837465734156289568249713385791642916324857472685391","fogLight":"","constraints":["custom","fog","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Mark nine cells such that there is one marked cell in each row, column and 3x3 box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"3DrNDGMDnG","ctcId":276,"ctcDifficulty":"HARD","title":"Shenanigans","author":"Jay Dyer","rules":"Normal sudoku rules apply. On renban lines (purple), digits on the line cannot repeat, and form a set of consecutive digits in some order. On German whisper lines (green), adjacent digits differ by at least 5. On region sum lines (blue), each time the line passes through a 3x3 region, the sum of digits on the line is the same. Each line is exactly one of the above constraint types, but some have been drawn in the wrong colour. The wrong-coloured lines are exactly those lines which have the digit D on them (D must be determined by the solver).","solution":"965283714483719652172645389657198243834572196291364578329457861718926435546831927","constraints":["custom","german-whispers","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each line is exactly one of the above constraint types, but some have been drawn in the wrong colour. The wrong-coloured lines are exactly those lines which have the digit D on them (D must be determined by the solver).","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"77hLMnt2bM","ctcId":345,"ctcDifficulty":"VERY HARD","title":"Fogrotto","author":"Math Pesto","rules":"Normal sudoku rules apply. The grid is covered mostly in darkness. Placing correct digits in cells will illuminate more of the grid. Cells are either wall or cave cells. Walls are orthogonally connected to the edge of the grid and the cave is one orthogonally connected area. A 2x2 area cannot be fully wall nor fully cave. White circles are cave cells and the value in a circle is the number of cave cells “seen” in that row and column, including the cell itself. Walls obstruct vision. A cage contains no repeated digits, and the values of the cave cells sum to the given total. Wall cells don’t count towards the sum. (Note: A cage’s clue doesn't necessarily appear in the uppermost nor leftmost cell.) A doubler appears exactly once in each row, column, and 3x3 box. For purposes of circles and cage sums, such cells’ digits are doubled in value. Each digit is doubled once.","solution":"359781426764392518128564937497136852516827349283459761642975183935618274871243695","fogLight":"R7C1,R8C1,R9C1,R7C2,R8C2,R9C2,R7C3,R8C3,R9C3","constraints":["cage","custom","fog"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"A cage contains no repeated digits, and the values of the cave cells sum to the given total.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"White circles are cave cells and the value in a circle is the number of cave cells “seen” in that row and column, including the cell itself. A doubler appears exactly once in each row, column, and 3x3 box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c12"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"Qd8gJRm7Fh","ctcId":360,"ctcDifficulty":"VERY HARD","title":"Full Rank Sudoku","author":"Gliperal","rules":"Normal sudoku rules apply. Considering all rows and columns as 9-digit numbers read from the direction of the clue and ranked from lowest (1) to highest (36), a clue represents where in the ranking that row/column lies.","solution":"987642153621835974345971628179283546568794312234156789852367491496518237713429865","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Considering all rows and columns as 9-digit numbers read from the direction of the clue and ranked from lowest (1) to highest (36), a clue represents where in the ranking that row/column lies.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"F4rth2r3mP","ctcId":361,"ctcDifficulty":"MEDIUM","title":"Turquoise","author":"bellsita","rules":"Normal sudoku rules apply. Digits along a blue line sum to the same value in each 3x3 box the line passes through. Different lines may have different sums. eg r1c2 + r2c2 + r3c2 = r4c3 + r5c3 + r6c3 = r7c2 + r8c2 + r9c2.  Cells separated by a black dot contain digits in a 1:2 ratio (ie one digit must be double the other). Cells separated by a white dot must contain consecutive digits. Not all dots are given.","solution":"749628351851743962632195784263871549975462813184359627598217436417536298326984175","constraints":["kropki","region-sum-line"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"m7HmnD8T8p","ctcId":362,"ctcDifficulty":"MEDIUM","title":"Bismuth","author":"bellsita","rules":"Normal sudoku rules apply. Cells separated by a black dot contain digits with a 1:2 ratio (ie one digit is double the other). Cells separated by a white dot must contain consecutive digits. Not all dots are given. The grey squares contain even digits. Digits along a blue line sum to the same value in each 3x3 box the line passes through. (eg r2c1+r2c2+r2c3=r1c4+r2c5+r1c6=r2c7+r2c8+r2c9). Different lines may have different sums.","rulesClarified":"Normal sudoku rules apply.\n\nA black dot between two cells means one of the two digits is double the other (a 1:2 ratio).\n\nA white dot between two cells means the two digits are consecutive.\n\nNot all dots are given. A cell pair with no dot between them gives no information.\n\nThe grey squares contain even digits.\n\nDigits along a blue line sum to the same value in each 3x3 box the line passes through. Only the cells of the line inside a given box count toward that box's total. Example: r2c1+r2c2+r2c3 = r1c4+r2c5+r1c6 = r2c7+r2c8+r2c9.\n\nDifferent blue lines may have different sums.","solution":"123689574657432891498715326571268943384951762962347158735124689219876435846593217","constraints":["even","kropki","region-sum-line"],"constraintFacts":[{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"2f49L7B6Tt","ctcId":384,"ctcDifficulty":"HARD","title":"Network","author":"Niverio","rules":"Normal sudoku rules apply. Digits along a line must have values between the digits on the circled ends of that line. Digits in a white circle must appear in at least one of the cells touching that circle.","solution":"721468935534129678968357241682791354145836792397245816856913427419672583273584169","constraints":["between-line","counting-circle"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"TBdjr7BB4J","ctcId":422,"ctcDifficulty":"HARD","title":"Swivel","author":"Tallcat","rules":"Place 1-9 in each row, column and marked region. A purple line contains a set of consecutive digits in any order.","solution":"912456783536198247764239518298743651349825176853671429125967834671584392487312965","constraints":["renban"],"constraintFacts":[{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"b8qfQH4qQ3","ctcId":423,"ctcDifficulty":"VERY HARD","title":"Ten-Oh","author":"Qodec","rules":"Normal sudoku rules apply. Each line consists of one or more contiguous groups of cells, each of which sums to 10. These groups of cells cannot overlap. Digits may repeat freely on lines and even within sums.","solution":"672548913489213675531697482294175368718364529356829741965481237147932856823756194","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each line consists of one or more contiguous groups of cells, each of which sums to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"RP7HfFgQdt","ctcId":424,"ctcDifficulty":"HARD","title":"Sandwich Counts","author":"RockyRoer","rules":"Normal sudoku rules apply. A number outside the grid indicates the sum of the digits in the cells sandwiched between the 1 and 9 in its column. A number in a circled cell indicates the total number of cells sandwiched between the 1's and the 9's in the row and column containing the circle. If a cell is simultaneously in a row sandwich and column sandwich, it is only counted once. Not all circles are necessarily given.","solution":"723184569896325174541697238138456927275931846469872315354269781687513492912748653","constraints":["custom","sandwich"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A number in a circled cell indicates the total number of cells sandwiched between the 1's and the 9's in the row and column containing the circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"b3QH7jB4FJ","ctcId":425,"ctcDifficulty":"VERY HARD","title":"Highway to the Danger Zone","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nDivide the entire grid into killer cages, each of which is a set of orthogonally connected cells. Each cage contains exactly one clue, which may be in any position in the cage, and gives the sum of the digits in that cage. Digits may not repeat in a cage. Single cell cages are allowed.\n\nDraw a single loop through the centres of some cells with no branches or crossings, which visits each cage exactly once. The loop moves orthogonally from cell to cell. If two cells share an edge but are in different cages, at least one of them must be visited by the loop. The digit in a clued cell equals the number of cells in that cage which are visited by the loop.","solution":"264953817591278346783641952126589734839427165457136298948715623675392481312864579","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Each cage contains exactly one clue, which may be in any position in the cage, and gives the sum of the digits in that cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single loop through the centres of some cells with no branches or crossings, which visits each cage exactly once. The digit in a clued cell equals the number of cells in that cage which are visited by the loop.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c9"]}]},{"id":"NNttMGHq7T","ctcId":426,"ctcDifficulty":"HARD","title":"Lace Agate","author":"Niverio","rules":"Normal sudoku rules apply. Blue lines in the grid are Region Sum Lines. For each blue line, digits on the line have an equal sum N within each 3x3 box the line passes through. Multiple entries to a 3x3 box sum separately. eg r3c3 = r2c4+r3c4 = r4c4+r5c4","solution":"348921657751436298269587134527164983693875421184392576412758369976243815835619742","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"For each blue line, digits on the line have an equal sum N within each 3x3 box the line passes through.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"jq4RbMd67t","ctcId":427,"ctcDifficulty":"VERY HARD","title":"Everything Is Rihgt","author":"DiMono","rules":"This is a puzzle that must be solved twice! Normal sudoku rules apply. Normal Killer, Little Killer, Quadruple, Kropki, Thermometer, Palindrome, Maximum, Minimum, and XV rules apply (see video description for detailed rules). Red clues are each at least one of normal Skyscrapers, X-Sum, or Sandwich clues. After solving the puzzle, save your solution, because it's time to solve it again as a Wrogn puzzle! All clues in the grid must be made invalid in the finished solution, and red clues cannot be ANY of valid Skyscrapers, X-Sum, or Sandwich clues. To be considered invalid, the maximum cell must be less than AT LEAST one adjacent cell, the minimum cell must be greater than AT LEAST one adjacent cell, thermometers must NOT increase from bulb to tip, and quadruple circles may have some BUT NOT ALL listed digits in the surrounding cells. Since 5 is not greater than or less than 5, < effectively becomes >= and > becomes <=. ADDITIONALLY, when solving the Wrogn version, no digit may be the same as it was in the Right version. i.e. if R1C1 was a 1 the first time, it may not be a 1 the second time. IT IS IMPOSSIBLE TO SOLVE THE WROGN VERSION WITHOUT FIRST SOLVING IT NORMALLY","solution":"678139425259476138314285679541697382726843951983512764432751896895364217167928543","constraints":["XV","cage","custom","kropki","little-killer","maximum","minimum","palindrome","quadruple","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Red clues are each at least one of normal Skyscrapers, X-Sum, or Sandwich clues. ADDITIONALLY, when solving the Wrogn version, no digit may be the same as it was in the Right version. i.e. if R1C1 was a 1 the first time, it may not be a 1 the second time.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"maximum","type":"maximum","variant":"modified","modifiers":[],"params":null,"note":"Normal Killer, Little Killer, Quadruple, Kropki, Thermometer, Palindrome, Maximum, Minimum, and XV rules apply (see video description for detailed rules).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"minimum","type":"minimum","variant":"modified","modifiers":[],"params":null,"note":"Normal Killer, Little Killer, Quadruple, Kropki, Thermometer, Palindrome, Maximum, Minimum, and XV rules apply (see video description for detailed rules).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"DRMqF6t8td","ctcId":445,"ctcDifficulty":"MEDIUM","title":"Peering Into The Fog","author":"Jay Dyer","rules":"Normal sudoku rules apply. Digits may not repeat along a main diagonal (marked in blue). In cages, digits must sum to the small clue in the top left corner of the cage (which is always given). Digits cannot repeat within a cage. Placing correct digits in the grid will clear the fog.","solution":"719562438436789521582134796163425879874691253295378164951243687347856912628917345","fogLight":"R1C1,R1C2,R2C1,R2C2,R1C8,R1C9,R2C8,R2C9,R8C1,R8C2,R9C1,R9C2,R8C8,R8C9,R9C8,R9C9","constraints":["cage","diagonal","fog"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"G7QHB4G3M9","ctcId":551,"ctcDifficulty":"HARD","title":"Can Of Worms","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Along thermometers, digits must increase from the bulb end.","solution":"871539462634271895529846371197324586253768149486195723742613958365987214918452637","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"rB3dmRbj7H","ctcId":554,"ctcDifficulty":"MEDIUM","title":"High Temperatures","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits on thermometers increase from the bulb end.","solution":"563192487417658923298734561371869245854213679629475138185326794936547812742981356","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"dLTrH6DM6F","ctcId":636,"ctcDifficulty":"MEDIUM","title":"Pac-Man Sudoku","author":"Math Pesto","rules":"Normal sudoku rules apply. The leftmost and rightmost cells of a row are considered orthogonally adjacent for the purposes of ALL rules below. Cells joined by a white dot contain consecutive digits. Not all white dots are necessarily given. Shade some cells in the grid and leave the rest unshaded such that all shaded cells are orthogonally connected and no 2x2 region is entirely shaded. A cell containing Pac-Man, Blinky, Pinky, Inky, or Clyde (yellow, red, pink, blue, and orange)—or part of a white dot—must be shaded. A cell containing a small clue in the top-left corner is a “killer clue” and must remain unshaded. Digits may not repeat within an orthogonally connected area of unshaded cells, and they sum to the killer clue. (Note: Unshaded regions may not touch each other orthogonally and not all regions necessarily have a killer clue.) Starting in R5C2, Pac-Man must travel orthogonally through the grid. His path may not touch itself orthogonally, although it may do so diagonally, and the path cannot intersect or overlap itself. Pac-Man must go directly through each white dot; his path is completed immediately after going through the final dot. Pac-Man's path cannot be orthogonally adjacent to any of the ghosts (red, pink, blue, and orange) nor can the path enter unshaded cells.","solution":"587126943139457862642893517796584231813672495254319786965741328471238659328965174","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits may not repeat within an orthogonally connected area of unshaded cells, and they sum to the killer clue.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The leftmost and rightmost cells of a row are considered orthogonally adjacent for the purposes of ALL rules below. Shade some cells in the grid and leave the rest unshaded such that all shaded cells are orthogonally connected and no 2x2 region is entirely shaded. A cell containing Pac-Man, Blinky, Pinky, Inky, or Clyde (yellow, red, pink, blue, and orange)—or part of a white dot—must be shaded. A cell containing a small clue in the top-left corner is a “killer clue” and must remain unshaded. Starting in R5C2, Pac-Man must travel orthogonally through the grid. Pac-Man must go directly through each white dot; his path is completed immediately after going through the final dot.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c6","c7","c10","c12"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"23rLgH2f6b","ctcId":747,"ctcDifficulty":"MEDIUM","title":"Read Between the Lines","author":"James Kopp","rules":"Normal sudoku rules apply. Neighbouring digits along green lines have a difference of at least five. Digits along a purple line are a set of consecutive numbers in any order with no repeats. Cells joined by black dots are in the ratio of 1:4.","solution":"138574962625398714749621358312947586864135279597862143473256891986713425251489637","constraints":["german-whispers","kropki","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"A different relation on the same cells","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"Mn6b323tMJ","ctcId":748,"ctcDifficulty":"HARD","title":"Gilded Cages","author":"James Kopp","rules":"Normal sudoku rules apply. Digits do not repeat on the marked diagonal. Digits in a cage do not repeat and their sum is given. Each digit inside a cage is consecutive with its orthogonally adjacent neighbours outside the cage.","solution":"854176293937285146126349758615432879279518634483967521798623415361754982542891367","constraints":["cage","custom","diagonal"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each digit inside a cage is consecutive with its orthogonally adjacent neighbours outside the cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"TGdG44jt84","ctcId":749,"ctcDifficulty":"MEDIUM","title":"Tower of Babel","author":"Jay Dyer","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow's circle.","solution":"436829715951764238782513496845196372169372854327458961294635187673281549518947623","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"PmLFFN27Hq","ctcId":777,"ctcDifficulty":"MEDIUM","title":"Consecutive Thermo","author":"clover!","rules":"Normal sudoku rules apply. Digits along thermometers must increase from the bulb end. In addition, digits along thermometers must be consecutive, such as 23456.","solution":"394657281685214397271398456836521749942786513157943862728165934519432678463879125","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In addition, digits along thermometers must be consecutive, such as 23456.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"pbb4pNb3T4","ctcId":818,"ctcDifficulty":"HARD","title":"Tatamidoku","author":"Math Pesto","rules":"Normal sudoku rules apply. Adjacent digits on a green line differ by 5 or more. \nDivide the grid into non-overlapping rectangular regions so that each region contains exactly one small clue (found in the top left corner of some cells). Four regions cannot share the same cell corner. Digits may not repeat within a region and sum to that region's small clue. The digit placed in a small clue cell gives information about that region:\n1–4: The region has a greater width than height.\n5: The region is a square. \n6–9: The region has a greater height than width.","solution":"816249753397568214254371896439816527581427369672935481943682175768153942125794638","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into non-overlapping rectangular regions so that each region contains exactly one small clue (found in the top left corner of some cells). Digits may not repeat within a region and sum to that region's small clue. The digit placed in a small clue cell gives information about that region:","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"v7oVqMfjTs","ctcId":823,"ctcDifficulty":"MEDIUM","title":"Pencilmark Sudoku","author":"Florian Wortmann","rules":"Normal Sudoku rules.\n\nSome cells have been pencilmarked with their candidates.","solution":"278569413916384752435127968123496587894275136567831249759643821642718395381952674","constraints":[],"constraintFacts":[]},{"id":"jPN8QBBnHr","ctcId":834,"ctcDifficulty":"HARD","title":"23 Renban","author":"Florian Wortmann","rules":"Normal sudoku rules apply. Each purple line contains a set of non-repeating consecutive digits. These digits can appear in any order.","solution":"965328471324761598178594632219647385487253169653189247746912853532876914891435726","constraints":["renban"],"constraintFacts":[{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"GhDbrNPh8h","ctcId":835,"ctcDifficulty":"MEDIUM","title":"Colorado 8","author":"Florian Wortmann","rules":"Normal sudoku rules apply. Cells connected by an X contain digits summing to 10. Cells connected by a V contain digits summing to 5. Not all possible Xs and Vs are given. The clue outside the grid gives the sum of the first X cells in the corresponding column, where X is the digit in the cell nearest to the clue.","solution":"912358764478926351356714928235497186867132549149685237521849673694273815783561492","constraints":["XV","x-sum"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"mt7pgJhd9q","ctcId":860,"ctcDifficulty":"MEDIUM","title":"Strands","author":"TotallyNormalCat","rules":"Totally normal sudoku rules apply. In cages, digits must sum to the small clue in the top left corner of the cage. Digits must not repeat in a cage. There is exactly one cage in the grid where the cage is broken ie either the sum is incorrect or digits are repeated or both.  The pink lines are 'incomplete arrows'.  The digit on one end of the line is the sum of the other digits on the same line.","solution":"256978341398146275741532869967321458823754916514869723439215687172683594685497132","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"In cages, digits must sum to the small clue in the top left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There is exactly one cage in the grid where the cage is broken ie either the sum is incorrect or digits are repeated or both. The pink lines are 'incomplete arrows'.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]}]},{"id":"dhm2Md99Mt","ctcId":895,"ctcDifficulty":"VERY HARD","title":"Reef","author":"zetamath","rules":"Normal sudoku rules apply. Shade some cells in the grid.  Those cells are part of the 'coral'.  The rest of the cells are 'water'.  All coral cells are orthogonally connected.  All bodies of water connect to the edge of the grid.  No 2x2 is entirely water or entirely coral. Digits do not repeat within cages, and the sum of the coral cells within each cage must equal the sum of the water cells within that cage. The digit in a circle gives the number of cells within its cage which match its colour (coral or water).  The total includes itself.","solution":"319548762426173859785962143891234576263785491574691328147829635938456217652317984","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells in the grid. Digits do not repeat within cages, and the sum of the coral cells within each cage must equal the sum of the water cells within that cage. The digit in a circle gives the number of cells within its cage which match its colour (coral or water).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c8","c9"]}]},{"id":"JFgdrLjrdQ","ctcId":896,"ctcDifficulty":"HARD","title":"Equal Sum Arrows","author":"Sumanta (ANU)","rules":"Normal sudoku rules apply. Where arrows point from the same cell, the sum of the digits along the two indicated diagonals (from that cell to the edge of the grid) is the same.","solution":"364971582725834916189256473872693145516742398493518267648125739237469851951387624","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Where arrows point from the same cell, the sum of the digits along the two indicated diagonals (from that cell to the edge of the grid) is the same.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"T3tMM749d7","ctcId":897,"ctcDifficulty":"MEDIUM","title":"Double The Mines","author":"Florian Wortmann","rules":"Normal sudoku rules apply. The black dot joins digits in a 1:2 ratio (ie one digit is double the other). Not all dots are given. The sum of the digits along a grey line is equal to the sum of the digits in the circles at either end of the line. Shade some cells such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected. No 2x2 area may be fully shaded or fully unshaded. The circles act as 'minesweeper' clues. Ie Cells containing a circle are always unshaded, and their value is the number of shaded cells in the surrounding 3x3 area (i.e. the up to eight cells that touch the circle either orthogonally or diagonally).","solution":"256174983317968524948523167693745812524816379871239645762391458435687291189452736","constraints":["custom","kropki","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits along a grey line is equal to the sum of the digits in the circles at either end of the line. The circles act as 'minesweeper' clues.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"mNjQBPt2QF","ctcId":912,"ctcDifficulty":"MEDIUM","title":"Three in the Corner","author":"James Kopp","rules":"Normal sudoku rules apply. Identical digits cannot appear a chess king's move away from each other. Along thermometers, digits increase from the bulb to the ends.","solution":"987365124612874395543912876261587439759431268438296751124653987395748612876129543","constraints":["antiking","thermometer"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"QDLp7pfG83","ctcId":913,"ctcDifficulty":"MEDIUM","title":"Staples","author":"Florian Wortmann","rules":"Normal sudoku rules apply. Digits along a thermometer increase from the bulb end.","solution":"176592348982341657435678912518429763629753184743186295891234576354967821267815439","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7bBDd6q2J8","ctcId":951,"ctcDifficulty":"MEDIUM","title":"Stumped","author":"James Kopp","rules":"Normal sudoku rules apply. Along thermometers, digits increase from the bulb to the end. The clue outside the grid indicates the sum of the digits along the indicated diagonal . Digits on the blue line have an equal sum N (to be determined by the solver) within each box it passes through. In the centre box the two segments of the line sum to N separately.","solution":"798235641351674829462189735573421968684793152129568374235917486816342597947856213","constraints":["little-killer","region-sum-line","thermometer"],"constraintFacts":[{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Digits on the blue line have an equal sum N (to be determined by the solver) within each box it passes through.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"t3tR9bGgjG","ctcId":952,"ctcDifficulty":"MEDIUM","title":"Duplicity","author":"zetamath","rules":"Normal sudoku rules apply.  A purple line must contain a set of non-repeating consecutive digits (which can appear in any order). Adjacent digits along a green line must differ by at least 5. Cells separated by a black dot must contain digits in a 1:2 ratio (ie one digit must be double the other). In cages, digits must sum to the small clue in the top left corner of the cage. Digits along an arrow must sum to the digit in that arrow’s (grey) circle. Digits along a thermometer must increase from the bulb end. A digit in a black circle must appear in at least one of the four cells surrounding that circle. Digits along a blue line have an equal sum within each 3x3 box the line passes through. Eg r6c2+r6c3=r5c4+r4c5","solution":"542138769397624158861795324129453876685279431734816295413567982958342617276981543","constraints":["arrow","cage","german-whispers","kropki","quadruple","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"GP464L8f2H","ctcId":991,"ctcDifficulty":"HARD","title":"3Z + X","author":"Walking Writer","rules":"Normal sudoku rules apply. Digits along an arrow sum to the number in the connecting circle. Digits connected by a black dot have a 2:1 ratio. Digits connected by a white dot are consecutive. A grey square contains an even digit. Digits along a marked diagonal may not repeat.","rulesClarified":"Normal sudoku rules apply.\n\nEach arrow starts at a circled cell. The digits in the other cells along the arrow add up to the digit in that circled cell. The circled cell itself is not part of the sum.\n\nDigits connected by a black dot have a 2:1 ratio.\n\nDigits connected by a white dot are consecutive.\n\nA grey square contains an even digit.\n\nDigits along a marked diagonal may not repeat.","solution":"643589721589712346172634985297146853856273194431895672915328467724961538368457219","constraints":["arrow","diagonal","even","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"QBq6nnqHr6","ctcId":1011,"ctcDifficulty":"MEDIUM","title":"A Little Off the Top","author":"Cane_Puzzles","rules":"Normal sudoku rules apply. Each purple line contains a set of non-repeating consecutive digits.  These digits can appear in any order. Neighbouring digits on a green line have a difference of at least 5.","solution":"861342759439657821572819346697283514248195637153764982714536298386921475925478163","constraints":["german-whispers","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"MdmM24fgr9","ctcId":1012,"ctcDifficulty":"MEDIUM","title":"Not Too High, Not Too Low","author":"Cane_Puzzles","rules":"Normal sudoku rules apply. The digits in a cage sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage. Neighbouring digits along a green line have a difference of at least 5.","solution":"716325984842196735539784261928543617367912458451678392675431829184269573293857146","constraints":["cage","german-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"gbp9G4tdJM","ctcId":1013,"ctcDifficulty":"MEDIUM","title":"Something Doesn't Add Up","author":"Cane_Puzzles","rules":"Normal sudoku rules apply. Digits within a cage must sum to the small clue in the top left corner of the cage (if given). Digits cannot repeat within a cage.","solution":"819254637652783149437169582946537821271846395385912764768495213124378956593621478","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"GtL8GpGbRJ","ctcId":1024,"ctcDifficulty":"MEDIUM","title":"Scooters","author":"Derektionary","rules":"Normal sudoku rules apply. Purple lines and white dots connect two digits that are consecutive. Black dots connect two digits that are in a 1:2 ratio. Not all dots or lines are necessarily given.","solution":"348571926627934851591268347932157684865342719174689235459723168783416592216895473","constraints":["kropki","renban"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"RmTRjp4dDb","ctcId":1025,"ctcDifficulty":"MEDIUM","title":"Walk in the Mist","author":"Derektionary","rules":"Normal sudoku rules apply. Fog is covering the grid. Your task is to remove the fog by placing correct digits in the grid (no guessing is required). Digits along a grey arrow must sum to the digit in that arrow's circle. Along blue thermometers, digits must increase from the bulb end. Cells separated by a white dot must contain consecutive digits. Cells separated by a black dot contain digits in a ratio of 1:2 (one digit is double the other). Not all dots are necessarily given.","solution":"672185493914236785835947621723514869591678342486329517348792156159463278267851934","fogLight":"R1C1,R2C1,R3C1,R1C2,R2C2,R3C2,R1C3,R2C3,R3C3","constraints":["arrow","fog","kropki","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"29hgDNf2qq","ctcId":1032,"ctcDifficulty":"MEDIUM","title":"Propellers","author":"Nordy","rules":"Normal sudoku rules apply. Each gray dot is the midpoint of a single, 3-cell long line segment that must be drawn into the grid. Line segments are fully straight, and can be oriented horizontally, vertically, or diagonally. The three digits along a line segment cannot repeat, and they sum to the value shown in the corresponding midpoint cell. Line segments do not cross, overlap, or share cells with each other.","rulesClarified":"Normal sudoku rules apply.\n\nEach grey dot is the middle cell of a single straight line segment that you draw into the grid. The segment is exactly three cells long, so the dot's own cell is the middle one of the three, and the two cells on either side of it belong to the same segment.\n\nSegments may run horizontally, vertically or diagonally.\n\nThe number printed in a dot's cell is not a digit. It is the sum of the three digits on that segment, including the digit in the dot's own cell.\n\nThe three digits on one segment cannot repeat.\n\nSegments do not cross, overlap, or share cells with each other.","solution":"213869754846751239759423618672318495431592867598674123987236541164985372325147986","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each gray dot is the midpoint of a single, 3-cell long line segment that must be drawn into the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"Q3NL4tDB7p","ctcId":1034,"ctcDifficulty":"MEDIUM","title":"Hopscotch (Remix)","author":"Nordy","rules":"Normal sudoku rules apply. Every 3x3 box contains one hidden 2x2 region called a Whisper Square. In a Whisper Square, orthogonally adjacent digits must have a difference of 5 or greater. Whisper Squares must not touch each other orthogonally, but they may touch diagonally. Within each cage, the sum of digits inside Whisper Squares equals the sum of digits outside Whisper Squares.","rulesClarified":"Normal sudoku rules apply.\n\nEvery 3x3 box contains one hidden 2x2 block of four cells, lying entirely inside that box. This block is a Whisper Square. The Whisper Squares are not drawn; the solver must find them.\n\nIn a Whisper Square, any two cells that share an edge must differ by 5 or more. Cells that touch only at a corner are not adjacent for this rule.\n\nWhisper Squares must not touch each other along an edge. Two Whisper Squares may touch at a corner.\n\nWithin each cage, the digits inside Whisper Squares add up to the same total as the digits outside Whisper Squares.","solution":"746291358592638417318754692167825943934176825285349176853917264671482539429563781","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In a Whisper Square, orthogonally adjacent digits must have a difference of 5 or greater. Whisper Squares must not touch each other orthogonally, but they may touch diagonally. Within each cage, the sum of digits inside Whisper Squares equals the sum of digits outside Whisper Squares.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5"]}]},{"id":"rT277BN3dF","ctcId":1035,"ctcDifficulty":"HARD","title":"Wormholes (Remix)","author":"Nordy","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow's circle. Numbers in the corner of cages indicate the number of cells in that 3x3 Box that form 'wormholes' with other boxes. A cell in a cage in Box A forms a wormhole with the central cell of Box B when the cell's position in Box A (eg top right cell) matches the position of Box B in the grid (eg top right box). Two cells in a wormhole relationship both contain the same digit. Note: Cage totals only count the number of wormholes that look out of that box and into the central cells of other boxes ie A wormhole from another box that looks into the central cell of a cage is not counted.","solution":"423518697659723481781964352348297516172456839965831274537649128296185743814372965","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Numbers in the corner of cages indicate the number of cells in that 3x3 Box that form 'wormholes' with other boxes.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"bb6fQng3Qn","ctcId":1037,"ctcDifficulty":"EASY","title":"Skateboards","author":"Derektionary","rules":"Normal sudoku rules apply. A purple line contains a set of consecutive digits in any order. Cells separated by a black dot contain digits with a 1:2 ratio. Cells separated by a white dot contain consecutive digits.","solution":"678354192154692873932187654867245319241839567395761428586973241723416985419528736","constraints":["kropki","renban"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"mJqT6RDG2L","ctcId":1039,"ctcDifficulty":"VERY HARD","title":"Layla","author":"Philip Newman","rules":"Normal sudoku rules apply. Digits in cages cannot repeat and must sum to the total given.","solution":"914325876725468193368791425591283764486157239237649518152836947649572381873914652","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"JHnRqh93pr","ctcId":1051,"ctcDifficulty":"MEDIUM","title":"Claudia Cum Cereo Circulat","author":"olima","rules":"Normal sudoku rules apply. Placing correct digits in the grid will clear the fog. Adjacent digits along a line must differ by at least 5. Cells separated by an X must contain digits summing to 10. Cells separated by a V must contain digits summing to 5. All X/V clues are given, but may be hidden in the fog.","solution":"894356712235971684761842539427185396958763421613429875586217943179534268342698157","fogLight":"R1C1,R2C1,R2C2,R1C2","constraints":["XV","fog","german-whispers"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"h6JTfRmMB2","ctcId":1062,"ctcDifficulty":"HARD","title":"Sumthing's Very Wrong","author":"Rangsk","rules":"Normal sudoku rules apply. Arrows in the grid can be correct or incorrect. On correct arrows the digits on the arrow sum to the value in the circle. Incorrect arrows do not sum to the value in the circle. It is up to the solver to determine which arrows are correct or incorrect. A number outside the grid is the sum of the circles in the row or column that are for correct arrows. Incorrect arrow circles do not contribute to the sum.","solution":"915382647736514982428976135293861574184795326657243891549137268371628459862459713","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"On correct arrows the digits on the arrow sum to the value in the circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Incorrect arrows do not sum to the value in the circle. A number outside the grid is the sum of the circles in the row or column that are for correct arrows.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c6"]}]},{"id":"q3R9PRg4qF","ctcId":1072,"ctcDifficulty":"MEDIUM","title":"That's [redacted] in the Corner","author":"James Sinclair","rules":"Normal sudoku rules apply. The grid is covered with fog, except for two initial light sources. Digits also act as light sources and, when placed correctly, illuminate the cells around them. Cages show their sums, and digits cannot repeat within a cage. Digits on arrows sum to the number in the connected circle, and can repeat if allowed by other rules. Along green lines, digits must differ from their neighbors by at least 5. Digits in cells with a gray square must be even. Digits in cells separated by a black dot have a 1:2 ratio.","solution":"574962183128347659936851472452739816397186245681524397265498731743215968819673524","fogLight":"R1C1,R1C2,R2C1,R2C2,R8C8,R8C9,R9C8,R9C9","constraints":["arrow","cage","even","fog","german-whispers","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"RRPttN2Dg2","ctcId":1074,"ctcDifficulty":"MEDIUM","title":"Wrogn Fogn","author":"James Sinclair","rules":"Normal sudoku rules apply. All clues are standard, and all clues are wrong. A clue is 'wrong' if it is not 100% correct. Specifically:\nDigits within a cage must not be a non-repeating set of digits that sum to the number in the corner (if given).\nDigits on arrows must not sum to the number in the connected circle.\nOn thermometers, digits must not increase from the bulb to the tip.\nAlong green lines, at least one pair of adjacent digits must not differ by at least 5.\nAlong orange lines, at least one pair of adjacent digits must not differ by at least 4.\n Large circles contain at least one digit which does not appear in the four surrounding cells.\nDigits in cells with a shaded circle must not be odd.\nDigits in cells separated by a V must not sum to 5.\nDigits in cells separated by an X must not sum to 10.\nDigits in cells separated by a small white dot must not be consecutive.\nDigits in cells separated by a black dot must not have a 1:2 ratio.\nClues outside the grid must not give the sum of the digits along the indicated diagonal.","solution":"256849317781326495934751628497538261825164739613297584162975843378412956549683172","fogLight":"R3C1,R3C2,R3C3,R1C3,R1C1,R1C2,R2C3,R2C1,R2C2","constraints":["XV","arrow","cage","dutch-whispers","even","fog","german-whispers","kropki","little-killer","quadruple","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"Digits in cells separated by a V must not sum to 5. Digits in cells separated by an X must not sum to 10.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12","c13"]},{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits on arrows must not sum to the number in the connected circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits within a cage must not be a non-repeating set of digits that sum to the number in the corner (if given).","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"modified","modifiers":[],"params":null,"note":"Along orange lines, at least one pair of adjacent digits must not differ by at least 4.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Along green lines, at least one pair of adjacent digits must not differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Digits in cells separated by a small white dot must not be consecutive. Digits in cells separated by a black dot must not have a 1:2 ratio.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c14","c15"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c16"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"On thermometers, digits must not increase from the bulb to the tip.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]}]},{"id":"HjmmTp4M6t","ctcId":1076,"ctcDifficulty":"MEDIUM","title":"Gauntlet","author":"James Sinclair","rules":"Normal sudoku rules apply. Cages show their sums, and digits cannot repeat within a cage. Digits on arrows sum to the two-digit number in the connected pill, which reads from left to right. These digits can repeat if allowed by other rules. A digit in a cell with a shaded square must be even.","solution":"374258196195463827286719534751382649642975318938641275517824963869137452423596781","constraints":["arrow","cage","even"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"N4LJbJP3TR","ctcId":1077,"ctcDifficulty":"MEDIUM","title":"Fanfare","author":"James Sinclair","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow's circle. Digits in cells separated by a white dot are consecutive. Digits in cells separated by a black dot have a 1:2 ratio (ie one digit is double the other).","solution":"925376148731284659846519237468152793579643812312897465284965371693721584157438926","constraints":["arrow","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"MLdnq2THJ4","ctcId":1089,"ctcDifficulty":"HARD","title":"x'clusion","author":"Florian Wortmann","rules":"Normal sudoku rules apply. Cells separated by a knight's move (in chess) cannot contain identical digits. Digits along a thermometer increase from the bulb end. Digits in a cage sum to the small clue in the top left corner of the cage.","solution":"752468931364917852819352746591836274627149583483725169948273615176594328235681497","constraints":["antiknight","cage","thermometer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"rD98HnbQFt","ctcId":1091,"ctcDifficulty":"EASY","title":"Question Everything","author":"James Sinclair","rules":"Normal sudoku rules apply. Cages show their sums. On thermometers, digits increase from the bulb. Digits in cells separated by a V sum to 5, and digits in cells separated by an X sum to 10. All possible V's and X's are given. Digits in cells with a gray square must be even.","solution":"135894726297613845684725139352481697461957382978362451713549268526138974849276513","constraints":["XV","cage","even","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"RGLfL4BgJ2","ctcId":1113,"ctcDifficulty":"HARD","title":"In the Proximity","author":"Lizzy01","rules":"Normal sudoku rules apply. A purple line contains a set of consecutive digits in any order. Along arrows, the digits add up to exactly one more or less than the digit in the circle.","rulesClarified":"Normal sudoku rules apply.\n\nA purple line contains a set of consecutive digits in any order.\n\nFor each arrow, the digits in the arrow add up to exactly one more or exactly one less than the digit in the circle at the arrow's start. The circle itself is not part of the sum.","solution":"792638154413925876586147923871356492659412738234879561948763215327581649165294387","constraints":["arrow","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Along arrows, the digits add up to exactly one more or less than the digit in the circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jfbnd2TR6H","ctcId":1114,"ctcDifficulty":"HARD","title":"Primal Instinct","author":"Agent","rules":"Normal sudoku rules apply. Digits in cages cannot repeat and must sum to a prime number. (For the avoidance of doubt, 1 is not a prime number!)","solution":"472318596685479312913652478758946123341285769296731854164827935827593641539164287","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"tJQLHFtF36","ctcId":1125,"ctcDifficulty":"HARD","title":"Seeing Double","author":"James Kopp","rules":"Normal sudoku rules apply. A number outside the grid is an X-sum for both its column or row, and also a Little Killer clue for the indicated diagonal. The number shows the sum of the first X digits in the row/column from that direction, where X is the first of those digits, and also indicates the sum of the indicated diagonal.","solution":"561974238732861594849325671915732486483156927276498153358649712627513849194287365","constraints":["little-killer","x-sum"],"constraintFacts":[{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"FFhHh3HD8p","ctcId":1135,"ctcDifficulty":"VERY HARD","title":"Serial Killers","author":"starwarigami","rules":"Normal sudoku rules apply.\nDigits may not repeat in a cage.\nThe totals of individual cages of the same colour form a set of consecutive numbers, in any order.","solution":"968432571257618934134795682381254769745961328692873415519327846876149253423586197","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The totals of individual cages of the same colour form a set of consecutive numbers, in any order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"3Gd3L4Q6rp","ctcId":1163,"ctcDifficulty":"VERY HARD","title":"Spiral Fillodoku","author":"AnalyticalNinja","rules":"Normal sudoku rules apply. Divide the grid into coloured regions, so that no two orthogonally adjacent regions have the same size (in terms of number of cells they contain). The regions must be rotationally symmetrical. Digits may not repeat in a region, and regions with a small number clue sum to the number indicated. (Not all number clues are given, and these number clues DON'T have to be in the top, leftmost cell of their region.)","solution":"254879136698135247137264895386942571415387962972516384549728613861453729723691458","constraints":["cage","custom","region"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits may not repeat in a region, and regions with a small number clue sum to the number indicated.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into coloured regions, so that no two orthogonally adjacent regions have the same size (in terms of number of cells they contain). The regions must be rotationally symmetrical.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"Lj72FhPr9B","ctcId":1175,"ctcDifficulty":"MEDIUM","title":"Converging Paths","author":"Cane_Puzzles","rules":"Normal sudoku rules apply. The digits on an arrow sum to the digit in that arrow's circle. Each purple line contains a set of non-repeating consecutive digits (which can appear in any order).","solution":"431579682287361459596842137962137548743985216815426793374218965658794321129653874","constraints":["arrow","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"NJgTqnNp9j","ctcId":1184,"ctcDifficulty":"MEDIUM","title":"Just Sum Ambiguity","author":"SSG","rules":"Normal sudoku rules apply. In addition, the sum of digits along a line must be the same within each 3x3 box the line passes through. eg r9c1+r9c2+r8c3 [line cells in box 7] = r9c4+r8c5 [line cells in box 8].\n\n Furthermore, each line satisfies one of the following:\n\nEntropic Lines: Along an entropic line any run of three cells contains exactly one low {1,2,3}, one medium {4,5,6}, and one high {7,8,9} digit.\n\nModular Lines: Along a modular line, the digits in any run of three cells must all have different remainders under division by 3. (ie So one digit must be from the set {1,4,7}, one from {2,5,8} and one from {3,6,9}).","solution":"316429875985637421247815639134258967679341258852976143723184596561792384498563712","constraints":["entropic-line","modular-line","region-sum-line"],"constraintFacts":[{"slug":"entropic-line","type":"entropic-line","variant":"modified","modifiers":[],"params":null,"note":"Entropic Lines: Along an entropic line any run of three cells contains exactly one low {1,2,3}, one medium {4,5,6}, and one high {7,8,9} digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"modular-line","type":"modular-line","variant":"modified","modifiers":[],"params":null,"note":"Modular Lines: Along a modular line, the digits in any run of three cells must all have different remainders under division by 3. (ie So one digit must be from the set {1,4,7}, one from {2,5,8} and one from {3,6,9}).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"dffJr73j2F","ctcId":1185,"ctcDifficulty":"HARD","title":"Fill-a-Renban","author":"SSG","rules":"Normal sudoku rules apply.\n\nFillomino: Divide the grid into regions along grid lines such that no two regions of the same size share an edge. Cells divided by a green wall are in different regions. Given digits specify the size of the region in which they appear. Each region must include a digit equal to its size.\n\nRenban: Each region contains a non-repeating set of consecutive digits that may appear in any order.","solution":"673218954598476213142395867485169732219734586367852149734521698921683475856947321","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Fillomino: Divide the grid into regions along grid lines such that no two regions of the same size share an edge. Cells divided by a green wall are in different regions. Given digits specify the size of the region in which they appear. Each region must include a digit equal to its size. Renban: Each region contains a non-repeating set of consecutive digits that may appear in any order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6"]}]},{"id":"dnnhqnhjRB","ctcId":1186,"ctcDifficulty":"MEDIUM","title":"Double Helpings","author":"Akash Doulani","rules":"Normal sudoku rules apply. A number outside the grid is both a frame sum for its column or row, and also a Little Killer clue for the indicated diagonal. The number shows the sum of the first three digits in the row/column from that direction, and also indicates the sum of the indicated diagonal.","solution":"963214785817653942524879361236985174751426893498731526349567218685192437172348659","constraints":["custom","little-killer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A number outside the grid is both a frame sum for its column or row, and also a Little Killer clue for the indicated diagonal.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"GnhgmHJH83","ctcId":1188,"ctcDifficulty":"HARD","title":"Table Tennis Timeout","author":"olima","rules":"Normal sudoku rules apply. Along thermos, digits increase from the bulb to the tip. Adjacent digits on a green line differ by at least 5. A purple line contains a set of consecutive numbers in any order. The digit sum on a blue line is equal in every box. A black dot joins digits with a 1:2 ratio; a white dot joins consecutive digits.","solution":"185743629674928351329165847763284195258391764491576238847652913512839476936417582","constraints":["german-whispers","kropki","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7g3F33FjQg","ctcId":1189,"ctcDifficulty":"EASY","title":"Easy Arrows","author":"Eric Rathbun","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow's circle. Cells separated by a white dot contain consecutive digits. Not all dots are given. Cells separated by a knight's move (in chess) cannot contain the same digit.","solution":"269457183351289764487163529693714852725398416148526397914872635576931248832645971","constraints":["antiknight","arrow","kropki"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"g4RJBfh4BJ","ctcId":1190,"ctcDifficulty":"MEDIUM","title":"Star Battle Sandwich Sudoku","author":"Panthera","rules":"Normal Sudoku Rules apply.\n\nNormal star battle rules apply. There must be 2 stars in each row, column, and box. Stars cannot touch each other (including diagonally)\n\nSandwich rules apply - sandwich clues give the total of the digits between the stars. Stars can have any value!\n\nAntiknight - digits a knights move away cannot be the same.","solution":"962837154751964283834152967243789615519643728678215349487321596325496871196578432","constraints":["antiknight","custom","sandwich"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Normal star battle rules apply.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"J3mq7L7GrN","ctcId":1207,"ctcDifficulty":"MEDIUM","title":"Grand Prix","author":"Blobz","rules":"Normal sudoku rules apply. Digits in cages sum to the clue in the top left corner. Two race cars (blue and green) start in box 1 and race around the track to the chequered flag line in box 2 (in the 16 cage). Draw green and blue lines to show the paths that the cars take. Each checkpoint (cage) shows which cell each car passes through. The cars may not enter grey shaded cells, and must avoid all oil slicks (given digits). The paths cross exactly 3 times during the race. The paths do not share cells. Digits along the blue path have an equal sum N within each 3x3 box the path passes through.  Adjacent digits along the green path must differ by at least 5.","solution":"859673214213498756674152839126385947938741625547926381395817462762534198481269573","constraints":["cage","custom","german-whispers","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Two race cars (blue and green) start in box 1 and race around the track to the chequered flag line in box 2 (in the 16 cage). The cars may not enter grey shaded cells, and must avoid all oil slicks (given digits).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"2QrQPp6qPp","ctcId":1208,"ctcDifficulty":"HARD","title":"YYSL Knights","author":"Blobz","rules":"Normal sudoku rules apply. Shade some cells such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected and no 2x2 area may be fully shaded or unshaded. White dots lie on the border between the shaded and unshaded regions. Additionally, white dots separate consecutive digits. Not all possible dots are shown. Digits in caged cells show the number of cells of the same color (shaded or unshaded) seen orthogonally from that position, including itself. The 'other' color blocks vision. Cells a (chess) knight's move apart cannot contain the same digit.","rulesClarified":"Normal sudoku rules apply.\n\nShade some of the cells and leave the rest unshaded. All shaded cells form one group joined edge to edge, and all unshaded cells form one group joined edge to edge. No 2x2 block may be entirely shaded or entirely unshaded.\n\nEach white dot sits on the edge between two neighbouring cells. Those two cells are different colours (one shaded, one unshaded), and their digits are consecutive.\n\nNot every possible dot is drawn. An edge without a dot gives no information.\n\nEach caged cell (a cell inside one of the drawn cage outlines) holds a count. The count is the number of cells of its own colour, shaded or unshaded, that it can see, including itself. From the cell, look straight up, down, left and right. Each direction stops at the grid edge or at the first cell of the other colour, which blocks sight.\n\nTwo cells a chess knight's move apart cannot contain the same digit.","solution":"146235987932781564587964321264157839791328645358649172625493718873512496419876253","constraints":["antiknight","custom","kropki","yin-yang"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in caged cells show the number of cells of the same color (shaded or unshaded) seen orthogonally from that position, including itself.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"mR3GPBqGnT","ctcId":1210,"ctcDifficulty":"MEDIUM","title":"159 RSL","author":"Blobz","rules":"Normal sudoku rules apply.\n\n159: Digits in column 1 indicate the column in which the digit 1 appears in that row (e.g. if r4c1 is a 6, r4c6 is a 1). The same applies to columns 5 and 9, with the digits 5 and 9 respectively.\n\nRegion Sum Lines: Digits along a blue line have an equal sum N within each 3x3 box the line passes through. Different lines may have different values for N.","solution":"783692145694751382215834967132965874857423619469178523578219436946387251321546798","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"159: Digits in column 1 indicate the column in which the digit 1 appears in that row (e.g. if r4c1 is a 6, r4c6 is a 1). The same applies to columns 5 and 9, with the digits 5 and 9 respectively.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"QtHJR7mqh9","ctcId":1211,"ctcDifficulty":"MEDIUM","title":"Domino Trails 3","author":"Blobz","rules":"Normal sudoku rules apply. Shade some cells (the “hedges”) such that the unshaded cells (the “trails”) form an orthogonally connected area (with no loops) where no 2x2 group of cells is either fully shaded or unshaded. Different parts of the trail may touch diagonally (so checkerboard patterns ARE allowed). Note that hedges do not need to connect to the edge of the grid. The trails are completely tiled with non-overlapping dominoes. Caged cells are always trail cells and indicate two things: (a) the digit placed in the cage shows how many trail cells (including itself) can be seen orthogonally from that position (where hedges obstruct the view); (b) the small clue in the corner of the cage shows the total sum of the corresponding domino. Not all dominoes are marked with a cage.","rulesClarified":"Normal sudoku rules apply.\n\nShade some cells. These are the hedges. The unshaded cells are the trails. The trails form one orthogonally connected area with no loops. No 2x2 block of cells is fully shaded or fully unshaded. Hedges need not connect to the edge of the grid.\n\nTrails may touch diagonally, so checkerboard patterns are allowed.\n\nThe trails are tiled completely by non-overlapping dominoes. Each domino is two orthogonally adjacent trail cells. Not every domino has a cage.\n\nA caged cell is always a trail cell, and each cage is a single cell. The small number in the cage's corner is the total of the two digits in the domino that covers that cell.\n\nThe digit in a cage is the number of trail cells that can be seen from that cell, including the cell itself. Look orthogonally from the cell in the four directions; a hedge blocks the view, a trail cell does not, and the view ends at the edge of the grid.","solution":"731498625948265713526317894472139568863572941159684372615743289284956137397821456","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells (the “hedges”) such that the unshaded cells (the “trails”) form an orthogonally connected area (with no loops) where no 2x2 group of cells is either fully shaded or unshaded. The trails are completely tiled with non-overlapping dominoes. Caged cells are always trail cells and indicate two things: (a) the digit placed in the cage shows how many trail cells (including itself) can be seen orthogonally from that position (where hedges obstruct the view); (b) the small clue in the corner of the cage shows the total sum of the corresponding domino.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c6"]}]},{"id":"N3fP8JrF2L","ctcId":1213,"ctcDifficulty":"VERY HARD","title":"Badminton","author":"Qodec","rules":"Normal sudoku rules apply. The thin diagonal running SW-NE in blue must contain the digits 1 to 9 once each. Odd-even parity is reflected across the red diagonal running NW-SE. (For example: if R6C2 is odd, R2C6 must also be odd.) Digits along an arrow must sum to the digit in that arrow's circle.","solution":"947612358832795146561483729276841593318259674495376281759164832124538967683927415","constraints":["arrow","custom","diagonal"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Odd-even parity is reflected across the red diagonal running NW-SE.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"JGG2RDFhJq","ctcId":1214,"ctcDifficulty":"HARD","title":"X-clusivity","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nEach line consists of one or more non-overlapping groups of consecutive cells, each of which sums to 10.\n\nNo two of these groups may have the same fill (including permutations), even if they are on different lines. For example, if one line had a group with digits 1315, and another line had a group with digits 5113, this would be invalid.","solution":"375496182814723965269185743786954321493612578521378694937241856648539217152867439","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each line consists of one or more non-overlapping groups of consecutive cells, each of which sums to 10. No two of these groups may have the same fill (including permutations), even if they are on different lines.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"6JfjT3N6L2","ctcId":1215,"ctcDifficulty":"MEDIUM","title":"Soliloquy","author":"zetamath","rules":"Normal sudoku rules apply. Adjacent digits along a green line must differ by at least 5. Digits on a purple line must form of a set of non-repeating consecutive digits. These digits can appear in any order. Digits along an arrow must sum to the digit in that arrow's circle. Along a thermometer, digits must increase from the bulb end. Golden lines are 'nabner' lines: No two digits selected from the set of digits on a nabner line can be consecutive.","solution":"426715938951382476378946152785691324613524897294873561532468719867159243149237685","constraints":["arrow","german-whispers","nabner-line","renban","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"fmRMNJ6TmT","ctcId":1216,"ctcDifficulty":"MEDIUM","title":"Decimation","author":"James Sinclair","rules":"Normal sudoku rules apply. In cages, digits must sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage. Digits in cells separated by an X sum to 10. All possible Xs are given.","rulesClarified":"Normal sudoku rules apply.\n\nEach cage has a total, the small clue in its top left corner. The digits in a cage add up to that total. Digits cannot repeat within a cage.\n\nAn X sits on the edge between two orthogonally adjacent cells. The two digits either side of an X add up to 10.\n\nAll possible Xs are given.","solution":"618729453947563281325184697259418376763952148184376925476891532531247869892635714","constraints":["XV","cage"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ttPm9G96h6","ctcId":1217,"ctcDifficulty":"EASY","title":"A Bit Cagey","author":"Walking Writer","rules":"Normal sudoku rules apply. Digits in cages may not repeat, and must sum to the total shown.","solution":"349781625826495137175623489987152346532946871461837952214568793658379214793214568","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"JhrhQh9G3M","ctcId":1218,"ctcDifficulty":"EASY","title":"6th Anniversary CTC","author":"Jodawo & Panthera","rules":"Normal sudoku rules apply. Neighbouring digits along a green line must have a difference of at least 5. Cells along a purple line must be a set of consecutive digits in any order. Cages read as 6, 8, 17, and 26 in an order that must be determined by the solver (reading order is left-to-right or up-to-down).","solution":"349561278127438596856729134972146385418375962563982417234617859691854723785293641","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cages read as 6, 8, 17, and 26 in an order that must be determined by the solver (reading order is left-to-right or up-to-down).","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"gJJJdH8TdN","ctcId":1219,"ctcDifficulty":"MEDIUM","title":"The Odd Road to 200","author":"Nordy","rules":"Normal sudoku rules apply. The digits along each blue/purple line multiply to 200. Draw a 1-cell wide, non-branching, orthogonally-connected road that does not touch itself orthogonally (but may diagonally). The two ends of the road are given as circles. The road contains only odd digits, and the digits along the road sum to 200. Except for the circles, the road CANNOT visit any cell that contains a given clue ie the road cannot visit the given digits in R2C9 and R9C1, nor any cell that contains a line segment.","solution":"825193746967845123143726958786952431312478569594631287278314695439567812651289374","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digits along each blue/purple line multiply to 200. Draw a 1-cell wide, non-branching, orthogonally-connected road that does not touch itself orthogonally (but may diagonally). The two ends of the road are given as circles. The road contains only odd digits, and the digits along the road sum to 200. Except for the circles, the road CANNOT visit any cell that contains a given clue ie the road cannot visit the given digits in R2C9 and R9C1, nor any cell that contains a line segment.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6"]}]},{"id":"TnR9996Ltn","ctcId":1229,"ctcDifficulty":"MEDIUM","title":"Beauty Mark","author":"zetamath","rules":"Normal sudoku rules apply.  Cells separated by the black dot contain digits in a 1:2 ratio (ie one digit will be double the other).  The golden lines are “nabner” lines.  Digits cannot repeat on a nabner line, and nabner lines cannot contain consecutive digits - regardless of order.  Eg. if a line has a 3 anywhere on it, 2 and 4 cannot appear on that line.  The blue lines in the grid are Region Sum Lines. The sum of digits on a blue line must be the same within each 3x3 box the line passes through. Eg r2c3+r3c2+r3c3 [box 1] = r1c4+r1c5+r1c6+r2c6+r2c7 [box 2] = r4c4+r4c5+r4c6 [box 5]","solution":"753418629218956347649732158382579416495163872176824935837645291564291783921387564","constraints":["kropki","nabner-line","region-sum-line"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"7fpRmpM7fT","ctcId":1236,"ctcDifficulty":"MEDIUM","title":"Toasty Jackpot","author":"Alaric Taqi A. (Crusader175)","rules":"Normal sudoku rules apply. Clues outside the grid shows the sum of the digits sandwiched between 1 and 9 in that row or column. Digits in column 1 indicate in which column the digit 1 is placed in the respective row. So, for example, if r7c1 was 6 then 1 would be placed in the sixth column of that row ie r7c6. Columns 5 and 9 have the same rule for the digits 5 and 9 respectively. Each red stripe contains exactly the same sequence of nine digits in the same order (the “slot machine”). The sequence can start at any point along a red stripe, and when it reaches the bottom, it wraps around again to the top.","solution":"341279586562318479897546312729865143138794265456123798685431927974652831213987654","constraints":["custom","sandwich"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in column 1 indicate in which column the digit 1 is placed in the respective row. Each red stripe contains exactly the same sequence of nine digits in the same order (the “slot machine”).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c6"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"LpPFjm9J7q","ctcId":1247,"ctcDifficulty":"HARD","title":"Zoom","author":"matyas","rules":"Normal sudoku rules apply. Maximum cell, kropki and anti-king rules still apply. German Whispers: Adjacent digits along the marked lines have a difference of at least 5.","solution":"364527891279381465158469327421935786683274159795816243847693512932158674516742938","constraints":["antiking","german-whispers","kropki","maximum"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"maximum","type":"maximum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"TMLnFRh86r","ctcId":1252,"ctcDifficulty":"MEDIUM","title":"A Different Kind of Magic","author":"Myxo","rules":"Place the digits 1-9 exactly once in each row, column and thick-outlined region. Digits separated by a white dot have a difference of the indicated number. Digits separated by a black dot have a ratio of the indicated number. All cages are Magic Squares: In a Magic Square, all rows, columns and length-3-diagonals sum to the same total. Digits may repeat in Magic Squares.","solution":"597231486975123864759312648312846795123468579231684957648597231864975123486759312","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All cages are Magic Squares: In a Magic Square, all rows, columns and length-3-diagonals sum to the same total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"hrDLhB43b8","ctcId":1254,"ctcDifficulty":"MEDIUM","title":"Prison Break","author":"Myxo","rules":"Normal sudoku rules apply. The digits in each cage do not repeat and sum to the small clue in the top left corner of the cage (if given). On a grey line, the digits sum to the same total as the two circles connected to the line. All double arrows in the grid are straight lines (ie. they do not turn at intersections).","solution":"356142798418967352927835641192784536634259187875613924749521863261398475583476219","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On a grey line, the digits sum to the same total as the two circles connected to the line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"Fmh8g3JR7G","ctcId":1255,"ctcDifficulty":"MEDIUM","title":"Fillomino 77","author":"Myxo","rules":"Normal Fillomino rules apply. ie Divide the grid along grid lines into regions. Into each cell, write the size of that cell's region. No two orthogonally adjacent regions can have the same size. The total sum of the numbers on the diagonals indicated by red question-marks is 77. The diagonals indicated by white question-marks cannot contain more than five regions of size 1 in total (but they may contain less).","solution":"315122122355514441325131433121233131215212212255533132315232231331214132122144412","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Normal Fillomino rules apply. ie Divide the grid along grid lines into regions. The total sum of the numbers on the diagonals indicated by red question-marks is 77. The diagonals indicated by white question-marks cannot contain more than five regions of size 1 in total (but they may contain less).","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c4","c5"]}]},{"id":"L9M2DLtfrh","ctcId":1256,"ctcDifficulty":"HARD","title":"Benebelte Nachbarschaft","author":"Myxo","rules":"Normal Sudoku rules apply. Digits connected by a white dot are consecutive. Digits connected by a black dot are in a ratio of 2:1 (ie one digit will be double the other). Not all dots are necessarily given. Coloured lines in the grid are “Renban” lines. Digits on a Renban line form a set of non-repeating, consecutive digits – these digits can appear in any order. All Renban lines in the grid move orthogonally between neighbouring cells, do not branch and do not overlap each other. Each line has a unique colour. The grid is covered with fog. Correctly placed digits will clear the fog around that cell.","solution":"219375486367842591845916327521784639693251748784639152478123965156498273932567814","fogLight":"R1C2,R1C3,R2C2,R2C3,R3C2,R3C3,R1C9,R2C9,R3C9","constraints":["fog","kropki","renban"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"P4frHfDRFb","ctcId":1257,"ctcDifficulty":"MEDIUM","title":"The Caribbean","author":"Niverio","rules":"Normal sudoku rules apply. Cells separated by an X contain digits summing to 10. Not all Xs are given. Shade some cells in the grid such that all the following conditions are fulfilled: 1) All shaded cells are orthogonally connected, without creating a 2x2 area of shaded cells. 2) Groups of orthogonally connected unshaded cells form ‘islands’. Each island has exactly one circle, and the number in the circle shows the size of the island. Each island contains digits 1 to N without repeats, where N is the size of the island. Each island is of a different size.","solution":"123647895876195342495238617784361529359782164261954783648523971512879436937416258","constraints":["XV","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells in the grid such that all the following conditions are fulfilled: 1) All shaded cells are orthogonally connected, without creating a 2x2 area of shaded cells. Each island has exactly one circle, and the number in the circle shows the size of the island.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c6"]}]},{"id":"qbr94BtQfJ","ctcId":1260,"ctcDifficulty":"MEDIUM","title":"Collider","author":"James Sinclair","rules":"Normal sudoku rules apply. On each diagonal (marked in blue) digits cannot repeat. Some cages show their sums, and digits cannot repeat within a cage. A digit inside a white circle must appear in at least one of the four cells surrounding that circle. Digits in cells with a shaded square must be even. Digits in cells separated by a black dot have a 1:2 ratio (ie one digit must be double the other).","solution":"594132687863574129127689453739265814452817396618943572246758931981326745375491268","constraints":["cage","diagonal","even","kropki","quadruple"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"Rf868QGJdj","ctcId":1268,"ctcDifficulty":"MEDIUM","title":"Regions in the Fog","author":"Oddlyeven","rules":"Normal sudoku rules apply.\nLines are Region Sum Lines: The sum of the digits on a line within a 3x3 box must be the same for each 3x3 box that line passes through. If a line passes through a 3x3 box more than once, each time it passes through counts separately. Lines do not branch or cross.\nFog of War: The grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells.","solution":"347952186891637452526418739784163925235894671169275843413589267672341598958726314","fogLight":"R6C6,R4C6,R5C6,R6C5,R4C4,R4C5,R6C4,R5C4,R5C5","constraints":["fog","region-sum-line"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"PQh7M7fFtt","ctcId":1294,"ctcDifficulty":"MEDIUM","title":"EXit Strategy","author":"Riffclown","rules":"Normal sudoku rules apply. In cages, digits may not repeat and must sum to the value in the top left corner of the cage. Digits may not repeat along the marked diagonals.","solution":"462738915813549672759162483524891367378624591691375248146283759287956134935417826","constraints":["cage","diagonal"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"dbG6M636hG","ctcId":1295,"ctcDifficulty":"MEDIUM","title":"Pairdoku Killer","author":"Riffclown","rules":"Must be solved with Pairdoku Arrow. Normal sudoku rules apply. Digits in cages cannot repeat and must sum to the small clue in the top left corner of the cage. Placing correct digits will clear the fog from surrounding cells. (Don't guess!) Use of Drawing tool is discouraged. All other conversation is encouraged.","solution":"657421983941863572823597641572146839189735264436982715264358197798214356315679428","fogLight":"R2C2,R2C3,R2C4,R3C2,R3C3,R3C4,R4C2,R4C3,R4C4","constraints":["cage","fog"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"nNrgt9P8Pg","ctcId":1296,"ctcDifficulty":"MEDIUM","title":"Pairdoku Arrow","author":"Riffclown","rules":"Must be solved with Pairdoku Killer. Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. Placing correct digits will clear the fog from surrounding cells. (Don't guess!) Use of Drawing tool is discouraged. All other conversation is encouraged.","solution":"657421983941863572823597641572146839189735264436982715264358197798214356315679428","fogLight":"R2C2,R2C3,R2C4,R3C2,R3C3,R3C4,R4C2,R4C3,R4C4","constraints":["arrow","fog"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"LFMR2HQNJP","ctcId":1312,"ctcDifficulty":"HARD","title":"Shuriken","author":"XeonRisq","rules":"Normal sudoku rules apply. The sequence of digits on a gray line reads the same from both directions. Circles are either quadruples or anti-quadruples, meaning: Each of the digits in a circle must appear in at least one of its four surrounding cells, OR Each of the digits in a circle must NOT appear in any of its four surrounding cells. Which circle is which must be deduced by the solver.","solution":"395427618842163795716985432581634279673298541924751386257849163439516827168372954","constraints":["palindrome","quadruple"],"constraintFacts":[{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"g8nbdG8674","ctcId":1313,"ctcDifficulty":"MEDIUM","title":"Rivets","author":"XeonRisq","rules":"Normal sudoku rules apply. A digit X in a cage points to a second digit Y located X cells away in its row or column. The number in the top left corner of the cage gives the sum of X+Y. Numbers that appear in the cells with a white dot between must be consecutive. Numbers that appear in the cells with a black dot between must have a ratio of 2:1.","solution":"752164893943852167618739452376548921491273685285916374169427538824395716537681249","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit X in a cage points to a second digit Y located X cells away in its row or column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"Q2FPmtQ8FN","ctcId":1314,"ctcDifficulty":"HARD","title":"The Door around the Corner","author":"XeonRisq","rules":"Normal sudoku rules apply. Clues outside the grid indicate that that clued digit X has to be placed in the Nth cell in the corresponding direction, where N is the digit placed in the first cell in that direction and N will always refer to the first occurrence of X. The arrow determines the diagonal direction of the clue AND once it hits the edge of the grid, it reflects at 90 degrees and continues until it hits the next edge at which it stops (so there are always nine possible cells for each clue).  Eg if r1c5 was a 6 then r6c2 would be a 5. Any set of three sequential cells along a beige line must contain a low (123), middle (456), and high (789) digit. Any set of three sequential cells along a blue line must NOT contain a low (123), middle (456), and high (789) digit.","solution":"371682594596413782824795613687934125412857936935261478748126359263579841159348267","constraints":["custom","entropic-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Clues outside the grid indicate that that clued digit X has to be placed in the Nth cell in the corresponding direction, where N is the digit placed in the first cell in that direction and N will always refer to the first occurrence of X. The arrow determines the diagonal direction of the clue AND once it hits the edge of the grid, it reflects at 90 degrees and continues until it hits the next edge at which it stops (so there are always nine possible cells for each clue).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"entropic-line","type":"entropic-line","variant":"modified","modifiers":[],"params":null,"note":"Any set of three sequential cells along a blue line must NOT contain a low (123), middle (456), and high (789) digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4","c5"]}]},{"id":"JBFRPT7RBF","ctcId":1315,"ctcDifficulty":"VERY HARD","title":"Someday We'll Meet Again","author":"Twototenth","rules":"Normal sudoku rules apply. Gold lines are 'nabner' lines; ie they cannot contain repeated digits and no two digits along a line may be consecutive. Any two lines that cross each other will each proceed straight through the intersection. The inequality points to the smaller of the two digits it separates.","solution":"759214863164783925382965174871359246293641587546827319918436752435172698627598431","constraints":["inequality","nabner-line"],"constraintFacts":[{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"Hq7FFftdtJ","ctcId":1323,"ctcDifficulty":"MEDIUM","title":"Phog of War","author":"apiyo","rules":"Normal sudoku rules apply. The grid is partially covered in fog. Placing correct digits will clear the fog from that digit’s surrounding cells. No domino in the grid sums to 3. The perimeter cells of the grid sum to 172. Digits along a thermometer must increase from the bulb end. Adjacent digits along a green line must differ by at least 5. Cells separated by a black dot must contain digits in a 1:2 ratio (ie one digit is double the other). Cells separated by a white dot must contain consecutive digits.","solution":"395864271841927356276531489529483617638715942417692835983156724752349168164278593","fogLight":"R3C3,R3C4,R3C4,R3C6,R3C7,R4C7,R6C7,R7C7,R7C6,R7C4,R7C3,R6C3,R3C5,R7C5,R4C3","constraints":["custom","fog","german-whispers","kropki","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No domino in the grid sums to 3. The perimeter cells of the grid sum to 172.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8","c9"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"fH46JBGT7L","ctcId":1341,"ctcDifficulty":"MEDIUM","title":"Dancing in the Rain","author":"Sumanta (ANU)","rules":"Normal sudoku rules apply. Along grey thermometers, digits must increase from the bulb end. Cages show their sums. White dots join consecutive digits; black dots join digits with a 1:2 ratio. Neighbouring digits differ at least by 5 along the green line.","solution":"251648793497523186386917254965481327823769415714235869142396578678154932539872641","constraints":["cage","german-whispers","kropki","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Along grey thermometers, digits must increase from the bulb end.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"Gf8B9FRD3h","ctcId":1356,"ctcDifficulty":"MEDIUM","title":"Kill  Them With Uniqueness","author":"AFrayedKnot","rules":"Normal sudoku rules apply. In cages, digits must sum to the small clue in the top left corner of the cage (if given).  Digits cannot repeat within a cage.  Cells separated by a white dot must contain consecutive digits.  Not all possible dots are given.  This puzzle has a computer-verified unique solution.  Feel free to use this fact during your solve.","solution":"589376214461285379372419658724598163198632745653741892216854937847963521935127486","constraints":["cage","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"bNjqp79Rpn","ctcId":1365,"ctcDifficulty":"HARD","title":"Coordinate Arrows","author":"Piatato","rules":"Normal sudoku rules apply. (ie Every row, column, and 3x3 box must contain the digits 1-9 with no repeats.) Digits on an arrow spell out the coordinates for the digit that is their sum. The row number is written on the start of the arrow, the column number is written on the arrow tip. If, for example, an arrow looks like this: -1 4-> then there must be a 5 in r1c4. All the arrows must correspond to different coordinates. Digits may repeat on an arrow if allowed by other rules.","solution":"239567418685491327471283965563728194948135672712946853154379286396852741827614539","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits on an arrow spell out the coordinates for the digit that is their sum.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"GLtpHJ9MhF","ctcId":1372,"ctcDifficulty":"MEDIUM","title":"Which Line Is It Anyway?","author":"Marty Sears","rules":"Normal sudoku rules apply. Each of the seven line types listed below appears once in the grid. You must determine which line is which. RENBAN LINE: Contains a set of non-repeating consecutive digits, in any order. GERMAN WHISPER LINE: Adjacent digits along the line have a difference of at least 5. THERMOMETER: Digits are arranged in ascending order, from one end to the other, without repeats. REGION SUM LINE: Along the line, digits within each 3x3 box have the same total. The line visits at least two different boxes. PALINDROME LINE: The sequence of digits along the line reads the same in either direction. PARITY LINE: All digits on the line have the same parity. UNLUCKY LINE: Adjacent digits along the line sum to at least 13.","solution":"514367289932841675687925413293678541768154392145293867859412736476539128321786954","constraints":["custom","german-whispers","palindrome","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each of the seven line types listed below appears once in the grid. You must determine which line is which. PARITY LINE: All digits on the line have the same parity. UNLUCKY LINE: Adjacent digits along the line sum to at least 13.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c10","c11"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"B8mntN82FD","ctcId":1373,"ctcDifficulty":"HARD","title":"Friend Zone","author":"Marty Sears","rules":"Normal sudoku rules apply. Any cages that have the same total are cage friends. A circled digit in a cage indicates how many friends that cage has. The blue, yellow and purple cages each have no friends :(","solution":"196738254372549618854162397763285941548916723219473865627351489931824576485697132","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any cages that have the same total are cage friends. The blue, yellow and purple cages each have no friends :(","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"QR7MMGHpfJ","ctcId":1374,"ctcDifficulty":"MEDIUM","title":"Parity Paradox","author":"Marty Sears","rules":"Normal sudoku rules apply. Each line within a 3x3 box has the same total, which is displayed in yellow in that box. (2-digit yellow totals read from left to right.) The digit in the purple square indicates how many of the yellow totals have the same parity (oddness/evenness) as itself (ie the purple square digit).","solution":"243869157679135248518274963835617492421598736796423581987352614362941875154786329","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each line within a 3x3 box has the same total, which is displayed in yellow in that box. The digit in the purple square indicates how many of the yellow totals have the same parity (oddness/evenness) as itself (ie the purple square digit).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"dqNLp6qJHR","ctcId":1375,"ctcDifficulty":"HARD","title":"Circular Reasoning","author":"Marty Sears","rules":"Normal sudoku rules apply. A circled digit indicates exactly how many circles contain that digit. Digits along an arrow sum to the digit in that arrow's circle.","solution":"635127849891364275724859316167942538583716492249583761372695184416238957958471623","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A circled digit indicates exactly how many circles contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"NqDbQ8QTG2","ctcId":1407,"ctcDifficulty":"MEDIUM","title":"Unpredictable Housing Conditions","author":"rockratzero","rules":"Normal sudoku rules apply. The digit in the grey circle is odd. In each set of digits outside the grid, exactly one digit is found in the corresponding row or column in the second box from the clue. All other digits in the set will be found within the first three cells in the row or column from the clue. For instance a '12' clue above column 1 could mean that '1' is found in r123c1 and '2' is found in r456c1, or vice versa.","rulesClarified":"Normal sudoku rules apply.\n\nThe digit in the grey circle is odd.\n\nEach set of digits outside the grid is a clue. Every digit in the set is found in the row or column that the clue points along. Count the cells from the clue: the first three cells are the first box, and the next three cells (four to six) are the second box.\n\nExactly one digit in each set is found in the second box. All the other digits in the set are found within the first box.\n\nFor example, a '12' clue above column 1 means that either 1 is in cells 4 to 6 of column 1 and 2 is in cells 1 to 3, or the other way round.","solution":"981237546352864971674519823268475319415396782739128654843951267197682435526743198","constraints":["custom","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In each set of digits outside the grid, exactly one digit is found in the corresponding row or column in the second box from the clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jgFjmHD7bb","ctcId":1409,"ctcDifficulty":"MEDIUM","title":"Heyawake Sudoku","author":"rockratzero","rules":"Normal sudoku rules apply. Shade some cells in the grid. Shaded cells cannot share an edge with each other. The unshaded cells must form a single orthogonally-connected area. The digit contained in each circle indicates how many cells must be shaded in that 3x3 box. A contiguous line (vertical or horizontal) of unshaded cells cannot span two 3x3 region borders. The digits in a cage may not repeat and must sum to the value given in the top left of the cage. Shaded cells do not contribute to the total.","solution":"394867521561243879728195463217436958489571632653928147132659784975384216846712395","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The digits in a cage may not repeat and must sum to the value given in the top left of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells in the grid. Shaded cells cannot share an edge with each other. The unshaded cells must form a single orthogonally-connected area. The digit contained in each circle indicates how many cells must be shaded in that 3x3 box. A contiguous line (vertical or horizontal) of unshaded cells cannot span two 3x3 region borders. Shaded cells do not contribute to the total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c8"]}]},{"id":"LTMQhdn3b7","ctcId":1410,"ctcDifficulty":"MEDIUM","title":"Liberty, cracked, Perseveres","author":"Rockratzero","rules":"Normal sudoku rules apply. Digits on a grey line must increase or stay the same from bulb to tip. A digit contained in a large white circle must appear at least once in the four cells it touches. Digits connected by a black dot must be in a 2:1 ratio. Digits connected by a white dot must be consecutive. Not all dots are necessarily given. Each set of three digits along a yellow line must comprise a full set of the digits modulo 3, i.e. one each of [147], [258], and [369].","solution":"167854293453269178298713546619325487572486931834971625941537862325698714786142359","constraints":["kropki","modular-line","quadruple","thermometer"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ivybocixpa","ctcId":1411,"ctcDifficulty":"EASY","title":"Stack 'em Up, Knock 'em Down","author":"rockratzero","rules":"Normal Sudoku Rules Apply.\nKropki Pairs. Digits connected by white dots are consecutive. Digits connected by black dots are in a 1:2 ratio. Not all dots are necessarily given.\nJENGA blocks are Killer Cages. The digits within a block must sum to the total (if given) in the top left corner of the block. Some block totals are replaced with the letters JENGA and must be determined by the solver. The values of the letters increase alphabetically. (i.e. A is less than E) \n[Note that two blocks have fallen and are skewed, the cage totals and dots apply within the blocks - imagine they only cover the two cells diagonally]","solution":"516748239983251476427639851271983645398465712645127983139876524764512398852394167","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The values of the letters increase alphabetically. (i.e. A is less than E)","evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"m4bG6rrtFH","ctcId":1415,"ctcDifficulty":"MEDIUM","title":"Equilibrium","author":"Xendari","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. Cells containing filled grey circles must contain odd digits. The value of r8c7 is less than that of r8c8.","solution":"293867541657214983841593276964375812718629435325481697539146728486732159172958364","constraints":["arrow","inequality","odd"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"H2Lb4hnFgm","ctcId":1416,"ctcDifficulty":"MEDIUM","title":"SYO Sum Lines","author":"Xendari","rules":"Normal sudoku rules apply. Shade some cells in the grid such that all shaded cells are orthogonally connected. The digit in a circle gives the number of shaded cells within its 3x3 box. Not all circles are given. Within each 3x3 box, every separate orthogonally connected group of shaded cells must sum to N, where N is the same for all boxes.","rulesClarified":"Normal sudoku rules apply.\n\nShade some cells in the grid so that all shaded cells form one orthogonally connected region.\n\nEach circle contains a digit, and that digit is the number of shaded cells in the 3x3 box that contains the circle. The circled cell is part of that box, so it counts if it is shaded. Not all circles are given. A box without a circle has no clue.\n\nWithin each 3x3 box, the shaded cells split into groups: two shaded cells are in the same group when they touch orthogonally inside that box. The digits in each such group add up to N. N is the same number for all nine boxes, and N is not given.","solution":"249753168687149235315268497163827954852694371794315682928476513571932846436581729","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells in the grid such that all shaded cells are orthogonally connected. The digit in a circle gives the number of shaded cells within its 3x3 box. Within each 3x3 box, every separate orthogonally connected group of shaded cells must sum to N, where N is the same for all boxes.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5"]}]},{"id":"H774tRHPbM","ctcId":1417,"ctcDifficulty":"HARD","title":"Chromatic Quiver","author":"Xendari","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. Cells separated by a chess knight's move cannot contain the same digit.","solution":"615497832493812657872356914784265391259173486136984275367548129948721563521639748","constraints":["antiknight","arrow"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"88RG83pNt7","ctcId":1418,"ctcDifficulty":"HARD","title":"Hiding Spots","author":"Xendari","rules":"Normal sudoku rules apply.\n\nDigits along an arrow must sum to the digit in that arrow's circle.","solution":"842695137397142586156837942239478615785916423614523879428359761571264398963781254","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"Dr42ftb8JG","ctcId":1419,"ctcDifficulty":"MEDIUM","title":"Cascade","author":"Xendari","rules":"Normal sudoku rules apply.\n Digits on a blue line must have an equal sum N within each 3x3 box the line passes through. If a line re-enters a 3x3 box, each segment sums to N separately. eg r3c1+r3c2=r4c2=r3c3+r2c3=r2c4=r1c2+r1c3","solution":"725431689984726315613985247576143892839672154142859736457218963361597428298364571","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"MTtdF66hqN","ctcId":1421,"ctcDifficulty":"VERY HARD","title":"Secrets and Lines","author":"Starwarigami","rules":"This TOP SECRET sudoku has had all its digits redacted. Every redaction is either a Renban, German Whispers or Anti-Factor line. All I can tell you is that row 1 uses exactly two Renban lines, and every other row, column, and 3x3 box uses at least two different types of line. Digits along a Renban line form a set of non-repeating consecutive digits in any order. Consecutive cells along a German Whispers line contain digits which differ by at least 5. Digits along an Anti-Factor line of length n may not be any multiple or factor of n (other than the digit 1), and must sum to a multiple of n. eg a line of length 4 could not contain 2,4 or 8 (but could contain 1).","solution":"192453768835267149746819352619375824458126937327984615974632581283591476561748293","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits along an Anti-Factor line of length n may not be any multiple or factor of n (other than the digit 1), and must sum to a multiple of n. eg a line of length 4 could not contain 2,4 or 8 (but could contain 1).","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Consecutive cells along a German Whispers line contain digits which differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Digits along a Renban line form a set of non-repeating consecutive digits in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"t7hNLh7tBT","ctcId":1422,"ctcDifficulty":"MEDIUM","title":"Foggy YYSL","author":"Blobz","rules":"Normal sudoku rules apply. Digits in large circles must appear in the surrounding 2x2 area. Digits separated by white dots are consecutive. Digits separated by black dots have a 2:1 ratio (ie. one is double the other). Not all such dots are shown. Shade some cells such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected and no 2x2 area is fully shaded or unshaded. Digits in caged cells indicate how many cells of the same colour (shaded or unshaded) are seen orthogonally from that position, including itself. The 'other' colour blocks vision. All dots lie on the boundary of the Yin-Yang pattern (ie. each dot touches one shaded and one unshaded cell). Finally, the grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells, possibly revealing more clues.","solution":"325984617418576329697231485734812596256349178189657234973425861562198743841763952","fogLight":"R2C9,R8C1,R8C2,R8C3","constraints":["custom","fog","kropki","quadruple","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in caged cells indicate how many cells of the same colour (shaded or unshaded) are seen orthogonally from that position, including itself. All dots lie on the boundary of the Yin-Yang pattern (ie. each dot touches one shaded and one unshaded cell).","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c9"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"jnp62DbhBf","ctcId":1424,"ctcDifficulty":"HARD","title":"50 Years of FKG","author":"olima","rules":"Normal sudoku rules apply. Along grey thermometers, digits must increase from the bulb end.","solution":"456139278371285694298674513162758349745963182839421756624817935913542867587396421","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6ddFPmQgFn","ctcId":1426,"ctcDifficulty":"VERY HARD","title":"Jousting Hurdles","author":"Rangsk","rules":"Normal sudoku rules apply. Cells separated by a knight's move (as in chess) cannot contain the same digit as each other. Digits on a purple line form a set of non-repeating, consecutive digits in any order. Adjacent digits along a green line must have a difference of at least 5. Digits along an arrow sum to the number in the circle.","solution":"648519372572843619139276845495168237287435961316927584951684723823751496764392158","constraints":["antiknight","arrow","german-whispers","renban"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"MB4PFfrnn3","ctcId":1430,"ctcDifficulty":"MEDIUM","title":"Funhouse","author":"zetamath","rules":"Normal sudoku rules apply. Adjacent digits along a green line must differ by at least 5. Each grey line consists of one or more non-overlapping groups of consecutive cells, each of which sums to 10.","solution":"491653728683972145527184639378296451254831967916745382732569814845317296169428573","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each grey line consists of one or more non-overlapping groups of consecutive cells, each of which sums to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"Ftfnn4L2tQ","ctcId":1431,"ctcDifficulty":"MEDIUM","title":"10 (Types of) Lines","author":"Math Pesto","rules":"Normal sudoku rules apply. Digits in a circle appear at least once each in the four surrounding cells. From left to right, top to bottom, the following lines have the following properties:\n\nWhisper (green): Adjacent digits differ by 5 or more.\nThermo (gray): Digits increase from the bulb to the end.\nRenban (purple): The line contains a set of consecutive digits (not necessarily in order).\nBetween (gray): Digits on the line are between the values in the circled ends. \nRegion Sum (blue): Digits on the line have the same sum in each box the line is in.\n10 Line (gray): The line consists of one or more contiguous groups of cells, each of which sums to 10. Groups cannot overlap.\nNabner (yellow): No two digits may be consecutive.\nParity (red): Adjacent digits alternate between odd/even parity.\nModular (black): Every set of three sequential digits contains one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}.\nEntropic (orange): Every set of three sequential digits contains one digit from {1,2,3}, one from {4,5,6}, and one from {7,8,9}.","solution":"239156784847239651165847293973625148581794326426381579698573412712468935354912867","constraints":["between-line","custom","entropic-line","german-whispers","modular-line","nabner-line","quadruple","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"10 Line (gray): The line consists of one or more contiguous groups of cells, each of which sums to 10. Parity (red): Adjacent digits alternate between odd/even parity.","evidence":"rules","lessonPolicy":"open","sectionIds":["c9","c12"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"NHMTqjJmRF","ctcId":1432,"ctcDifficulty":"HARD","title":"Vice Versa","author":"Mr.Menace","rules":"Normal sudoku rules apply. Blue lines are “region sum lines”: Along a line, each line segment within a different 3x3 box must sum to the same total. Different lines may have different totals for their line segments.","solution":"176298534592143876483657921824519367937826145615374298241965783758432619369781452","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Blue lines are “region sum lines”: Along a line, each line segment within a different 3x3 box must sum to the same total.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"FRph2b4g2g","ctcId":1433,"ctcDifficulty":"MEDIUM","title":"House Par(i)ty","author":"AnalyticalNinja","rules":"Clues outside the grid are Parity Party clues and give the sum of the digits up to and including the first even digit or up to and including the first odd digit from that side. Single digit clues might give the first digit only. (i.e. a 7 clue could mean the first cell seen contains a 7, the first two cells contain an even and an odd that sum to 7, or the first two cells have a 24 pair and the third cell contains a 1.) Digits within cages cannot repeat, and sum to the small number shown. This puzzle is solved in two stages: Stage 1: Each 3x3 box is solved independently as a 3x3 “mean mini”. (ie each box uses exactly three digits from 1-9 without repeating in the rows or columns of that box.) Outside clues are for the first box seen in this stage (ie they “work” for the box next to the clue). Stage 2: Delete all digits except for the central cell of each 3x3 box. then solve the puzzle as a regular 9x9 sudoku using the remaining digits as givens. Outside clues can now see further than just the first box seen.","rulesClarified":"Normal sudoku rules apply to the final grid.\n\nDigits within a cage cannot repeat, and the digits in each cage sum to the small number shown in that cage.\n\nClues outside the grid are Parity Party clues. Each one sits beside a row or column and reads the cells of that line from its own side, starting with the edge cell. Its number is the sum of the digits up to and including the first even digit or up to and including the first odd digit from that side.\n\nSingle digit clues might give the first digit only. (i.e. a 7 clue could mean the first cell seen contains a 7, the first two cells contain an even and an odd that sum to 7, or the first two cells have a 24 pair and the third cell contains a 1.)\n\nThe puzzle is solved in two stages.\n\nStage 1: each 3x3 box is solved independently as a 3x3 \"mean mini\". Each box uses exactly three digits from 1-9, without repeating in the rows or columns of that box. In this stage an outside clue applies only to the first box it sees, the box next to the clue.\n\nStage 2: delete all digits except the central cell of each 3x3 box, then solve the puzzle as a regular 9x9 sudoku using the remaining digits as givens. In this stage outside clues can see further than just the first box.","solution":"317268459859714632246953781672849315483571296195632874761325948538496127924187563","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Clues outside the grid are Parity Party clues and give the sum of the digits up to and including the first even digit or up to and including the first odd digit from that side. This puzzle is solved in two stages: Stage 1: Each 3x3 box is solved independently as a 3x3 “mean mini”. (ie each box uses exactly three digits from 1-9 without repeating in the rows or columns of that box.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c4"]}]},{"id":"GNtrQQQ88q","ctcId":1435,"ctcDifficulty":"VERY HARD","title":"Vibrations","author":"Niverio","rules":"Normal sudoku rules apply. Digits may not repeat within cages. Cages show their sums. Digits along a thermo increase, starting from the bulb end.","solution":"347965812961328475825174936673891254598243167412657389239516748786432591154789623","constraints":["cage","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"MgMbF23hm6","ctcId":1436,"ctcDifficulty":"MEDIUM","title":"ʜɪ ʀᴇɴ","author":"ZegreS","rules":"Normal sudoku rules apply. Digits along an arrow sum to the number in its circle. Adjacent digits on a green line have a difference of at least 5. The digit in the gray circle is odd. A black dot joins digits with a 1:2 ratio. A white dot joins consecutive digits. Each dot shown is black or white or both.","solution":"763451892584269713129873645312796584876524139495138276637912458241385967958647321","constraints":["arrow","german-whispers","kropki","odd"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"uy5efqsnus","ctcId":1437,"ctcDifficulty":"HARD","title":"Loop Limit","author":"Dorlir and Marty Sears","rules":"• Normal Sudoku rules apply.\n• Draw a loop (one cell wide) of orthogonally connected cells, which does not touch itself, not even diagonally.\n• Each digit on the loop indicates exactly how many times that digit appears on the loop. Eg: If there's a 5 on the loop, it means there are five 5s on the loop.\n• The loop must pass through the bulb of every thermometer.\n• Digits along a thermometer increase from the bulb end.\n• Digits separated by a white dot are consecutive.","solution":"369158472728694315415273869946532781872461593153987624591846237634729158287315946","constraints":["custom","kropki","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Draw a loop (one cell wide) of orthogonally connected cells, which does not touch itself, not even diagonally. • Each digit on the loop indicates exactly how many times that digit appears on the loop. Eg: If there's a 5 on the loop, it means there are five 5s on the loop. • The loop must pass through the bulb of every thermometer.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"FRDLJb8j8p","ctcId":1439,"ctcDifficulty":"HARD","title":"Search 8 or 9","author":"Qodec","rules":"Normal sudoku rules apply. A digit in an arrow shows the distance to a cell containing an 8 or a 9 in the indicated direction (not necessarily the 8 or 9 closest to it). For example a 1 points to the cell directly adjacent to it. Not all arrows are necessarily given.","solution":"932174685681952743745386912863529471129748356574631829496217538258493167317865294","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in an arrow shows the distance to a cell containing an 8 or a 9 in the indicated direction (not necessarily the 8 or 9 closest to it).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"y74wrbb125","ctcId":1440,"ctcDifficulty":"MEDIUM","title":"Twenty Lines","author":"Rangsk","rules":"Normal Sudoku rules apply.\n\nTwenty Lines: Each line must be completely divided into one or more non-overlapping strings of adjacent digits which add to 20.  Note that repeats are still allowed within these sums within the normal constraints of Sudoku.\n\nDigits separated by a black dot have a 1:2 ratio. Not all dots are necessarily given.","solution":"395427618682319574174856932869735421527641893431982756953164287716298345248573169","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Twenty Lines: Each line must be completely divided into one or more non-overlapping strings of adjacent digits which add to 20.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"F2nGdPj2GH","ctcId":1441,"ctcDifficulty":"VERY HARD","title":"Call My Bluff","author":"Tallcat","rules":"Normal sudoku rules apply. All clue types are standard. However, exactly one instance of every clue type is lying to you! Constraints that do not lie work as follows: \nBetween Lines: Cells along lines between two blue circles must have values between those in the circles. \nBlack Kropki: Cells separated by a black dot contain digits with a ratio of 1:2.\nEven: A cell with a grey square must contain an even digit.\nGerman Whispers: Adjacent digits along a green line have a difference of at least 5.\nOdd: A cell with a grey circle must contain an odd digit.\nRenban: Cells along a purple line must contain a set of consecutive digits.\nSandwich: Clues outside the grid give the sum of digits sandwiched between the 1 and 9 in that row/column.\nV: Cells separated by a V must contain digits summing to 5.\nWhite Kropki: Cells separated by a white dot must contain consecutive digits.\nX: Cells separated by an X must contain digits summing to 10.","solution":"897621543625394781413857926176283495549716832238945167951462378764538219382179654","constraints":["XV","between-line","even","german-whispers","kropki","odd","renban","sandwich"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"V: Cells separated by a V must contain digits summing to 5. X: Cells separated by an X must contain digits summing to 10.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12","c14"]},{"slug":"between-line","type":"between-line","variant":"modified","modifiers":[],"params":null,"note":"Between Lines: Cells along lines between two blue circles must have values between those in the circles.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"even","type":"even","variant":"modified","modifiers":[],"params":null,"note":"Even: A cell with a grey square must contain an even digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"German Whispers: Adjacent digits along a green line have a difference of at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Black Kropki: Cells separated by a black dot contain digits with a ratio of 1:2. White Kropki: Cells separated by a white dot must contain consecutive digits.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6","c13"]},{"slug":"odd","type":"odd","variant":"modified","modifiers":[],"params":null,"note":"Odd: A cell with a grey circle must contain an odd digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Renban: Cells along a purple line must contain a set of consecutive digits.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]}]},{"id":"w0jq5h9rti","ctcId":1442,"ctcDifficulty":"MEDIUM","title":"Breakout","author":"BremSter","rules":"- Normal Sudoku rules apply.\n- Digits in red-shaded cells in column 1 indicate the position of 1 in that row. The same is true in columns 5 and 9 for 5's and 9's respectively.\n- Digits in a Quadruple circle must be placed at least once in the four cells touching that circle.","solution":"842365719361987254579214683986473521457126398213859476724698135695731842138542967","constraints":["custom","quadruple"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Digits in red-shaded cells in column 1 indicate the position of 1 in that row. The same is true in columns 5 and 9 for 5's and 9's respectively.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"MF82TJGnB3","ctcId":1443,"ctcDifficulty":"MEDIUM","title":"Forgiven","author":"James Sinclair","rules":"Normal sudoku rules apply. Digits cannot repeat on the indicated diagonal. Digits along blue lines have the same sum within each 3x3 box the line enters. Digits in cells with a shaded square must be even. Digits in cells with a shaded circle must be odd.","solution":"495631782861472395732598416674329851153786924289145637527963148916854273348217569","constraints":["diagonal","even","odd","region-sum-line"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"7D4Bdb3NJg","ctcId":1444,"ctcDifficulty":"MEDIUM","title":"Mods","author":"Marty Sears & ThePedallingPianist","rules":"Normal sudoku rules apply. Yellow lines are 'Same Difference' lines. Each pair of adjacent digits on one of these lines has the same difference. However, this 'difference value' may be different for different lines. A digit in a circle indicates exactly how many circles contain that digit.","solution":"983216457567943812421785369346159728712864935895327146238591674679432581154678293","constraints":["custom","same-difference-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle indicates exactly how many circles contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"bn8DQjnR7D","ctcId":1445,"ctcDifficulty":"MEDIUM","title":"BETWEEEEEEEEN","author":"Twototenth","rules":"Normal sudoku rules apply. Grey lines are 'between lines'; the digits along the line must have values between the digits in the grey circles at the line's ends. Digits in a black circle must appear at least once within the four cells touching the circle.","solution":"198546327326781594754392618937265481415839762862174935671958243589423176243617859","constraints":["between-line","quadruple"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"4mH66tpGmM","ctcId":1446,"ctcDifficulty":"MEDIUM","title":"Effervescence","author":"Oddlyeven","rules":"Normal sudoku rules apply. A number in a circle gives how many times that number appears in circles (anywhere in the puzzle). A clue outside the grid gives the sum of the first X digits from that direction where X is the digit next to the clue.","solution":"917846523325719846864325971159437268432168759678592314541283697286971435793654182","constraints":["custom","x-sum"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A number in a circle gives how many times that number appears in circles (anywhere in the puzzle).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9rb4h4qbQG","ctcId":1447,"ctcDifficulty":"MEDIUM","title":"Butterfly","author":"Aron Lidé (Aspartagcus)","rules":"Normal sudoku rules apply. Digits on an arrow sum to the digit in the circle of that arrow.","solution":"741259638389617245652843917136725489975481326824936751493568172268174593517392864","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6rPQDFRNh8","ctcId":1448,"ctcDifficulty":"MEDIUM","title":"Gallimaufry","author":"Jay Dyer","rules":"Normal sudoku rules apply. Digits may not repeat on the marked diagonal. Digits on a purple line form a set of nonrepeating consecutive digits, which may be in any order. Any three consecutive cells on an orange line must all have different remainders modulo 3 (ie in three consecutive cells there must be one digit from [147], one digit from [258] and one from [369]. Digits along a thermometer line increase from the bulb end. Digits in a cage sum to the indicated total. Digits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio (ie one digit is double the other).","solution":"368975412742138659915624378871243596629517843534896721187352964493761285256489137","constraints":["cage","diagonal","kropki","modular-line","renban","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"g2DNj8FHm2","ctcId":1449,"ctcDifficulty":"HARD","title":"Säntis","author":"ICHTUES & Florian Wortmann","rules":"Normal sudoku rules apply. Digits may not repeat on the marked diagonal. Digits in a cage do not repeat and sum to the small number in the top left corner of the cage.","solution":"357912684218643597496758321681537249974261853532894176745326918823179465169485732","constraints":["cage","diagonal"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6mwnfr1jiy","ctcId":1450,"ctcDifficulty":"MEDIUM","title":"It's a Non-Factor","author":"SSG","rules":"Normal sudoku rules apply.\n\nKiller: Digits in cages may not repeat and must sum to the total in the top left corner.\n\nAnti-Factor Lines: A line may contain no digit that is a multiple or factor of its length other than 1, and the digits along a line must sum to a multiple of its length. Digits may repeat along a line if allowed by the other rules.","solution":"836295174274681395195473826587964213369812547412357968948526731753149682621738459","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Anti-Factor Lines: A line may contain no digit that is a multiple or factor of its length other than 1, and the digits along a line must sum to a multiple of its length.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"gfr7xipywo","ctcId":1451,"ctcDifficulty":"HARD","title":"Mods, Quads & Odds","author":"Marty Sears & ThePedallingPianist","rules":"Normal sudoku rules apply.\n\nSame Difference lines: adjacent digits on a turquoise line must have the same difference, though this difference can be different for different lines.\n\nQuads: each quad circle contains all the digits in the surrounding 4 cells. Unfortunately these quad clues have all been written in white text, and so are invisible.\n\nOdds: digits in a grey circle must be odd.\n\nCircles: a digit in a circle (odd or quad clue) shows how many times that digit appears in a circle. E.g. if there is a 5 in a quad clue, then there must be 5 total appearances of 5s in quad clues and odd circles combined.","solution":"814965327296374158735281469683129745471853296529647813147536982362498571958712634","constraints":["counting-circle","odd","quadruple","same-difference-line"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"h7FRNL2nM6","ctcId":1452,"ctcDifficulty":"HARD","title":"Ancient Altar","author":"Myxo","rules":"Normal sudoku rules apply. Any three adjacent digits along a yellow line include one digit from each entropy group, i.e. one digit from [1,2,3], one digit from [4,5,6] and one digit from [7,8,9]. If the line is only 2 cells long, both of its digits have different entropy. Digits do not repeat along the indicated diagonal.  Digits separated by a white dot are consecutive. Digits separated by a black dot are in a ratio of 2:1.","solution":"491387265526914738783526941648152379235879614179643852364295187917438526852761493","constraints":["diagonal","entropic-line","kropki"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"r89wh6qj90","ctcId":1453,"ctcDifficulty":"VERY HARD","title":"Crux","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nDivide the grid entirely into '15-clumps' - non-overlapping orthogonally connected groups of cells, each of which contains no repeated digits and sums to 15.\n\nAn arrow in a grid indicates that exactly N 15-clumps can be seen in the direction of the arrow, where N is the digit in the arrow's cell. The arrow's cell is not counted, though that cell's clump may be counted if other cells in it are visible in that direction. Two arrows in the same cell are counted as independent clues.","solution":"839147265716253849245968731482316957367592184951874623673489512128735496594621378","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid entirely into '15-clumps' - non-overlapping orthogonally connected groups of cells, each of which contains no repeated digits and sums to 15. An arrow in a grid indicates that exactly N 15-clumps can be seen in the direction of the arrow, where N is the digit in the arrow's cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"26w1k7rwci","ctcId":1454,"ctcDifficulty":"MEDIUM","title":"The Fourth Killer","author":"Marty Sears","rules":"• Normal sudoku rules apply.\n• Four yellow killer cages are hiding in the fog. Enter correct digits to clear the nearby fog. No guessing is necessary (or allowed!)\n• Digits in a killer cage sum to the small number in the top left corner of that cage. \n• Digits CAN repeat within a cage. In fact, a digit in a cage indicates exactly how many times that digit appears in that cage. Eg: a 5 in a cage means that there are five 5s in that cage.\n• Grey lines are bulbless thermometers. Digits along a grey line must be arranged in ascending order, from one end to the other.\n• White dots connect two consecutive digits. Not all possible white dots are shown.","rulesClarified":"Normal sudoku rules apply.\n\nKiller cages: the small number in the top-left corner of a cage is the sum of the digits in that cage.\n\nDigits CAN repeat within a cage. A digit in a cage indicates exactly how many times that digit appears in that cage. For example, a 5 in a cage means there are five 5s in that cage.\n\nFour yellow killer cages are hiding in the fog. Enter correct digits to clear the nearby fog. No guessing is necessary (or allowed!)\n\nGrey lines are bulbless thermometers. Digits along a grey line must be arranged in ascending order, from one end to the other. No bulb marks which end holds the lower digit.\n\nA white dot connects two consecutive digits: the two digits in the cells on either side of the dot differ by exactly 1. Not all possible white dots are shown, so a place with no dot gives no information.","solution":"315698274968742135724531986583427691642319758179856423457263819896175342231984567","fogLight":"R1C5,R2C6,R3C7,R4C8,R5C9,R2C1","constraints":["cage","fog","kropki","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"• Four yellow killer cages are hiding in the fog. Enter correct digits to clear the nearby fog. No guessing is necessary (or allowed!)","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"• Grey lines are bulbless thermometers. Digits along a grey line must be arranged in ascending order, from one end to the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"HN92M3RT3n","ctcId":1456,"ctcDifficulty":"MEDIUM","title":"79","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. The sum of two neighbouring digits on a grey line is always either 7 or 9.","solution":"924687531531924687687531924192468753753192468468753192319246875875319246246875319","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of two neighbouring digits on a grey line is always either 7 or 9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"nPNp4LMHGQ","ctcId":1463,"ctcDifficulty":"HARD","title":"Phoenix","author":"ICHTUES","rules":"Normal sudoku rules apply. The marked diagonal must contain all of the digits 1-9. In cages, digits must sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage.","solution":"863795412591482376472613958784526139139847625625139784918354267257961843346278591","constraints":["cage","diagonal"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"BJ4djnjq82","ctcId":1464,"ctcDifficulty":"HARD","title":"Klappstuhl","author":"ICHTUES","rules":"Normal sudoku rules apply. Clues outside the grid indicate the sum of the digits sandwiched between the 1 and 9 in that row/column. Digits along an arrow must sum to the digit in that arrow’s circle (ie in this puzzle all arrow tips must contain the same digit as their circle!).","solution":"496372185135986274872451693681234957954167832723895416568729341249513768317648529","constraints":["arrow","sandwich"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"r8R7M39bQB","ctcId":1468,"ctcDifficulty":"MEDIUM","title":"Cross Reference","author":"Celery","rules":"Normal sudoku rules apply.Digits along the ORANGE line indicate the column in which the digit 5 appears in that ROW (from left to right). Digits along the BLUE line indicate the row in which the digit 5 appears in that COLUMN (from top to bottom).Adjacent digits along a GREEN line must differ by at least 5.","solution":"796142538512983764834576129358217946927654381461398257189435672643721895275869413","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Normal sudoku rules apply.Digits along the ORANGE line indicate the column in which the digit 5 appears in that ROW (from left to right). Digits along the BLUE line indicate the row in which the digit 5 appears in that COLUMN (from top to bottom).Adjacent digits along a GREEN line must differ by at least 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"TrP3GQTJ7h","ctcId":1471,"ctcDifficulty":"MEDIUM","title":"Crevices","author":"Celery","rules":"Normal sudoku rules apply. Each segment of a line within a different 3x3 box must sum to the same value. If a line re-enters the same box it must also sum to the value for that line. For example, r5c7 + r5c8 = r6c6 = r7c7 + r8c7. Different lines may have different sums.","solution":"147265389269843175385197642851672934693584721724319856478921563932756418516438297","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Each segment of a line within a different 3x3 box must sum to the same value.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"2Q9hBtb8Dg","ctcId":1472,"ctcDifficulty":"HARD","title":"Escalation.","author":"Celery","rules":"Normal sudoku rules apply. Cells with the same relative position within a 3x3 box must contain different digits. For example, all cells in the top-left corner of each box must contain a different digit. Digits cannot repeat along the indicated diagonal. Along a blue line, each line segment within a different 3x3 box must sum to the same total. Blue lines may have different totals to one another!","solution":"395421687726983415418756329573148962842369571961275843239814756154637298687592134","constraints":["diagonal","disjoint-groups","region-sum-line"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"8nmhP8pFhR","ctcId":1476,"ctcDifficulty":"MEDIUM","title":"Less Is More","author":"Jodawo","rules":"Normal sudoku rules apply. Identical digits cannot be a chess knight`s move apart. Digits along an arrow sum to the digit in the circle. Digits in a cage sum to the total given. A black dot indicates a 1:2 ratio between the digits it connects.","solution":"316847952592316847784592613841723569957681324623459178239175486178964235465238791","constraints":["antiknight","arrow","cage","kropki"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"rTBnqH2N7f","ctcId":1477,"ctcDifficulty":"MEDIUM","title":"Nine Is The Key","author":"Jodawo","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the number in the circle. Digits joined by a black dot are in a 1:2 ratio. Numbers along a 'Between Line' must have a value between the values of the numbers on its circles.","solution":"283576941456981723971324865692743518715298436834165297568432179327819654149657382","constraints":["arrow","between-line","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"rL2QBLRhRd","ctcId":1478,"ctcDifficulty":"MEDIUM","title":"Outside Whisper","author":"Jodawo","rules":"Normal sudoku rules apply. A digit outside the grid must be inserted in one of the first three cells of the row or column as seen from that direction. Neighbouring digits along a green line must have a difference of at least 5.","solution":"946275813378194256512386974293451687165827349784963125631548792427619538859732461","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit outside the grid must be inserted in one of the first three cells of the row or column as seen from that direction.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"MTDHBrRB3Q","ctcId":1479,"ctcDifficulty":"MEDIUM","title":"Dotween","author":"Jodawo","rules":"Normal sudoku rules apply. Digits along a 'Between Line' must have a value between the values of the numbers in its circles. A black Kropki dot indicates a 1:2 ratio between its digits. A white Kropki dot indicates that its two digits are consecutive.","solution":"134578629625439781879612453496381275213745896758926314567893142942167538381254967","constraints":["between-line","kropki"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"fB4rmjbndh","ctcId":1480,"ctcDifficulty":"MEDIUM","title":"Rising Tide","author":"Nordy","rules":"Normal Sudoku: Place the digits 1 to 9 in every row, column, and 3x3 box.\n\nGerman Whispers: Along green lines, adjacent digits must have a difference of 5 or greater.\n\nCoral Variant: Some cells are coral and others are water. The high digits and 5 {5,6,7,8,9} are all part of the coral. All coral cells are orthogonally connected. The low digits {1,2,3,4} are all part of the water. There may be multiple bodies of water, and all bodies of water are orthogonally connected to the edge of the grid. No 2x2 area is entirely coral or entirely water.","solution":"168953427439172658275468931793214586524689713816735249641327895957841362382596174","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Coral Variant: Some cells are coral and others are water.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"vzcs2pu8w6","ctcId":1481,"ctcDifficulty":"HARD","title":"BYO Arrows","author":"Celery","rules":"Normal sudoku rules apply.\n\nA digit in a circle indicates exactly how many circles contain that digit.\n\nAdditionally, circles function as the circles of an arrow. Draw arrows that move orthogonally from the circle such all arrows are 2 cells in length and cannot pass through other arrow cells or circles. Digits along an arrow must sum to the value in the attached circle. Cells containing given digits cannot be on an arrow.","solution":"871469532953218476426357198182694357764532981539871624348926715297145863615783249","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Additionally, circles function as the circles of an arrow.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle indicates exactly how many circles contain that digit. Cells containing given digits cannot be on an arrow.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]}]},{"id":"TQjF8PBmDN","ctcId":1482,"ctcDifficulty":"HARD","title":"Killer Sudoku 117","author":"Akash Doulani","rules":"Normal sudoku rules apply. Digits in a cage cannot repeat and sum to the given total.","solution":"128947653436528179975136248861295734349781562257364981513872496682459317794613825","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"38fLLNhq84","ctcId":1483,"ctcDifficulty":"MEDIUM","title":"Nine Rooms","author":"zetamath","rules":"Normal sudoku rules apply.  Cells with a solid grey square contain an even digit.  Cells with a solid grey circle contain an odd digit. The circle or pill in box N records the sum of all the digits within box N that are orthogonally adjacent to the digit N within the box.  Two digit totals are read left to right, top to bottom. For example, the pill in box 6 contains the sum of each digit that is BOTH in box 6 and orthogonally adjacent to the 6 in box 6.","solution":"583614792621978453974253681367891245842765139195432867718549326439126578256387914","constraints":["custom","even","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The circle or pill in box N records the sum of all the digits within box N that are orthogonally adjacent to the digit N within the box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"Gnb2TrBHnF","ctcId":1487,"ctcDifficulty":"MEDIUM","title":"Drunkard's Walk","author":"FullDeck and Missing A Few Cards","rules":"Normal sudoku rules apply. After a night of celebrating, our hero leaves r1c1, through the fog, trying to get home to r9c9. With each step, they move to an orthogonally adjacent cell, forming a modular line as they go. (This means that any set of three contiguous cells along their path must include one digit from [147], one digit from [258] and one digit from [369].)\n\n They stagger from streetlamp (yellow circle) to streetlamp along the way. Some of the streetlamps are visible from the start but others are hidden by the fog and will only be revealed when correct digits are placed nearby. Their path must lead them to every streetlamp. All streetlamps are from the same modular set and, whenever a number from that set is on the path, it appears as a streetlamp. Numbers from that modular set which are not on the path are not streetlamps.\n\n In cages, digits cannot repeat and must sum to the small clue in the top left corner of the cage (if given). If our hero enters a cage, they must completely traverse the cage before exiting it. Some killer cages may be avoided entirely.","solution":"267453189845971263913268574526719348491385726738624951172836495659142837384597612","fogLight":"R1C1,R2C3,R1C5,R3C4,R3C7,R1C8,R4C2,R9C8,R9C9","constraints":["cage","custom","fog","modular-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"After a night of celebrating, our hero leaves r1c1, through the fog, trying to get home to r9c9. They stagger from streetlamp (yellow circle) to streetlamp along the way. Their path must lead them to every streetlamp. All streetlamps are from the same modular set and, whenever a number from that set is on the path, it appears as a streetlamp. Numbers from that modular set which are not on the path are not streetlamps. If our hero enters a cage, they must completely traverse the cage before exiting it.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c7","c8","c9","c11"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"N9TnrTD43m","ctcId":1489,"ctcDifficulty":"VERY HARD","title":"I'll Cry If I Want To","author":"FullDeck and Missing a Few Cards","rules":"Normal sudoku rules apply. Along modular lines, every set of three contiguous digits has three different remainders when divided by 3. Numbers outside the grid give the sum of the first X digits (the 'X-Sum') along that row or column, where X is the first digit seen from the direction of the clue. In addition to any modular lines revealed as the fog lifts, every X-sum forms a hidden straight modular line at least X cells long starting from the cell closest to the clue. Digits separated by a black dot are in a 1:2 ratio. ALL blacks dots are given. As correct digits are placed, fog will lift, potentially revealing more clues.","solution":"627354981458196273913872645864529137579431826132687594745268319296713458381945762","fogLight":"","constraints":["custom","fog","kropki","modular-line","x-sum"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In addition to any modular lines revealed as the fog lifts, every X-sum forms a hidden straight modular line at least X cells long starting from the cell closest to the clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"LMh4tRr2bP","ctcId":1490,"ctcDifficulty":"HARD","title":"Thermo Dot","author":"FullDeck and Missing a Few Cards","rules":"Normal sudoku rules apply. Along thermos digits must strictly increase from the bulb to the tip. Digits in the same relative position in different boxes cannot be the same. Digits separated by a white dot form a consecutive pair.","solution":"623457981415689723987213654394768215852941367761325498546132879278594136139876542","constraints":["disjoint-groups","kropki","thermometer"],"constraintFacts":[{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"p8FLjRMMJ6","ctcId":1493,"ctcDifficulty":"HARD","title":"Chromosomesx","author":"Bellal & ThePedallingPianist","rules":"Normal sudoku rules apply.\n\nEqual sums line: digits on the blue line have an equal sum, N, within each box through which it passes. If the line passes through the same box more than once, each line segment sums to N separately.\n\nDoublers: there is exactly one 'doubler' in each row, column and 3x3 box. These are the digits 1-9 once each. For the purpose of the equal sums line, a digit in a 'doubler' cell counts as twice the digit's value.\n\nThe yellow line between r6c5 and r6c6 is purely aesthetic, i.e. box 5 has two distinct line segments.","solution":"192657348548931627637842591254798163873416259961523874489165732316274985725389416","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Doublers: there is exactly one 'doubler' in each row, column and 3x3 box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Equal sums line: digits on the blue line have an equal sum, N, within each box through which it passes.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"2nqGgL8L7h","ctcId":1494,"ctcDifficulty":"MEDIUM","title":"Hangman","author":"ThePedallingPianist & his Granddad","rules":"Normal sudoku rules apply. The letters A, G, H, M and N all represent different numbers (not necessarily from 1-9). Digits along an arrow sum to the digit in the attached circle. Digits in a cage sum to the given total in the top left corner. Along the blue line, each line segment within a different 3x3 box must sum to the same total. Clues outside the grid show the sum of the digits sandwiched between the 1 and 9 in that row. Digits along a thermometer increase from the bulb end.","solution":"312975468475368291689412375893721654724536189156849723941687532537294816268153947","constraints":["arrow","cage","custom","region-sum-line","sandwich","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The letters A, G, H, M and N all represent different numbers (not necessarily from 1-9).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"4mtPGFb6dm","ctcId":1496,"ctcDifficulty":"MEDIUM","title":"Circular Unreasoning","author":"ThePedallingPianist","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. A digit in a circle shows how many circles DO NOT contain that digit. Additionally, a digit on an arrow shows how many arrows DO NOT contain that digit.","rulesClarified":"Normal sudoku rules apply.\n\nEach arrow starts at a circle, its bulb. The digits along the arrow, not counting the bulb, add up to the digit in that bulb.\n\nA digit in a circle is how many of the other circles in the grid do not contain that digit. The circle with the digit is not counted.\n\nAdditionally, a digit on an arrow shows how many arrows DO NOT contain that digit.","solution":"681542973794368251253719846178635429429187635536294187915823764867451392342976518","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle shows how many circles DO NOT contain that digit. Additionally, a digit on an arrow shows how many arrows DO NOT contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"4ftr2ntfg4","ctcId":1497,"ctcDifficulty":"MEDIUM","title":"Bag of Tricks","author":"James Sinclair","rules":"Normal sudoku rules apply. Digits cannot repeat on the indicated diagonal. Cages show their sums. Digits along an arrow sum to the digit in that arrow’s circle. Purple lines contain a set of consecutive, non-repeating digits. These digits can appear in any order. Digits in cells with a shaded square must be even.","solution":"687195432952346871431278695514629783728431569369857124295764318846913257173582946","constraints":["arrow","cage","diagonal","even","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"TrgbQfmrtH","ctcId":1498,"ctcDifficulty":"MEDIUM","title":"Point of View","author":"Nordy","rules":"Normal sudoku rules apply. Digits along each blue line have an equal sum N within each box the line passes through. Different lines may have different sums. Digits joined by a white dot are consecutive. Digits joined by a black dot are in a ratio of 2:1. Along the marked diagonal, digits cannot repeat.","solution":"597183462216497538348625791923746185785312649164859273639271854852964317471538926","constraints":["diagonal","kropki","region-sum-line"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"8NGMPRj4Dt","ctcId":1507,"ctcDifficulty":"VERY HARD","title":"Big Mac","author":"Adem Jaziri","rules":"Normal sudoku rules apply. Digits in a cage cannot repeat and must sum to the small clue in the top left corner of the cage. A clue outside the grid indicates the sum of the digits between X and Y, and also the sum of the digits between Y and Z in the corresponding row or column. X, Y and Z are the same for all the clues and must be determined by the solver. (For example, if X = 1, Y = 6 and Z = 9, the 7 clue indicates that the sum of the digits between 1 and 6 is equal to 7 and the sum of the digits between 6 and 9 is also equal to 7.) A '?' could represent any digit from 0 to 9. Different '?'s may represent different digits.","solution":"946357821583612749172489653764135982319826574258794316491573268837261495625948137","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A clue outside the grid indicates the sum of the digits between X and Y, and also the sum of the digits between Y and Z in the corresponding row or column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"J6GdmRM6JT","ctcId":1528,"ctcDifficulty":"MEDIUM","title":"Pyramidal Arrows v2","author":"Dorlir","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. The sum of the digits within a cage must sum to the small clue in the top-left corner of the cage.","solution":"985312467724596318163478592239847651648251973571639284416983725852764139397125846","constraints":["arrow","cage"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"7p8BFPqG4M","ctcId":1530,"ctcDifficulty":"EASY","title":"Rising Circles","author":"Dorlir","rules":"Normal sudoku rules apply. A digit in a circle indicates exactly how many circles contain that digit. For example, if there is a 5 in any circle, then there are five 5s in circles.","solution":"936825714147936825258147936693582471714693582825714693369258147471369258582471369","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle indicates exactly how many circles contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"489rPm6j4f","ctcId":1532,"ctcDifficulty":"HARD","title":"Yin-Yang Thermos","author":"Dorlir","rules":"Normal sudoku rules apply. Shade some cells such that all shaded cells are orthogonally connected, and all unshaded cells are orthogonally connected, and no 2x2 area may be fully shaded or unshaded. Each cell in row 9 reveals how many shaded cells are in that column. Furthermore, in each column the shaded digits in that column, must increase in value, going from either top to bottom or bottom to top. Cells separated by a red dot sum up to 9. A digit on a circle has its value increased by 9.","solution":"167328459248659731359741682491572863582963174673184295734815926815296347926437518","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each cell in row 9 reveals how many shaded cells are in that column. Furthermore, in each column the shaded digits in that column, must increase in value, going from either top to bottom or bottom to top. Cells separated by a red dot sum up to 9. A digit on a circle has its value increased by 9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c6"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"NTdGT2L7Fj","ctcId":1535,"ctcDifficulty":"HARD","title":"Nabner In the Nebula v2","author":"gdc","rules":"Normal sudoku rules apply. The grid is covered in fog. Placing correct digits reveals clues in the surrounding 3 by 3 area. All golden lines are 'nabner' lines ie they cannot contain repeated digits and no two digits along a line may be consecutive.  Eg if 5 is on a line, 4,5 and 6 cannot appear anywhere else on the line. Clues outside the grid give the sum of the first X digits along that row or column (the 'X-sum'), where X is the first digit seen from the direction of the clue. In addition to any nabner lines revealed as the fog lifts, every X-sum forms a hidden nabner line at least X cells long starting from the cell closest to the clue.","rulesClarified":"Normal sudoku rules apply.\n\nThe grid is covered in fog. Placing a correct digit reveals the clues in the surrounding 3 by 3 area.\n\nGolden lines are 'nabner' lines. A nabner line cannot contain a repeated digit, and no two digits on the line may be consecutive. Consecutive means differing by one, anywhere on the line, not only in neighbouring cells. For example, if 5 is on a line, then 4 and 6 cannot appear anywhere else on that line.\n\nClues outside the grid give the sum of the first X digits along their row or column, where X is the first digit seen from the direction of the clue. Such a clue is an 'X-sum'.\n\nEvery X-sum also forms a hidden nabner line, at least X cells long, starting from the cell closest to the clue. These hidden lines are in addition to any golden nabner lines revealed as the fog lifts.","solution":"728134659416895372593276184132749568985362741647518293264953817851427936379681425","fogLight":"","constraints":["custom","fog","nabner-line","x-sum"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In addition to any nabner lines revealed as the fog lifts, every X-sum forms a hidden nabner line at least X cells long starting from the cell closest to the clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"m3GGq4Ht96","ctcId":1536,"ctcDifficulty":"HARD","title":"Guess the Renban","author":"gdc","rules":"Normal sudoku rules apply. The grid is covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area. Digits separated by a black dot are in a 1:2 ratio (ie one is double the other). Digits separated by a white dot are consecutive. Not all possible dots are given. Digits on a line form a set of consecutive, non-repeating digits - these digits can appear in any order. All lines are exactly 5 cells long, don't branch, don't share cells with other lines and only move orthogonally.","solution":"418736592735298641629415738256341879871569324394827156183974265962153487547682913","fogLight":"R7C7","constraints":["fog","kropki","renban"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"sbufo2e9yn","ctcId":1537,"ctcDifficulty":"MEDIUM","title":"Lavender in the Fog","author":"gdc","rules":"The grid is partially covered in fog. Placing correct digits reveals clues in the surrounding 3 by 3 area.\nDigits an equal distance from the center of a lavender 'Zipper Line' sum to the digit in the middle of that line.\nAll Zipper Lines are 5 cells long, only move orthogonally and can't share cells with other Zipper Lines\nDigits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. Not all dots are given.","rulesClarified":"The grid is partially covered in fog. Placing correct digits reveals clues in the surrounding 3 by 3 area.\n\nZipper Lines: the lavender lines are Zipper Lines. Each Zipper Line runs through five cells, moving orthogonally from one cell to the next. No two Zipper Lines share a cell.\n\nAlong each Zipper Line, digits an equal distance from the middle cell sum to the digit in the middle cell.\n\nDigits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio.\n\nNot all dots are given. A pair of neighbouring cells with no dot between them has no dot rule.","solution":"697134852123985476485276391532619784941728635876543219268391547714852963359467128","fogLight":"R5C6,R4C5","constraints":["fog","kropki","zipper-line"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"co8u58tluq","ctcId":1538,"ctcDifficulty":"EASY","title":"Zip-a-Dee-Doo-Dah","author":"gdc","rules":"Normal sudoku rules apply.\nDigits an equal distance from the center of a lavender 'Zipper Line' must sum to the digit in the middle of that line.\nDigits on the marked diagonals may not repeat.","solution":"568291734329487615471635829184962573652374198793518462246159387835726941917843256","constraints":["diagonal","zipper-line"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"i94uhivr9x","ctcId":1540,"ctcDifficulty":"MEDIUM","title":"A Zip From the Devil's Cup","author":"gdc","rules":"Normal sudoku rules apply\nDigits an equal distance from the centre of a lavender 'Zipper Line' sum to the digits in the middle of that line.","solution":"947651328531298764268347159154726983396485217782139645879562431613874592425913876","constraints":["zipper-line"],"constraintFacts":[{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6t4pFDGtBq","ctcId":1546,"ctcDifficulty":"HARD","title":"You're Going Places","author":"Jeet Sampat","rules":"Normal sudoku rules apply. Cells separated by a knight's move (in chess) must contain different digits. On thermometers, digits must strictly increase from the bulb-end.","solution":"287463915391527846645198723478315692913246587562789134754831269839652471126974358","constraints":["antiknight","thermometer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"P7DpbRmpJH","ctcId":1547,"ctcDifficulty":"HARD","title":"Above Average On Average","author":"Jeet Sampat","rules":"Normal sudoku rules apply. A clue outside the grid gives the sum of digits along the indicated diagonal. Digits within a cage sum to the small clue in the top-left corner of the cage. The green line connects digits with a difference of 5 or more.","solution":"971546328536289714284371596428615937157493682693827145362958471749162853815734269","constraints":["cage","german-whispers","little-killer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"BLJqNdB389","ctcId":1556,"ctcDifficulty":"MEDIUM","title":"Miracle Junior","author":"Just Kirb","rules":"Normal sudoku rules apply. (ie Place the digits 1 through 9 once each in every row, column and 3x3 box). Cells separated by a king's move (in chess) cannot contain the same digit. Cells separated by a knight's move (in chess) cannot contain the same digit. No domino in the grid can contain digits summing to 5 or 10.","solution":"675981243243675981981243675367598124124367598598124367436759812812436759759812436","constraints":["antiking","antiknight","custom"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No domino in the grid can contain digits summing to 5 or 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"rNqtfFJFhB","ctcId":1557,"ctcDifficulty":"MEDIUM","title":"Royal Self Defense","author":"Just Kirb","rules":"Normal sudoku rules apply. Digits on an arrow sum to the value in the attached circle. Identical digits cannot be separated by a king's move in chess.","solution":"385419627697832154124576389973628415418795236562143798749351862851264973236987541","constraints":["antiking","arrow"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"tPFdpb8H78","ctcId":1560,"ctcDifficulty":"MEDIUM","title":"Pointing Fingers","author":"Just Kirb","rules":"Normal sudoku rules apply. The digits along each arrow must sum to the digit in the circled cell.","solution":"867412953153869427294735186618293745379654218425187639731526894942378561586941372","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"588su8gaub","ctcId":1586,"ctcDifficulty":"MEDIUM","title":"Double The Fun","author":"Sandra & Nala","rules":"It’s a very special day for Nala because she gets a visitor. It is her best friend Nelly! Nala and Nelly have been best friends since their earliest puppy weeks. Whenever they come together all the fun is doubled, but the backyard will be left in chaos and a huge cloud of dust. \n\nHow will the backyard look like once the dust settled?\n\nNormal Sudoku rules apply: Place the digits 1-9 in every row, column and box exactly once each. \n\nEach of the digits 1-9 appears as a „Doubler“ exactly once in the grid. There is only one „Doubler“ in each row, column and 3x3 box. Digits that appear as „Doubler“ have a value that is double their size. \n\nThe value of digits in a dashed cage must sum to the total in the top left corner of the cage. Digits may not repeat within their own cage, although values may. \n\nThe value of digits along an arrow must sum to the value of the digit in the corresponding circle. Each arrow has its own color. Arrows of the same color are connected. \n\nAdditionally the grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells, possibly revealing more clues.","solution":"318549267279136854546782319127853946684971532953624178431268795865397421792415683","fogLight":"R1C1,R1C2,R2C1,R3C1,R3C2","constraints":["arrow","cage","custom","fog"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"The value of digits along an arrow must sum to the value of the digit in the corresponding circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The value of digits in a dashed cage must sum to the total in the top left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each of the digits 1-9 appears as a „Doubler“ exactly once in the grid. Each arrow has its own color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c13"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c15"]}]},{"id":"1c1i6cf4wu","ctcId":1587,"ctcDifficulty":"MEDIUM","title":"Beautiful Day","author":"Sandra & Nala","rules":"When a day - no matter how perfect it is - can only take you so far and the fear of hitting that wall where everything stops to flow grows big enough - it is understandable that you will start to look for another solution to your problems. Once found, everything will flow again in all the different directions that seemed blocked just a moment ago.\n\nWhat kind of solution will you seek out when you don’t seem to be able to come any further?\n\nNormal Sudoku rules apply: Place the digits 1-9 in every row, column and box exactly once each. \n\nDigits on an arrow must sum to the digit in that arrows circle. Each arrow has its own color. Arrows of the same color are connected. \n\nDigits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. Not all possible dots are given. (There is no negative constraint.)\n\nOne cell in the grid is your newly found motivation. Cells must increase in value as they move away from this point in every straight-line direction (i.e. vertically, horizontally and diagonally) until they reach the edge of the grid. Once found, everything will start to flow again. \n\nAdditionally the grid is partially covered in fog just as your thinking might be impaired sometimes and not allow clear thoughts. Placing correct digits will clear the fog from surrounding cells, possibly revealing more clues.","rulesClarified":"Flavour (no rule): the opening lines are about a day that stops flowing and the search for a new solution. Once found, everything will flow again.\n\nNormal Sudoku rules apply: place the digits 1-9 once each in every row, column and box.\n\nArrows: digits on an arrow must sum to the digit in that arrow's circle. Each arrow has its own colour, and arrows of the same colour are connected.\n\nWhite dots: digits separated by a white dot are consecutive.\n\nBlack dots: digits separated by a black dot are in a 1:2 ratio, so one is double the other.\n\nNot all possible dots are given. A pair of cells with no dot between them is not constrained by a dot. There is no negative constraint.\n\nMotivation: one cell in the grid is your newly found motivation. From that cell, digits must increase as you move away from it in every straight-line direction (vertically, horizontally and diagonally) until you reach the edge of the grid.\n\nFog: the grid is partly covered in fog. Placing correct digits clears the fog from the surrounding cells, possibly revealing more clues.","solution":"745369821629518473813247956274186395136925748598473162461732589987651234352894617","fogLight":"R1C1,R1C2,R2C1,R2C2,R2C3,R3C2,R3C3","constraints":["arrow","custom","fog","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"One cell in the grid is your newly found motivation.","evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c15"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8","c9"]}]},{"id":"2v5h5o63ej","ctcId":1588,"ctcDifficulty":"MEDIUM","title":"Nori Nori Christmas","author":"Sandra & Nala","rules":"Christmastime is coming soon and it’s probably not too early to do some baking! Nala is eager to help out with anything, but she may not be the best fit when it comes to cutting out the cookies and placing them on the tray so they don’t touch each other when they go into the oven. She might need some help with that. Would you mind?\n\nNormal sudoku rules apply: Place the digits 1-9 in every row, column and box exactly once each.\n\nDigits in a dashed cage must sum to the value in the top left corner of the cage (if given). Digits may not repeat within their own cage.\n\nNori Nori Christmas: Shade exactly two cells in each cage. Each shaded area forms a domino (cookie), not necessarily within a cage. Shaded dominoes may touch diagonally, but not orthogonally. A shaded domino functions as a black Kropki dot, i.e. digits in a shaded domino are in a ratio of 2:1. It is possible for unshaded dominoes to be in a 2:1 ratio. \n\nDigits separated by a white sugar decoration dot are consecutive. Not all possible dots are given. \n\nAdditionally the grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells, possibly revealing more clues.","solution":"485637219796812354213954867127485936538796421964321785372169548841573692659248173","fogLight":"R1C2,R2C2,R2C3","constraints":["cage","custom","fog","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Nori Nori Christmas: Shade exactly two cells in each cage. Each shaded area forms a domino (cookie), not necessarily within a cage. Shaded dominoes may touch diagonally, but not orthogonally.","evidence":"rules","lessonPolicy":"open","sectionIds":["c8","c9","c10"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c15"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11","c13"]}]},{"id":"8m29x14m56","ctcId":1590,"ctcDifficulty":"MEDIUM","title":"Slalom mit Ablenkung","author":"Sandra & Nala","rules":"Have you ever heard of Rally Obedience? It's a type of dog sport that Nala has recently discovered for herself. There is a course to walk and it has signs placed on the ground explaining what tricks to perform before moving on to the next sign. It is a team sport and while Nala is really good at it, her human counterpart gets literally everything wrogn on the course. The result: chaos and confusion. We might need help to finish this.. \n\nNormal sudoku rules apply. Place the digits 1-9 in each row, column and box exactly once each. \n\nAll clues are standard and in the final grid all clues need to be wrong. A clue is wrong when the placed digits cause it to be invalid. Placing digits that successfully make clues invalid will help clearing the fog from surrounding cells, possibly revealing more nonsense (clues). \n\nClues are valid if: \nDigits in a killer cage sum up to the number on it's top left (if given) and do NOT contain repeated digits. \n\nDigits on arrows sum to the number in the connected circle. (Each arrow is a separate clue, even if multiple arrows share the same circle).\n\nDigits on a slow thermometer increase or stay the same as they move from the bulb to the tip.\n\nDigits on a (thin) green whisper line have a difference of at least 5. \n\nDigits on a (thick) orange whisper line have a difference of at least 4. \n\nDigits in an orange odd shaded circle are odd.\n\nDigits in a blue shaded square are even.\n\nAll digits in a (larger) white circle appear in the 4 cells touching it.\n\nDigits joined by a white dot are consecutive.\n\nDigits joined by a black dot are in a ratio of 1:2.\n\nWho would have expected the beginner level to be this complex already?!","solution":"783459126465231879912768534679543281358612947241897365537124698194386752826975413","fogLight":"R8C3,R9C1,R9C2,R9C3,R7C1","constraints":["arrow","cage","dutch-whispers","even","fog","german-whispers","kropki","odd","quadruple","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits on arrows sum to the number in the connected circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c14"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a killer cage sum up to the number on it's top left (if given) and do NOT contain repeated digits.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c13"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"modified","modifiers":[],"params":null,"note":"Digits on a (thick) orange whisper line have a difference of at least 4.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c18"]},{"slug":"even","type":"even","variant":"modified","modifiers":[],"params":null,"note":"Digits in a blue shaded square are even.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c20"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Digits on a (thin) green whisper line have a difference of at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c17"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Digits joined by a white dot are consecutive. Digits joined by a black dot are in a ratio of 1:2.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c22","c23"]},{"slug":"odd","type":"odd","variant":"modified","modifiers":[],"params":null,"note":"Digits in an orange odd shaded circle are odd.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c19"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c21"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Digits on a slow thermometer increase or stay the same as they move from the bulb to the tip.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c16"]}]},{"id":"701zcuaz8b","ctcId":1593,"ctcDifficulty":"MEDIUM","title":"Parity Cave","author":"Dorlir","rules":"Normal sudoku rules apply. Shade some cells such that all shaded cells are orthogonally connected, and all unshaded cells are orthogonally connected (a 2x2 area MAY be fully shaded or unshaded). For each N, row N and box N both have exactly N shaded cells, which contain exactly the digits from 1 to N. Adjacent cells on the red line have different parities i.e. one digit is odd and the other digit is even.","solution":"258349671369175482471268593583692714694713825712854936825936147947521368136487259","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For each N, row N and box N both have exactly N shaded cells, which contain exactly the digits from 1 to N. Adjacent cells on the red line have different parities i.e. one digit is odd and the other digit is even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"J8MMb74TPM","ctcId":1598,"ctcDifficulty":"MEDIUM","title":"Loop With A Difference","author":"Scruffamudda","rules":"Normal sudoku rules apply. The solver must draw a single loop which travels along the grid lines but not on the outer perimeter. The loop must not branch or touch itself. A digit in a blue cell shows the number of that cell's corners (grey dots) which touch the loop. Pairs of digits separated by the loop have a difference of 1.","solution":"596734182147825639238691745329186457871549326465273891754362918613958274982417563","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The solver must draw a single loop which travels along the grid lines but not on the outer perimeter. A digit in a blue cell shows the number of that cell's corners (grey dots) which touch the loop. Pairs of digits separated by the loop have a difference of 1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c5"]}]},{"id":"TfMt9NDLQ8","ctcId":1599,"ctcDifficulty":"MEDIUM","title":"Cryptic Rune","author":"Scruffamudda","rules":"Normal sudoku rules apply. Eight grey palindromes, reading the same from each end, all begin at the central cell of the grid. Inequality signs ‘point’ to the lower digit of the adjoining pair.","solution":"914836752762951384853274961195683427427195638386427195549768213231549876678312549","constraints":["inequality","palindrome"],"constraintFacts":[{"slug":"inequality","type":"inequality","variant":"modified","modifiers":[],"params":null,"note":"Inequality signs ‘point’ to the lower digit of the adjoining pair.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"MDBMQfF877","ctcId":1600,"ctcDifficulty":"MEDIUM","title":"Limiting Factors","author":"Scruffamudda","rules":"Normal sudoku rules apply. Orthogonally adjacent digits must not be consecutive. A digit in a circle or square must not be a multiple or divisor of any orthogonally adjacent digit. Grey circles contain odd digits. Grey squares contain even digits.","solution":"251738694694251837837496251372649518518372946946815372469183725183527469725964183","constraints":["custom","even","non-consecutive","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle or square must not be a multiple or divisor of any orthogonally adjacent digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"Lf4B9t2p29","ctcId":1615,"ctcDifficulty":"HARD","title":"Shadow Circles","author":"Celery","rules":"Normal sudoku rules apply. The grid is covered with fog. Placing correct digits will reveal the fog around that digit. Guessing is not required! A digit in a red circle indicates exactly how many red circles contain that digit. Additionally, a digit in a red circle must reappear at least once in its 8 surrounding cells. The two given circles contain the same digit. Digits along a purple arrow sum to the value in the attached circle. Red circles may or may not have arrows attached. Arrows do not share cells and do not cross.","solution":"674359812893421765215867349457986231938172654162543978586794123329615487741238596","fogLight":"R5C7,R7C3,R4C8","constraints":["arrow","custom","fog"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a red circle indicates exactly how many red circles contain that digit. Additionally, a digit in a red circle must reappear at least once in its 8 surrounding cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"fffPBhPDtG","ctcId":1617,"ctcDifficulty":"HARD","title":"Eiger","author":"Qodec","rules":"Normal sudoku rules apply. In cages, digits must sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage.","solution":"671459328285736491439821765156398247928147653743562189594213876367984512812675934","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"FMGPBBt24p","ctcId":1630,"ctcDifficulty":"MEDIUM","title":"Lines in the Fog","author":"apetersen","rules":"Normal sudoku rules apply. The grid is covered in fog. Correctly entering digits will remove the fog in the surrounding cells. Each line has a distinct colour. Lines do not branch, cross, and only move orthoganally. All lines are renban (ie contain a set of non-repeating consecutive digits, in any order). All lines are “region sum” (ie along a line, each line segment within a different 3x3 box must sum to the same total (N). N may be different for each line.) All lines have a length of 3 or more. One line is also a thermometer and digits will increase from its bulb. (The bulb may be in the middle of the line.)","solution":"431872596576914832298563147654729381912438675783156429145287963329645718867391254","fogLight":"R1C5,R2C7,R3C2,R6C4,R7C3,R7C8,R8C6,R5C7,R9C3,R1C9","constraints":["fog","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"mM7R76NrpR","ctcId":1635,"ctcDifficulty":"MEDIUM","title":"R is for arrows","author":"Chameleon","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle.","solution":"215643789894752361637189425371596842528437196469821537746918253182365974953274618","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9JLLbT9Jj7","ctcId":1637,"ctcDifficulty":"MEDIUM","title":"Re-framed","author":"Nordy & Riffclown","rules":"Normal sudoku rules apply. Along a blue line, each line segment within a different 3x3 box must sum to the same total. Different lines may have different totals. Each grey line consists of one or more contiguous groups of cells, each of which sums to 10. These groups of cells cannot overlap. Adjacent digits on a green German Whisper line must differ by at least 5.","solution":"286451397593827164714936258431678925928514736657293841862749513145382679379165482","constraints":["custom","german-whispers","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each grey line consists of one or more contiguous groups of cells, each of which sums to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"b8BGpH9Nrj","ctcId":1638,"ctcDifficulty":"VERY HARD","title":"From Pillar to Post","author":"Mr.Menace","rules":"Normal sudoku rules apply. Digits in a cage may not repeat and sum to the number shown. Digits on a marked diagonal may not repeat.","solution":"175936248438725169629481753763592481892147536514368927241873695356219874987654312","constraints":["cage","diagonal"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"LLM2t7G4NG","ctcId":1644,"ctcDifficulty":"MEDIUM","title":"Strawberry Fields","author":"Cris Moore","rules":"Normal sudoku rules apply. Each red cell either indexes the 5 in its row or in its column, i.e. it either equals the row of the 5 in its column, or the column of the 5 in its row. For instance, if r3c6 is a 7, then either r7c6 or r3c7 is a 5. Fives are antiknights: no two 5s can be a knight's move apart. Digits in a gray circle must be odd. A white dot joins a consecutive pair of digits.","rulesClarified":"Normal sudoku rules apply. Rows and columns are numbered 1 to 9 from the top and from the left, so every row and every column contains exactly one 5.\n\nEach red square holds a digit that points to a 5. It either equals the row number of the 5 in its own column, or it equals the column number of the 5 in its own row.\n\nFor example, if the cell in row 3, column 6 holds a 7, then either the 5 in column 6 is in row 7, or the 5 in row 3 is in column 7.\n\nFives are antiknights: no two 5s can be a knight's move apart.\n\nDigits in a grey circle must be odd.\n\nTwo digits joined by a white dot are consecutive: one is exactly one more than the other.","solution":"387954621954612837261387549716295483435876912829143765143769258572438196698521374","constraints":["custom","kropki","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each red cell either indexes the 5 in its row or in its column, i.e. it either equals the row of the 5 in its column, or the column of the 5 in its row. Fives are antiknights: no two 5s can be a knight's move apart.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"HtjBggbNfq","ctcId":1647,"ctcDifficulty":"VERY HARD","title":"Privy","author":"dumediat","rules":"Normal sudoku rules apply. Adjacent digits along a green line must differ by at least 5. Each purple line contains a set of consecutive digits in any order. A clue outside the grid indicates the sum of the digits between the 1 and the 9 in the corresponding row or column.","rulesClarified":"Normal sudoku rules apply.\n\nEach purple line contains a set of consecutive digits, in any order.\n\nAdjacent digits along a green line differ by at least 5.\n\nA clue outside the grid gives the sum of the digits strictly between the 1 and the 9 in the row or column it points at. A clue to the left of a row refers to that row. A clue above a column refers to that column.\n\nThe 1 and the 9 themselves are not counted in that sum. Normal sudoku places one 1 and one 9 in every row and column, so the clue's line contains exactly one 1 and one 9.","solution":"469172853271538649385946172714385296658294317932761485897423561143657928526819734","constraints":["german-whispers","renban","sandwich"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"p9x40zygp1","ctcId":1656,"ctcDifficulty":"MEDIUM","title":"First Advent Sunday Lake Tour","author":"Sandra & Nala","rules":"It’s the first advent Sunday and we want to go for a walk. Nala doesn’t know where we planned to go, yet, so it’s a surprise for her and she loves to explore her surroundings!\n\nNormal Sudoku rules apply: Place the digits 1-9 in every row, column and box exactly once each.   \n\nDigits in a dashed cage must sum to the value in the top left corner of the cage. Digits may not repeat within their own cage.  \n\nLake Tour Path: Help Nala find the path around the lake by following these rules: The path must be orthogonally connected and visit all cells of all cages. The path forms a loop (ie it has no start or end points). The path can touch itself diagonally, however it is not allowed to touch orthogonally (ie no cell on the path can share edges with more than two other cells on the path). Digits along the path differ by AT MOST 2.\n\nDigits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. Not all possible dots are given. (There is no negative constraint.)  \n\nAdditionally the grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells, possibly revealing more clues.","solution":"195467283684325719732189645871256394953874126246913578317548962429631857568792431","fogLight":"R8C3,R9C3,R7C5,R8C5,R8C6,R6C2","constraints":["cage","custom","fog","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Lake Tour Path: Help Nala find the path around the lake by following these rules: The path must be orthogonally connected and visit all cells of all cages.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10","c11"]}]},{"id":"pTPD72D9qP","ctcId":1658,"ctcDifficulty":"HARD","title":"Everything in its Right Place","author":"Marty Sears","rules":"Normal sudoku rules apply. Draw 3 snakes which must each begin and end at a different grey spot. Snakes are lines which may move orthogonally and diagonally between cells. They may touch each other (or themselves), and can even cross each other, but they must not branch, share cells with each other, or enter cages. A digit on a snake indicates exactly how many times that digit appears on that snake. Eg: If there is a 5 on a snake, there are five 5s on that snake. One snake is a “German Whisper” line; along it, adjacent digits must differ by at least 5. One snake is a “slow thermometer”; along this line, reading from one end to the other, digits must always increase or stay the same. One snake is “entropic”; along it, any group of 3 adjacent cells must contain one low digit (1, 2 or 3), one medium digit (4, 5 or 6) and one high digit (7, 8 or 9.) Digits in a cage must sum to the small clue given in that cage. Digits separated by a V sum to 5.","solution":"236794581578136924419852736621489357985673412347521698193267845864315279752948163","constraints":["XV","cage","custom","entropic-line","german-whispers","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw 3 snakes which must each begin and end at a different grey spot. A digit on a snake indicates exactly how many times that digit appears on that snake.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"8n6RPbqntg","ctcId":1659,"ctcDifficulty":"MEDIUM","title":"Bidirectional 34","author":"just kirb","rules":"Normal sudoku rules apply. The digits along an arrow must sum to the digit in the circled cell. Digits must not repeat at corresponding box positions.","rulesClarified":"Normal sudoku rules apply: each row, column and box holds the digits 1 to 9 once each.\n\nArrows. Each arrow starts at a circled cell and runs along its drawn line. The digits on the arrow, not counting the circle, sum to the digit in the circled cell.\n\nCorresponding box positions. Digits must not repeat at corresponding box positions. For each position within a box (for example the top-left cell), the nine cells in that position across the nine boxes hold nine different digits.","solution":"219683457453917682867452913972345861345168729186729345728594136591836274634271598","constraints":["arrow","disjoint-groups"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"5yfegmxam3","ctcId":1660,"ctcDifficulty":"MEDIUM","title":"Modular Zipper","author":"gdc","rules":"Normal Sudoku rules apply.\nAny set of three sequential cells along a teal modular line contains one digit from (1,4,7), (2,5,8), and (3,6,9). \nDigits an equal distance from the center of a lavender 'Zipper Line' sum to the digit in the middle of that line.","solution":"489372156251689734376514829762943518534861297918725463193458672645237981827196345","constraints":["modular-line","zipper-line"],"constraintFacts":[{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"jq8DH93ND3","ctcId":1661,"ctcDifficulty":"MEDIUM","title":"Taco Sudoku","author":"DiMono","rules":"Normal sudoku rules apply.\n\nTaco rules apply: A 2-digit Taco clue XY outside the grid gives the sum of X + Y + the digits between X and Y in the indicated row or column.\n\nExample: A valid taco sum for 18 could be 8361","solution":"794236185382157946651948372813694257476521893925873461147385629569412738238769514","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Taco rules apply: A 2-digit Taco clue XY outside the grid gives the sum of X + Y + the digits between X and Y in the indicated row or column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"crqk2uytmu","ctcId":1662,"ctcDifficulty":"HARD","title":"Bridging The Mines","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nDigits joined by a white dot are consecutive. Digits joined by a black dot are in a 1:2 ratio. Not all dots are given.\n\nFor each line, one attached circle contains an odd digit and the other circle contains an even digit. The odd digit indicates the number of odd digits along the line (not including itself), and the even digit indicates the number of even digits along the line (not including itself).\n\nShade some cells such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected. No 2x2 area may be fully shaded or fully unshaded.\n\nThe circles act as 'minesweeper' clues. Circles are always unshaded, and their value is the number of shaded cells in the surrounding 3x3 area (i.e. the up to eight cells that touch the circle either orthogonally or diagonally).","solution":"251387946647592183839461527986753412425916378713248659392175864564829731178634295","constraints":["custom","kropki","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For each line, one attached circle contains an odd digit and the other circle contains an even digit. The circles act as 'minesweeper' clues.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"814oz1tj0e","ctcId":1663,"ctcDifficulty":"MEDIUM","title":"Zip of the Iceberg","author":"gdc","rules":"Normal Sudoku rules apply.\nThe grid is covered in fog. Placing correct digits reveals clues in the surrounding 3 by 3 area.\nRotational Symmetry: If the grid is rotated 180 degrees, the matching cells add up to 10 e.g. R3C2+R7C8=10.\nDigits an equal distance from the center of a lavender 'Zipper Line' sum to the digit in the middle of that line.\nAdjacent digits on a green line differ by 5 or more.\nAll lines are exactly 5 cells long, only move orthogonally and don't share cells with other lines.","solution":"149236758376584291582917346691742583834159672725863914467391825918625437253478169","fogLight":"R0C0","constraints":["custom","fog","german-whispers","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Rotational Symmetry: If the grid is rotated 180 degrees, the matching cells add up to 10 e.g. R3C2+R7C8=10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"5tw5gusn3p","ctcId":1664,"ctcDifficulty":"MEDIUM","title":"The Big Zipper","author":"Marty Sears","rules":"Normal sudoku rules apply.\nAlong a lavender zipper line, any pair of digits that are the same distance from the centre cell of the line (marked by a spot) sum to the digit in that centre cell.","solution":"921836574643759821758124963874965132539271648216483795387612459192547386465398217","constraints":["zipper-line"],"constraintFacts":[{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jB7njtNrM6","ctcId":1665,"ctcDifficulty":"HARD","title":"Corner Prison","author":"Dorlir","rules":"Normal sudoku rules apply. Digits in a cage don't repeat and sum to the given clue in the top left corner of the cage (the clue is always given and must be located in the leftmost cell of the uppermost row of the cage.) Digits separated by a white dot are consecutive digits. Additionally the grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells, possibly revealing more clues.","solution":"683459271571326489492718653869534712234187596715692834948271365327965148156843927","fogLight":"R1C1,R2C1,R3C1,R1C4","constraints":["cage","fog","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"rPgh724D6H","ctcId":1666,"ctcDifficulty":"MEDIUM","title":"Castle Keep","author":"ZegreS","rules":"Normal sudoku rules apply. Along a blue line, each line segment within a different 3x3 box must sum to the same total. Blue lines may have different totals to one another. The digit in the grey square is even. Cells separated by a white dot must contain consecutive digits.","solution":"469371852815629437723584619352798164674152398981463275296815743547236981138947526","constraints":["even","kropki","region-sum-line"],"constraintFacts":[{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"3hQ4Dmd6q4","ctcId":1667,"ctcDifficulty":"MEDIUM","title":"Trouble","author":"Oddlyeven","rules":"Normal sudoku rules apply. One cell in every row, column and box is a doubler. This cell counts as double its value on the lines. Each of the digits 1 to 9 appears exactly once in a doubler cell. One cell in every row, column and box is a tripler. This cell counts as triple its value on the lines. Each of the digits 1 to 9 appears exactly once in a tripler cell. Doublers and triplers do not share cells and no doubler or tripler cell is within a king's move of any other doubler or tripler cell. Lines are Region Sum Lines: the values of the digits on each line segment within a different 3x3 box must sum to the same total (say a total of X). If a line passes through a box more than once, each line segment in that box must sum to X separately. Each blue lines may have a different value for X. Eg [the values of]  r8c1+r9c2+r9c3 = r8c4+r7c4 = r6c4+r6c5+r6c6 = r6c7+r5c7 = r5c6","solution":"941257836635184297782936451128369745379845162456721983567418329294673518813592674","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"One cell in every row, column and box is a doubler. Each of the digits 1 to 9 appears exactly once in a doubler cell. One cell in every row, column and box is a tripler. Each of the digits 1 to 9 appears exactly once in a tripler cell. Doublers and triplers do not share cells and no doubler or tripler cell is within a king's move of any other doubler or tripler cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c5","c7","c8"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Lines are Region Sum Lines: the values of the digits on each line segment within a different 3x3 box must sum to the same total (say a total of X).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]}]},{"id":"7ugarx7gji","ctcId":1668,"ctcDifficulty":"EASY","title":"Incomplete Squares","author":"gdc","rules":"Normal sudoku rules apply.\nDigits an equal distance from the center of a lavender 'Zipper Line' must sum to the digit in the middle of that line.","rulesClarified":"Normal sudoku rules apply.\n\nEach lavender line is a zipper line. Every zipper line has an odd number of cells, so it has a single middle cell.\n\nPair the other cells of the line by equal distance from the middle: each pair is two cells the same distance from the middle, one on each side.\n\nEach pair's two digits sum to the digit in the middle cell of that line. The middle digit is not part of any pair.","solution":"329764518547182396168359742695213487473598621281647935734825169856931274912476853","constraints":["zipper-line"],"constraintFacts":[{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"vw1q7megqm","ctcId":1670,"ctcDifficulty":"MEDIUM","title":"The Slowest Snake","author":"Dorlir","rules":"Normal sudoku rules apply. Draw a snake which starts at a grey circle and ends at the other grey circle, and never passes through a grey square. The snake moves orthogonally and/or diagonally and can cross itself and acts as a slow thermometer i.e. reading from one end to the other, digits on the snake increase or stay the same (the direction must be determined by the solver). Furthermore, the snake passes through at least 27 cells. The sum of the digits within a cage must sum to the small clue in the top-left corner of that cage.","solution":"349218576726593184185647329952461738834759261617382945471825693298136457563974812","constraints":["cage","custom","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a snake which starts at a grey circle and ends at the other grey circle, and never passes through a grey square.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"atbh8bj6bp","ctcId":1671,"ctcDifficulty":"HARD","title":"Spot the Difference","author":"Marty Sears","rules":"• Normal sudoku rules apply.\n• Connect each pair of matching coloured spots with a snake. Snakes may only move orthogonally through the grid, not diagonally. They may touch each other (and themselves), but cannot share cells.\n• Each pair of adjacent digits along a snake has the same difference, but this 'difference value' may be different for different snakes.\n• A grey square contains an even digit.\n• A black dot connects two digits with a 1:2 ratio (one is double the other.)","solution":"432169785517284369689753142765891423894372651123546897351428976978635214246917538","constraints":["custom","even","kropki","same-difference-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Connect each pair of matching coloured spots with a snake. Snakes may only move orthogonally through the grid, not diagonally. They may touch each other (and themselves), but cannot share cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"77hB996Dn8","ctcId":1672,"ctcDifficulty":"VERY HARD","title":"Sumthing","author":"ThePedallingPianist","rules":"Normal sudoku rules apply. If the digits at each end of a line are X and Y, then the first X digits on the line starting from X must sum to the same total as the first Y digits on the line starting from Y. (X and Y need not necessarily be different numbers; X and Y may not exceed the number of cells on the line).","solution":"216548973794613285583279641165482397348796512972135468429851736631927854857364129","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If the digits at each end of a line are X and Y, then the first X digits on the line starting from X must sum to the same total as the first Y digits on the line starting from Y. (X and Y need not necessarily be different numbers; X and Y may not exceed the number of cells on the line).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"omtjde4f3k","ctcId":1675,"ctcDifficulty":"MEDIUM","title":"Tannenbaumino","author":"Cris Moore","rules":"Gather around the tree! Divide it into pentominoes, i.e. 5-cell cages. No two pentominoes have the same shape even when rotated or reflected. Digits may not repeat in a pentomino.\n\nThe tree has ornaments (dots) of several colors. If a pentomino contains a green dot, it is a Germanimo: adjacent pairs of digits inside it differ by at least 5. If it contains a red dot, it is a Renbanimo: it contains 5 consecutive digits.\n\nBlack, white, and silver dots show a boundary between two pentominoes. Black means their totals are in a 1:2 ratio. White means their totals differ by one. Silver means their totals are equal.\n\nDigits increase along a candle (i.e. a thermometer).","solution":"736582149459617328182394567273148695814956732965273814647839251528461973391725486","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide it into pentominoes, i.e. 5-cell cages. If a pentomino contains a green dot, it is a Germanimo: adjacent pairs of digits inside it differ by at least 5. If it contains a red dot, it is a Renbanimo: it contains 5 consecutive digits. Black means their totals are in a 1:2 ratio. White means their totals differ by one. Silver means their totals are equal.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6","c7","c9","c10","c11"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c12"]}]},{"id":"GM9HHd6Pqh","ctcId":1676,"ctcDifficulty":"HARD","title":"Poly","author":"Jay Dyer","rules":"Normal sudoku rules apply. Along a line, the sum of digits on the line is the same in each region the line passes through. The sum may be different for different lines.","solution":"724315896391286574568947132436872915152693487879154263683421759947538621215769348","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"BbRDTfQDJh","ctcId":1677,"ctcDifficulty":"EASY","title":"9M","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Adjacent digits on a grey line must sum to 7, 8 or 9.","solution":"347261895928375416165948273813459627476832951592716348781694532259183764634527189","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent digits on a grey line must sum to 7, 8 or 9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"Bqqp8Fr3PH","ctcId":1679,"ctcDifficulty":"MEDIUM","title":"Kalimba","author":"Aron Lidé (Aspartagcus)","rules":"Normal sudoku rules apply. Reading from the bulb end to the tip, digits along a thermometer must either increase or stay the same.","solution":"642581739185937264379462581794625813236148975851379642513796428427853196968214357","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"JG3BQrB63T","ctcId":1683,"ctcDifficulty":"HARD","title":"Triple Threat","author":"James Kopp","rules":"Normal sudoku rules apply. Numbers outside the grid are little killer clues, look-and-say little killer clues and sandwich clues: Digits along diagonals indicated by arrows sum to the number given. Also, the first digit in a clue indicates the number of times the second digit in the clue appears along the indicated diagonal. Also, a clue outside the grid shows the sum of the digits sandwiched between the 1 and the 9 in that row/column. Cells separated by a V sum to 5.","solution":"235178694749623158618594273897431562324965817561287349173859426482716935956342781","constraints":["XV","custom","little-killer","sandwich"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Also, the first digit in a clue indicates the number of times the second digit in the clue appears along the indicated diagonal.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"ori9jgdrak","ctcId":1686,"ctcDifficulty":"MEDIUM","title":"Tulpenblüte","author":"Myxo","rules":"Sudoku: Place the digits 1-9 exactly once in each row, column and box.\n\nRenban: Digits along a thick magenta line form a consecutive sequence without repeats, in any order.\n\nGerman Whisper: Digits connected by a thin green line must differ by at least 5.","solution":"678921354524378196913546782849632571735194628261857943187265439496783215352419867","constraints":["german-whispers","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"mpphgLMpfg","ctcId":1688,"ctcDifficulty":"MEDIUM","title":"Push Me Pull You","author":"Die Hard","rules":"Normal sudoku rules apply. Digits in cages must sum to the small clue in the top left corner of the cage. Digits on arrows must sum to the digit in that arrow's circle. Digits on grey palindrome lines must read the same in both directions. (Arrows are different colours purely to clarify which arrow is which when they cross.)","solution":"753912684892746135614538729379254861165873942248691573927385416531467298486129357","constraints":["arrow","cage","palindrome"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"Tt9Mt697pd","ctcId":1689,"ctcDifficulty":"VERY HARD","title":"Clowns and Jokers","author":"Die Hard","rules":"Normal sudoku rules apply. Digits in cages must sum to the cage total. The digit on the circle is odd. Digits on a purple line form a consecutive set in any order. Digits on purple lines can also be used to index the cell's column number in its row. For example, if R3C1 was a 7, then 1 would have to be positioned in R3C7.","solution":"732958164158624739694731852549816273867392415213547698475189326926473581381265947","constraints":["cage","custom","odd","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits on purple lines can also be used to index the cell's column number in its row.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"DN7P93mMt9","ctcId":1690,"ctcDifficulty":"MEDIUM","title":"Ninja Turtle","author":"Die Hard","rules":"Each row, column, and nine cell region must contain the digits 1 to 9, once each. Digits along an arrow must sum to the digit in that arrow's circle.","solution":"937428615412735869685391247194862573278546931763159482541287396856973124329614758","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"L8HrDHNbHL","ctcId":1691,"ctcDifficulty":"HARD","title":"Foggy Knight","author":"Die Hard","rules":"Normal sudoku rules apply. The grid is covered by fog and correctly placing digits may reveal additional digits. Each digit satisfies only one of the following conditions: \n\na) It is exactly one chess knight's move away from at least one cell containing the same digit. \nb) It is in its own 3x3 box (3x3 boxes are arranged in normal reading order. So eg 9 in box 9 meets this condition).\nc) It is the digit 5. \n\nThere is one exception: the digit in the very centre of the grid satisfies exactly two conditions. \n\nNo guessing is required or allowed.","rulesClarified":"Normal sudoku rules apply. The grid is covered by fog. Correctly placed digits may reveal additional digits. No guessing is required or allowed.\n\nEvery digit satisfies exactly one of these three conditions:\n\na) It is exactly one chess knight's move away from at least one cell containing the same digit.\n\nb) It is in its own 3x3 box. The 3x3 boxes are numbered in normal reading order, so a 9 in box 9 meets this condition.\n\nc) It is the digit 5.\n\nThe digit in the very centre of the grid is the exception: it satisfies exactly two of the three conditions.","solution":"174925863238746591659318742326874915487159326591632487863297154915463278742581639","fogLight":"","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each digit satisfies only one of the following conditions:","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ifd8mehebc","ctcId":1692,"ctcDifficulty":"HARD","title":"Ménage à Trois","author":"Die Hard","rules":"Normal sudoku rules apply. Digits must not repeat on the marked diagonal. Digits in cages must sum to the cage total. Each N-sum line can be divided into two or more non-overlapping groups of adjacent digits that sum to N. No two lines have the same value for N.","solution":"375912684826534791941876235719485362234761958658329147497153826582697413163248579","constraints":["cage","custom","diagonal"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each N-sum line can be divided into two or more non-overlapping groups of adjacent digits that sum to N. No two lines have the same value for N.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"t6Rd7d8JD7","ctcId":1693,"ctcDifficulty":"MEDIUM","title":"2023","author":"Die Hard","rules":"Normal sudoku rules apply. Digits in cages cannot repeat and must sum to the small clue in the top left corner of the cage. Digits an equal distance from the centre of a blue zipper line must sum to the same total. For odd length lines, the total is the digit in the centre of the line. The grey line is a palindrome and must read the same forwards and backwards. A digit on any line also indicates how many times that digit appears on all lines in the puzzle.","solution":"427169853653847129891235746385716294164592378972384561719653482548921637236478915","constraints":["cage","custom","palindrome","zipper-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit on any line also indicates how many times that digit appears on all lines in the puzzle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"ft3J69J2hG","ctcId":1699,"ctcDifficulty":"MEDIUM","title":"The Tilted Crown","author":"fritzdis","rules":"Normal sudoku rules apply.\n\nMinimal between lines:\nDigits on a line must be between the digits in the connected circles.  The difference between the circled digits must be as small as allowed by normal sudoku rules.  For example, a circle in R1C2 connected with a straight line to a circle in R5C6 would have a difference of 2 because it is possible (and necessary) to repeat the same digit in all 3 spots along the line.\n\nClones:\nThe grey 4x4 regions must contain the same digits in the same arrangement.\n\nSkyscrapers:\nEach digit N in the grid represents a building of height N.  Numbers outside the grid indicate how many buildings can be seen from that direction in the row, with taller buildings blocking shorter buildings from being seen.","solution":"415762389376918452298453167159346728723891645684527913831675294967284531542139876","constraints":["between-line","clone","custom","skyscraper"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The difference between the circled digits must be as small as allowed by normal sudoku rules.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"skyscraper","type":"skyscraper","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"FBFJ4jMdQd","ctcId":1705,"ctcDifficulty":"MEDIUM","title":"Pincer","author":"kuraban","rules":"Normal sudoku rules apply. Along thermometers, digits must increase from the bulb end. Digits along an arrow must sum to the digit in that arrow's circle. The purple line contains a set of consecutive digits. Digits may not repeat along the marked diagonal.","solution":"781654329259783614463291875195478236832569147674312598548127963316945782927836451","constraints":["arrow","diagonal","renban","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hrQdLRJG82","ctcId":1706,"ctcDifficulty":"HARD","title":"Extragalactic","author":"ZegreS","rules":"Normal sudoku rules apply. The middle dot is the centre of the “galaxy”. The galaxy is 180° rotationally symmetric and orthogonally connected. Digits in cages that are not part of the galaxy sum to the given total (in the cage’s top left corner).","solution":"825641973976835241314279586162358497459712638783964125631427859297586314548193762","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in cages that are not part of the galaxy sum to the given total (in the cage’s top left corner).","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The middle dot is the centre of the “galaxy”.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"iql7m9a36u","ctcId":1707,"ctcDifficulty":"HARD","title":"Zip Zero","author":"gdc","rules":"Normal Sudoku rules apply. The grid is covered in fog. Placing correct digits lifts it. Values of cells with an equal distance to the circled center of a zipper line sum to the value of the center. Shade some cells orange such that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected and no 2x2 area is fully shaded or fully unshaded. The value of a shaded cell is its digit. The value of an unshaded cell is zero minus its digit (a negative number).","solution":"865931472273458169149762583526819734738645291914273658391527846652384917487196325","fogLight":"R8C7,R8C8,R8C9,R9C7,R9C8,R9C9","constraints":["fog","yin-yang","zipper-line"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"2sly4fnrqh","ctcId":1708,"ctcDifficulty":"MEDIUM","title":"Exclusivity","author":"zetamath","rules":"Normal sudoku rules apply. Additionally, no digit may appear more than once on a particular clue type. Type 1: Digits on a purple line form a set of non-repeating, consecutive digits in any order. Type 2: Along green lines, adjacent digits must differ by at least 5. Type 3: Digits separated by a black dot have a 1:2 ratio, meaning one is exactly double the other. Type 4: Digits along a grey thermometer must increase from the bulb end. Type 5: Digits along an arrow sum to the digit in that arrow's circle.","solution":"591728364746193528382654791938246175415987632627315489179432856864579213253861947","constraints":["arrow","custom","german-whispers","kropki","renban","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Additionally, no digit may appear more than once on a particular clue type.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"i9wx9vdy41","ctcId":1710,"ctcDifficulty":"HARD","title":"Onion","author":"the_cogito","rules":"- Normal sudoku rules apply.\n- A digit in a circled cell indicates the total number of times that digit appears in circled cells in the grid.\n- Lines connecting circled cells are between lines. Digits on a between line must be strictly between the digits on that line's circled endpoints.","solution":"327614589814957623659238147243176895961825374578349216432761958796582431185493762","constraints":["between-line","custom"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- A digit in a circled cell indicates the total number of times that digit appears in circled cells in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"pR4gN2n7pT","ctcId":1727,"ctcDifficulty":"MEDIUM","title":"Pigeonhole","author":"Miky","rules":"Normal sudoku rules apply. Each purple line contains a consecutive set of non-repeating digits in any order. Cells separated by a black dot contain digits with a 1:2 ratio (ie one digit must be double the other). Cells separated by a white dot must contain consecutive digits. Not all dots are given.","solution":"672348951358291467491657238139786542724519386586423719847132695213965874965874123","constraints":["kropki","renban"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"493Jt84qfp","ctcId":1728,"ctcDifficulty":"HARD","title":"Mean World Syndrome","author":"Miky","rules":"Normal sudoku rules apply. Circled digits must be the mean (average) of any arrows that leave the circle. Cells separated by a black dot contain digits with a 1:2 ratio (ie one digit is double the other). Cells separated by a white dot must contain consecutive digits. Not all possible dots are given.","solution":"253479861194268357687315924861593472435127698729846135578931246946782513312654789","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Circled digits must be the mean (average) of any arrows that leave the circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"sj0yv59u4t","ctcId":1729,"ctcDifficulty":"HARD","title":"Leehwnip","author":"Miky","rules":"Rules:\n1) Normal Sudoku Rules: each row, column, and box contain the digits from 1 through 9 with no repeats.\n2) Nabner Rules: golden lines form sets of non-repeating digits where no digits can be consecutive\n3) Odd/Even Rules: the grey circles are odd and the grey squares are even","solution":"512639847749582163368147295957468321681325974234971658425816739896753412173294586","constraints":["even","nabner-line","odd"],"constraintFacts":[{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"jMg44R2tpb","ctcId":1732,"ctcDifficulty":"VERY HARD","title":"Broken Secrets","author":"TotallyNormalCat","rules":"When Simon was young, he used to hide his secrets in 9 cell cages. On his 45th birthday he decided to revisit his childhood toys and found out the cages broke! Help him put them together to reveal the secrets of the universe! Any resemblance to actual persons, living or dead, or actual events is purely intentional. Normal sudoku rules apply. There are 18 cages in the grid. Digits cannot repeat within a cage. Each cage has exactly one partner such that, when combined together, they would form a valid 9-cell cage (ie containing no repeated digits). Along a thermometer, digits must increase from the bulb end. Cells with grey squares must contain even digits.","solution":"186937245932541867457682391673219458819475632524863719265794183741358926398126574","constraints":["cage","custom","even","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each cage has exactly one partner such that, when combined together, they would form a valid 9-cell cage (ie containing no repeated digits).","evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"or128b1uu1","ctcId":1733,"ctcDifficulty":"HARD","title":"Intersections","author":"James Kopp","rules":"Normal sudoku rules apply. \nNumbers increase from the bulb to the end of the thermometers.\nThe blue line is an equal sum line. All digits along the line must sum to the same number in each 3x3 box the line visits.\nThe green line is a German Whispers line. Adjacent digits along the green line have a difference of at least five.\nCells separated by an X sum to 10. Not all Xs are given.","solution":"295618743861347295734259618357486921648192357129573864473961582586724139912835476","constraints":["XV","german-whispers","region-sum-line","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"p6s6me7gcf","ctcId":1735,"ctcDifficulty":"HARD","title":"Grist for the Gossip Mill","author":"FullDeck and Missing a Few Cards","rules":"- Normal Sudoku rules apply.\n\n- On green German Whisper Lines adjacent digits must have a difference of at least 5.\n\n- Digits placed on an arrow must sum to the digit placed in that arrow's circle.","solution":"716493528593827461284561739859234176361975842427186395632718954175649283948352617","constraints":["arrow","german-whispers"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6GhDq9bDFL","ctcId":1737,"ctcDifficulty":"VERY HARD","title":"Arvada","author":"Philipp Blume, aka glum_hippo","rules":"Normal sudoku rules apply. Cells separated by an X contain digits summing to 10. 'Beachcomber' rules apply ie A digit N in a circle means that a total of N digits smaller than N are visible in all orthogonal directions from the circle (ie looking North, South, East & West). Digits larger than N block the view.","solution":"145983267638752194279641385581237946496518732327496518953874621764129853812365479","constraints":["XV","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"'Beachcomber' rules apply ie A digit N in a circle means that a total of N digits smaller than N are visible in all orthogonal directions from the circle (ie looking North, South, East & West).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"g93fPBLdtJ","ctcId":1738,"ctcDifficulty":"MEDIUM","title":"Australia Day 2024","author":"WombatBreath","rules":"Digits do not repeat in any row, column or marked diagonal. Each orange line in the grid serves three purposes: it is a palindrome (digits on it must read the same in both directions, e.g 94349); it is also a thermometer (pair) with its bulb in the centre of the line; and it is also a pair of arrows that meet in the centre with circles at the ends. The shared arrow digit is in the thermometer bulb and digits on thermometers must strictly increase from the bulb. A white dot between cells indicates that their digits are consecutive - not all dots are shown.","solution":"259476831168534279437285916943128657815947362672359148386712594721693485594861723","constraints":["arrow","diagonal","kropki","palindrome","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Each orange line in the grid serves three purposes: it is a palindrome (digits on it must read the same in both directions, e.g 94349); it is also a thermometer (pair) with its bulb in the centre of the line; and it is also a pair of arrows that meet in the centre with circles at the ends.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Each orange line in the grid serves three purposes: it is a palindrome (digits on it must read the same in both directions, e.g 94349); it is also a thermometer (pair) with its bulb in the centre of the line; and it is also a pair of arrows that meet in the centre with circles at the ends.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"m7fj6dp5si","ctcId":1739,"ctcDifficulty":"HARD","title":"Overflow","author":"IcyFruit","rules":"Normal sudoku rules apply. Digits may not repeat within a cage. Cage clues show the sum of the digits in the cage plus the sum of all digits that aren't in any cage. (For example, if the digits 1, 2, and 3 are always placed outside of cages, and all other digits appear in a cage at least once, then all cages have 6 (=1+2+3) added to their total.) A '>' between two cells points to the smaller digit.","solution":"982156734675439812143278569396785421524961387817342956461593278259817643738624195","constraints":["cage","inequality"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Cage clues show the sum of the digits in the cage plus the sum of all digits that aren't in any cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"fGbtDGPpTN","ctcId":1740,"ctcDifficulty":"VERY HARD","title":"String Quartet","author":"IcyFruit","rules":"Normal sudoku rules apply. Divide the grid into 4 sections of orthogonally-connected cells such that each section shares an edge with every other section and no 2x2 area is occupied by only one section. Cells on the same line belong to the same section. Each section has a different constraint, which ALL of its lines must obey. The constraints for each section are: i) RENBAN: Digits on a line do not repeat and form a consecutive set, in any order; ii) PALINDROME: The digits along a line read the same forwards and backwards; iii) GERMAN WHISPER: Adjacent digits on a line must have a difference of at least 5; iv) REGION SUM: Along a line, if it crosses a 3x3 box border, each line segment within a different 3x3 box must sum to the same total. The sum may be different for different lines.","solution":"396248571184753926527916843942375618718629354635184792859461237261537489473892165","constraints":["custom","german-whispers","palindrome","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into 4 sections of orthogonally-connected cells such that each section shares an edge with every other section and no 2x2 area is occupied by only one section.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"The constraints for each section are: i) RENBAN: Digits on a line do not repeat and form a consecutive set, in any order; ii) PALINDROME: The digits along a line read the same forwards and backwards; iii) GERMAN WHISPER: Adjacent digits on a line must have a difference of at least 5; iv) REGION SUM: Along a line, if it crosses a 3x3 box border, each line segment within a different 3x3 box must sum to the same total.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"palindrome","type":"palindrome","variant":"modified","modifiers":[],"params":null,"note":"The constraints for each section are: i) RENBAN: Digits on a line do not repeat and form a consecutive set, in any order; ii) PALINDROME: The digits along a line read the same forwards and backwards; iii) GERMAN WHISPER: Adjacent digits on a line must have a difference of at least 5; iv) REGION SUM: Along a line, if it crosses a 3x3 box border, each line segment within a different 3x3 box must sum to the same total.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"The constraints for each section are: i) RENBAN: Digits on a line do not repeat and form a consecutive set, in any order; ii) PALINDROME: The digits along a line read the same forwards and backwards; iii) GERMAN WHISPER: Adjacent digits on a line must have a difference of at least 5; iv) REGION SUM: Along a line, if it crosses a 3x3 box border, each line segment within a different 3x3 box must sum to the same total.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"The constraints for each section are: i) RENBAN: Digits on a line do not repeat and form a consecutive set, in any order; ii) PALINDROME: The digits along a line read the same forwards and backwards; iii) GERMAN WHISPER: Adjacent digits on a line must have a difference of at least 5; iv) REGION SUM: Along a line, if it crosses a 3x3 box border, each line segment within a different 3x3 box must sum to the same total.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"7mse59d0ww","ctcId":1741,"ctcDifficulty":"HARD","title":"Sigma Pi","author":"IcyFruit","rules":"Normal sudoku rules apply. Digits around an X sum to 10. Multiplying the digits on each end of a brown line gives the sum of all digits on that line. For example, a line could have the digits 3-5-4, because 3x4 = 3+5+4.","solution":"965283741832417956417695283579132468623854179184976532756321894248769315391548627","constraints":["XV","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Multiplying the digits on each end of a brown line gives the sum of all digits on that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"laj1tzweyh","ctcId":1742,"ctcDifficulty":"VERY HARD","title":"The 12 Regions Of Christmas","author":"IcyFruit","rules":"Normal sudoku rules apply.  Draw 12 orthogonally connected regions of different sizes which do not overlap. The regions do not need to cover the entire grid.\nWithin a region, a digit may only repeat if it appears on a gold ring, in which case it can only appear on gold rings. A digit on a gold ring indicates the number of gold rings within its region. \nA digit on a pear tree is equal to the number of cells in its region.\nThe 3 digits on red baubles sum to 25.","solution":"295381674467295183138476259973124568612853947854769312781532496526947831349618725","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw 12 orthogonally connected regions of different sizes which do not overlap. Within a region, a digit may only repeat if it appears on a gold ring, in which case it can only appear on gold rings. A digit on a gold ring indicates the number of gold rings within its region. A digit on a pear tree is equal to the number of cells in its region. The 3 digits on red baubles sum to 25.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c5","c6","c7"]}]},{"id":"iqv3bub9ae","ctcId":1743,"ctcDifficulty":"MEDIUM","title":"Icon","author":"IcyFruit","rules":"Normal sudoku rules apply. \nDivide the grid into rectangular regions which do not overlap. Each region must include exactly two circled cells, and the digits in those cells indicate the width and height of that region (in either order). \nDigits on a line must have a value between the digits in the two attached circles.","solution":"625719483943685721178432695759823146862541937314967258481256379537194862296378514","constraints":["between-line","custom"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"modified","modifiers":[],"params":null,"note":"Digits on a line must have a value between the digits in the two attached circles.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each region must include exactly two circled cells, and the digits in those cells indicate the width and height of that region (in either order).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"mNj477fmL9","ctcId":1749,"ctcDifficulty":"HARD","title":"Subzero2","author":"Pacattack25 & Schwupel","rules":"Normal sudoku rules apply. Each cell in the grid has to be marked either hot or cold such that i) all hot cells form a single orthononally connected region; ii) all cold cells form a single orthogonally connected region; and iii) no 2x2 area is entirely hot or cold. Values on a thermometer must be increasing from the bulb to the tip. Cold cells on a thermometer are considered to be negative values.","rulesClarified":"Normal sudoku rules apply.\n\nEvery cell is either hot or cold. Mark each cell of the grid as one or the other, so that:\n- all hot cells form a single orthogonally connected region;\n- all cold cells form a single orthogonally connected region;\n- no 2x2 area is entirely hot, and no 2x2 area is entirely cold.\n\nThermometers: the digits on a thermometer increase from its bulb to its tip. The bulb is the circled end of the thermometer.\n\nOn a thermometer, a cold cell is a negative value: a cold cell showing digit d counts as -d. A hot cell keeps its digit. The increase from bulb to tip is measured on these values.","solution":"579163428641829375823547961734912586215386749986475213367298154198754632452631897","constraints":["custom","thermometer","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cold cells on a thermometer are considered to be negative values.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Values on a thermometer must be increasing from the bulb to the tip.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"gmgD4L8pF4","ctcId":1750,"ctcDifficulty":"VERY HARD","title":"Low Tide","author":"Schwupel","rules":"Normal sudoku rules apply. Adjacent digits on a green line differ by at least 5. Cages must contain an equal number of low (1,2,3,4) and high (6,7,8,9) digits AND an equal number of even (2,4,6,8) and odd (1,3,7,9) digits. Digits CAN repeat in cages, but they cannot contain 5.","solution":"495123867217689543368745219526314978731896452849257631154972386983461725672538194","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cages must contain an equal number of low (1,2,3,4) and high (6,7,8,9) digits AND an equal number of even (2,4,6,8) and odd (1,3,7,9) digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"rM7bbtdT6r","ctcId":1757,"ctcDifficulty":"MEDIUM","title":"Seven Arrows","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. In this puzzle, all circles must contain different digits.","solution":"637482951154639782982517346476325819391874265528196437763958124849261573215743698","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In this puzzle, all circles must contain different digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"fR6qnrR7Rb","ctcId":1762,"ctcDifficulty":"HARD","title":"Poison Pill Killer","author":"Jeff Wajes","rules":"Normal Sudoku rules apply. Digits in a cage must sum to the given total. Except...\n\nOne of the digits, 1-9, is poison. If a cage contains the poisoned digit, then digits in the cage must NOT sum to the given total. Digits in a cage may not repeat, regardless of poison.","solution":"394785216578162493162493758816279534457631982239548167943817625621354879785926341","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a cage must sum to the given total.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If a cage contains the poisoned digit, then digits in the cage must NOT sum to the given total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"36fdw51b62","ctcId":1763,"ctcDifficulty":"HARD","title":"Circles and Sets","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nIn each cage, digits do not repeat and sum to the given total.\n\nA digit in a circle indicates how many times that digit appears in circles.","rulesClarified":"Normal Sudoku rules apply.\n\nCages: in each outlined cage the digits do not repeat, and they sum to the total shown in that cage.\n\nCircles: some cells are circled. A digit written in a circled cell says how many circled cells in the whole grid contain that digit. The circled cell itself counts toward that total.\n\nFor example, a circled 2 means exactly two circled cells in the grid contain the digit 2, including its own cell.","solution":"721543986864129537593687421958462713642731895137958642216874359479315268385296174","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle indicates how many times that digit appears in circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"rjkytrn10q","ctcId":1775,"ctcDifficulty":"MEDIUM","title":"Barely a Whisper","author":"Eclectic Hoosier & Riffclown","rules":"Normal sudoku rules apply. Orthogonally adjacent digits may not be consecutive. Adjacent digits along a green line must differ by at least 5. A clue outside the grid gives the sum of the indicated diagonal.","solution":"572938164836471592419625837164297385728513649953846271295364718647182953381759426","constraints":["german-whispers","little-killer","non-consecutive"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9onywsf67u","ctcId":1776,"ctcDifficulty":"VERY HARD","title":"Catch the Zippersnake","author":"Marty Sears and Dorlir","rules":"• Normal sudoku rules apply.\n• Draw a snake that starts and ends at a purple spot and has a purple spot exactly at its centre. The snake can only move orthogonally from cell to cell, and may not touch itself, not even diagonally.\n• The snake functions as a zipper line; any pair of digits that are an equal distance from the central spot sum to the digit on that central spot.\n• Any pair of cells connected by a clue (dot, diamond, X or V) must either both be on the snake, or both be off the snake.\n• Cells connected by a white dot are consecutive.\n• Cells connected by black dot are in a 1:2 ratio (one is double the other.)\n• Cells connected by a green dot must have a difference of at least 5.\n• Cells connected by red diamond have the same parity (they're both odd or both even.)\n• Cells connected by an X sum to 10.\n• Cells connected by a V sum to 5.","solution":"395641782246978315178235694819427563457386129623519847731892456582764931964153278","constraints":["XV","custom","kropki","zipper-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Any pair of cells connected by a clue (dot, diamond, X or V) must either both be on the snake, or both be off the snake.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"• Cells connected by a green dot must have a difference of at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5","c6","c7","c8"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"xvflagdkmy","ctcId":1777,"ctcDifficulty":"MEDIUM","title":"All the Dots are Brown","author":"gdc","rules":"...and the Fog is Grey...\n\nNormal Sudoku rules apply.\nThe grid is covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area.\nDigits separated by a brown dot are either consecutive or in a 1:2 ratio. Not all dots are necessarily given.","solution":"478563912165429783932817546541936827789245631326781459653198274894372165217654398","fogLight":"R5C5","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits separated by a brown dot are either consecutive or in a 1:2 ratio.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"smwplnh6vb","ctcId":1778,"ctcDifficulty":"MEDIUM","title":"Glyph","author":"FullDeck and Missing a Few Cards","rules":"- Normal sudoku rules apply.\n- Renban Lines: Digits on pink Renban Lines contain a set of consecutive digits in some order.\n- Entropic Lines: Every set of three adjacent digits along a peach Entropic Line contains one low digit (123), one middle digit (456), and one high digit (789).","solution":"893124567612537489754968231281796345439852176567413928978241653126375894345689712","constraints":["entropic-line","renban"],"constraintFacts":[{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ng69xsjco3","ctcId":1779,"ctcDifficulty":"MEDIUM","title":"Seventeen","author":"Blobz","rules":"Normal sudoku rules apply. Digits in cages sum to the small clue in the top left corner. Digits do not repeat in cages. Digits separated by a white dot differ by one (not all such dots are shown).","solution":"478625391695731248312948576286197435153482967947356812564873129831269754729514683","constraints":["cage","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"gjyydhf4pm","ctcId":1780,"ctcDifficulty":"MEDIUM","title":"YNWA - Jurgen Klopp Tribute","author":"Celery","rules":"-- As a Liverpool fan, the news that Klopp was leaving the club left me broken. I, and many others, are immensely grateful for what he achieved and how he revolutionised the club. This is a puzzle as a tribute to Jurgen Klopp. You'll Never Walk Alone. --\n\nNormal sudoku rules apply.\n\nThe 3x3 grey squares are additional regions of the puzzle whereby digits cannot repeat within a grey square. \n\nThe YNWA lines (in boxes 2,4,6, and 8) are GERMAN whisper lines whereby adjacent digits upon the line must differ by at least 5. \n\nA digit in a football (white circle) indicates how many footballs contain that digit.","solution":"271846539369215874584379216957183462132654987648792351426537198713928645895461723","constraints":["counting-circle","german-whispers","region"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"DtnH4LnTPM","ctcId":1781,"ctcDifficulty":"HARD","title":"Where Is The 8th?","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. Cells separated by a single knight's move (in chess) cannot contain the same digit.","solution":"978123546146895327523647189257361894461958273389274651892736415614589732735412968","constraints":["antiknight","arrow"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"mfGtTnRHt7","ctcId":1783,"ctcDifficulty":"VERY HARD","title":"Mount Elbrus","author":"Qodec","rules":"Normal sudoku rules apply. Digits in a cage cannot repeat and must sum to the small clue in top left corner of the cage. However nine cells in the grid are “doublers”. A digit in such a cell counts as double its value towards the cage sums. There is exactly one doubler in each row, column, and 3x3 box – and the doublers form a set of the digits 1 to 9.","solution":"135968274278134965649527183324691758781345692596782341412876539863259417957413826","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a cage cannot repeat and must sum to the small clue in top left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"However nine cells in the grid are “doublers”.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9g93q6jrmB","ctcId":1784,"ctcDifficulty":"HARD","title":"Intersections","author":"IcyFruit","rules":"Place a digit in each cell such that in any row, column, or 3x3 box, if a digit is present, it appears exactly its own number of times (in that row, column, 3x3 box). Digits may not repeat within a cage.","solution":"333224444155333555555444554333242444551333555555444455333422444555444545515333555","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits may not repeat within a cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"k763dyf84l","ctcId":1785,"ctcDifficulty":"MEDIUM","title":"Aesthete","author":"Lizzy01","rules":"Normal sudoku rules apply. Along thermometers, values strictly increase from the bulb end. There are nine doubler cells in the grid, one in every row, column and box. Each digit from 1-9 appears in a doubler cell exactly once. A doubler cell's value counts as double its digit.","solution":"437982156196354278852176349673821495285749631941563782329418567568237914714695823","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There are nine doubler cells in the grid, one in every row, column and box. Each digit from 1-9 appears in a doubler cell exactly once. A doubler cell's value counts as double its digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Along thermometers, values strictly increase from the bulb end.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"f92ld5yxt0","ctcId":1787,"ctcDifficulty":"MEDIUM","title":"Teenage Love","author":"Blobz","rules":"Normal sudoku rules apply.\n\nEvery adjacent pair of digits along the line do not repeat and must sum to 13 or 14.\n\nDigits in cages do not repeat and must sum to 13 or 14.\n\nDigits along the arrow (which may repeat) sum to the value in the attached circle.","solution":"256749813839516742147283569961427358572831496483695271395172684724968135618354927","constraints":["arrow","cage","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every adjacent pair of digits along the line do not repeat and must sum to 13 or 14.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"4hq3qvqmnk","ctcId":1788,"ctcDifficulty":"MEDIUM","title":"Mirrored Zippers","author":"gdc","rules":"Normal Sudoku rules apply.\nValues an equal distance to the circled center of a zipper line sum to the value of the central digit.\nIn every row, column and box, is a mirrored digit. It takes the value opposite to its digit on the 1-9 scale. (In other words, 1 takes the value of 9, 2 the value of 8... 9 the value of 1) Each digit 1-9 is mirrored once. Unmirrored digits use their digits as values.","solution":"493721685276589143581436729149258376725693418638147592814965237367812954952374861","constraints":["custom","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In every row, column and box, is a mirrored digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"zipper-line","type":"zipper-line","variant":"modified","modifiers":[],"params":null,"note":"Values an equal distance to the circled center of a zipper line sum to the value of the central digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"bba52ml2te","ctcId":1789,"ctcDifficulty":"HARD","title":"Ocean Spray","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nBox borders divide each blue line into segments with the same sum.","solution":"371986254842315796965274813627849135198537462453621978516498327289753641734162589","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hm580ts3a9","ctcId":1790,"ctcDifficulty":"VERY HARD","title":"Dutch Baby","author":"Philipp Blume, aka glum_hippo","rules":"Normal Sudoku rules apply. Each row, column, and 3x3 box contains the digits 1-9 exactly once each.\n\nThere is an orange snake in the grid, which moves from one cell center to the next horizontally or vertically (i.e., never diagonally). It may not cross itself nor touch orthogonally. The snake divides the non-snake cells into 8 different regions, one of each size 1-8 cells. Each of these regions is orthogonally contiguous and acts like a killer cage. Each cage encloses exactly one sum clue, which indicates the sum of the digits in that cage, and digits may not repeat in any cage. (The sum clue need not be in the top left corner of the cage.)\n\nThe snake itself is a so-called 'Dutch Whisper' line, i.e., neighboring digits on the snake must differ by 4 or more.\n\nThe white dot indicates that digits in R1C2 and R2C2 are consecutive.","solution":"739264518146758932528319467682593741417826395953471826264987153895132674371645289","constraints":["cage","custom","dutch-whispers","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Each cage encloses exactly one sum clue, which indicates the sum of the digits in that cage, and digits may not repeat in any cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There is an orange snake in the grid, which moves from one cell center to the next horizontally or vertically (i.e., never diagonally).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"p2qL4hj8DG","ctcId":1791,"ctcDifficulty":"MEDIUM","title":"Angular Arrows","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. Digits cannot repeat along a blue main diagonal.","solution":"513698724287514693694372158832957416456123987971846235745281369168439572329765841","constraints":["arrow","diagonal"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"GqRgj6rq3h","ctcId":1792,"ctcDifficulty":"MEDIUM","title":"XV Binairo","author":"Panthera","rules":"Normal Sudoku rules apply. \n\nBinairo rules apply. You cannot have 3 even digits adjacent in a row (or column) and you cannot have 3 odd digits adjacent in a row (or column). Each even/odd pattern must be different in the rows , and each even/odd pattern must be different in the columns. \n\nThe thermo has the smaller number in the bulb.\n\nXV rules apply. Digits separated by an X add to 10, digits separated by a V add to 5.","solution":"891637452764512839235849761549761328318254697627983145983126574176495283452378916","constraints":["XV","custom","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Binairo rules apply. You cannot have 3 even digits adjacent in a row (or column) and you cannot have 3 odd digits adjacent in a row (or column). Each even/odd pattern must be different in the rows , and each even/odd pattern must be different in the columns.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"748nmm3bpM","ctcId":1793,"ctcDifficulty":"HARD","title":"Cobra's Curse","author":"IcyFruit","rules":"Normal sudoku rules apply. Blue lines are ‘region sum lines’ ie 3x3 box borders divide each blue line into segments with the same sum. Brown lines are ‘product sum lines’ ie the digits on each end of the line must multiply together to give the sum of ALL digits on the line. Draw a 1-cell-wide snake which moves orthogonally and does not touch itself (even diagonally). The snake must enter every 3x3 box exactly once and may not include any cell which is on a line (but may include circled cells). The snake acts as both a region sum line and a product sum line. A digit in a circle indicates the number of times that digit appears on the snake.","solution":"365921784278546913194873265529364871847195326631287549412759638986432157753618492","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Brown lines are ‘product sum lines’ ie the digits on each end of the line must multiply together to give the sum of ALL digits on the line. Draw a 1-cell-wide snake which moves orthogonally and does not touch itself (even diagonally). The snake acts as both a region sum line and a product sum line. A digit in a circle indicates the number of times that digit appears on the snake.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c6","c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]}]},{"id":"nrGRHthTj2","ctcId":1795,"ctcDifficulty":"HARD","title":"Kropki Kounting","author":"Myxo","rules":"Normal sudoku rules apply. Assign each circle (dot) in the grid a digit from 1-9. If a digit N is assigned to a circle, that digit must be assigned to exactly N circles in the grid. Digits separated by a black circle have a ratio of 1:N, where N is the digit assigned to the circle. Digits separated by a white circle have a difference of N, where N is the digit assigned to the circle.","rulesClarified":"Normal sudoku rules apply.\n\nEach circle is a dot on the border between two neighbouring cells. Write a digit from 1 to 9 on every circle. Black and white circles are both circles, and the count rule applies to all of them together.\n\nCount rule: if a circle has digit N, then exactly N circles in the whole grid have digit N. The circle itself is one of those N.\n\nBlack circle: the two digits either side of it have a ratio of 1 to N, so one is N times the other.\n\nWhite circle: the two digits either side of it differ by N. The difference is the absolute difference, so the order of the two digits does not matter.","solution":"427563918596184372831927546259831467764259831318746259942615783173498625685372194","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If a digit N is assigned to a circle, that digit must be assigned to exactly N circles in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Digits separated by a black circle have a ratio of 1:N, where N is the digit assigned to the circle. Digits separated by a white circle have a difference of N, where N is the digit assigned to the circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4","c5"]}]},{"id":"cedvkcdyrb","ctcId":1797,"ctcDifficulty":"VERY HARD","title":"Miami Zipper","author":"Dorlir","rules":"Normal sudoku rules apply. Digits an equal distance from the centre of the purple line must sum to the digit in the centre of that purple line.","solution":"471956823985273416632148795324891567596732148718465932843529671259617384167384259","constraints":["zipper-line"],"constraintFacts":[{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"0ham0u0jtt","ctcId":1798,"ctcDifficulty":"HARD","title":"Pseudoscience","author":"Marty Sears","rules":"• Normal sudoku rules apply.\n• In each row, column and box there is exactly one 'pseudo cell.'\n• The digits 1-9 each appear once in a pseudo cell.\n• The real value of a pseudo cell (for the purposes of the coloured lines) is determined by multiplying its row number by its column number. Eg; if there is a pseudo cell in r6c3, it has the value of 18, regardless of which digit appears in that cell.\n\nGERMAN WHISPER: The values of adjacent cells on a green line have a difference of at least 5.\nRENBAN: The values of the cells along a purple line form a non-repeating consecutive set, which can be arranged in any order.\nNABNER: The value of a cell on a yellow line may not be consecutive with (or the same as) any other values on that line.\nREGION SUM: The value of cells within each 3x3 box along a darker blue line sum to the same amount.\nSAME DIFFERENCE: The values of adjacent digits on a turquoise line always have the same difference.\nDIFFERENT DIFFERENCE: The difference between the values of adjacent cells on a peach line must be different for every pair of adjacent cells on that line. Eg: if there are two cells with values of 7 and 9 next to each other on the line, then cells with values of 4 and 6 may not appear next to each other on the same line (as both pairs would have a difference of 2.)","solution":"285694731314857692976321458521739864693418275847265913439186527752943186168572349","constraints":["custom","german-whispers","nabner-line","region-sum-line","renban","same-difference-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• In each row, column and box there is exactly one 'pseudo cell.' DIFFERENT DIFFERENCE: The difference between the values of adjacent cells on a peach line must be different for every pair of adjacent cells on that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c10"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"GERMAN WHISPER: The values of adjacent cells on a green line have a difference of at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"REGION SUM: The value of cells within each 3x3 box along a darker blue line sum to the same amount.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"jpGbTb7jBF","ctcId":1799,"ctcDifficulty":"MEDIUM","title":"Ancient Artifacts","author":"Scojo","rules":"Normal sudoku rules apply. Placing a correct digit in the grid will clear any fog in the surrounding cells.\n\nLines are Renbans, German Whispers, or Region Sum Lines. The identity of each line must be deduced. Lines never cross or branch in this puzzle. Therefore, if two line segments enter the same cell, those line segments must be connected.\n\nRenbans are a sequence of non-repeating digits in any order. Along German Whispers adjacent digits on the line have a difference of at least 5. Region Sum Lines have the same sum in every 3x3 box they visit. If a Region Sum Line visits a box multiple times, each visit is counted as a separate sum.\n\nA dot between two digits means that those digits are either consecutive or have a 1:2 ratio. Not all dots are given.","solution":"749852613125364978638791254314985726867123549592476381986547132273618495451239867","fogLight":"R3C3,R3C1,R3C2,R1C3,R1C1,R1C2,R2C3,R2C1,R2C2","constraints":["custom","fog","german-whispers","kropki","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The identity of each line must be deduced.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"A dot between two digits means that those digits are either consecutive or have a 1:2 ratio.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c11"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"gP3MLq8HTr","ctcId":1800,"ctcDifficulty":"MEDIUM","title":"Sneaky Killers","author":"Scojo","rules":"Normal sudoku rules apply. Digits may not repeat within a cage. The digits in each cage sum to an unknown total. A white dot between two cages indicates that the totals in those two cages have a difference of X. The value of X is the same for every white dot, but must be deduced.","solution":"286314579579268413314795268897153642123647985465982137748526391932471856651839724","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A white dot between two cages indicates that the totals in those two cages have a difference of X. The value of X is the same for every white dot, but must be deduced.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"fmDD3m73nh","ctcId":1801,"ctcDifficulty":"MEDIUM","title":"Anti-Ratio Astronomy","author":"Scojo","rules":"Normal sudoku rules apply. Divide the grid into “galaxies”, which are orthogonally connected groups of cells that have 180 degree rotational symmetry about their centres, and do not overlap with other galaxies. All cells must be part of a galaxy. The centre of every galaxy is marked by a red dot. Digits may not repeat within a galaxy. No two adjacent cells in the grid (ie no domino) may have digits that are in a 1:2 ratio.","solution":"358146972946752318271398546614583297839274651527619834183465729465927183792831465","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into “galaxies”, which are orthogonally connected groups of cells that have 180 degree rotational symmetry about their centres, and do not overlap with other galaxies. No two adjacent cells in the grid (ie no domino) may have digits that are in a 1:2 ratio.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]}]},{"id":"qkrzgnhqew","ctcId":1802,"ctcDifficulty":"EASY","title":"Clone Squares","author":"Scojo","rules":"Irregular Sudoku: Place the digits 1-9 once each in every row, column, and outlined region.\n\nClone Squares: There are three sets of clones in the grid, the locations of which must be determined. Each clone is a 3x3 square, and each set consists of three clones. Clones within the same set must contain identical digits in exactly the same positions. Rotations and reflections are not allowed. Clones do not overlap with other clones.","solution":"381654729138546972813465297729381654972138546297813465654729381546972138465297813","constraints":["clone"],"constraintFacts":[{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"f2ajiy0h66","ctcId":1803,"ctcDifficulty":"HARD","title":"Counting Thermos","author":"Scojo","rules":"Chaos Construction Sudoku: Place the digits 1-9 once each in every row, column, and 9 cell orthogonally connected region. The location of each region must be determined.\n\nCounting Thermos: Along a thermometer, digits must increase from bulb to tip. The digit in the bulb of a thermometer indicates how many thermometer bulbs contain that digit. Additionally, the digit in the bulb of a thermometer indicates how many times that thermometer crosses a border between regions.\n\nSquares: A digit in a square indicates how many cells in its region are on a thermometer.\n\nInequality: A V shape between two digits points to the lower digit.","solution":"456912387197236458231845679978621543865374912784569231523198764649783125312457896","constraints":["custom","inequality","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Chaos Construction Sudoku: Place the digits 1-9 once each in every row, column, and 9 cell orthogonally connected region. The digit in the bulb of a thermometer indicates how many thermometer bulbs contain that digit. Additionally, the digit in the bulb of a thermometer indicates how many times that thermometer crosses a border between regions. Squares: A digit in a square indicates how many cells in its region are on a thermometer.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c4","c5","c6"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"jfejlvb9ab","ctcId":1804,"ctcDifficulty":"MEDIUM","title":"The Crustler Building","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nClues outside the grid are both Sandwich AND Skyscraper clues. As a sandwich, the clue gives the sum of the digits between 1 and 9 in that row or column. As a skyscraper, the clue represents how many digits would be visible when standing at the clue looking at its row or column, if each digit were a building with the height of its value. For example, the sequence 132495678 would have a skyscraper clue of 4, because you could see the buildings of heights 1, 3, 4, and 9, but the 5, 6, 7, and 8 would be hidden behind the 9, and the 2 is hidden by the 3. A \"?\" in a clue may represent any integer value.\n\nDigits along a thermometer must increase from bulb to tip.\n\nDigits on an arrow must sum to the digit in that arrow's circle.","solution":"371589426928467513645312978159726384764893152283145769596231847837654291412978635","constraints":["arrow","sandwich","skyscraper","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits on an arrow must sum to the digit in that arrow's circle.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"skyscraper","type":"skyscraper","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"2p785kmt7f","ctcId":1805,"ctcDifficulty":"EASY","title":"Cascade","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nThermos: Along each thermometer shape, digits must increase from bulb to tip.","solution":"936825714147936825258147936693582471714693582825714693369258147471369258582471369","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"gFLGDRnLL7","ctcId":1806,"ctcDifficulty":"MEDIUM","title":"Electric Explosion","author":"Scojo","rules":"Normal sudoku rules apply. Adjacent digits along a green line must have a difference of at least 5.","solution":"341685729592731846786942513123476985954813672678529134215367498439158267867294351","constraints":["german-whispers"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"P44pbrqtfP","ctcId":1807,"ctcDifficulty":"VERY HARD","title":"Whisper Doublers","author":"yttrio","rules":"Normal sudoku rules apply. Adjacent values along a line must differ by at least 5. Nine cells in the grid are 'doublers', which count as double their value for the purpose of the lines. There is exactly one doubler in each row, column, and box, and they form a set of the digits 1-9.","solution":"549382716236174598781596432164829357892753641357461829915638274478215963623947185","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Nine cells in the grid are 'doublers', which count as double their value for the purpose of the lines.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Adjacent values along a line must differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"nHJJ9Hh9BN","ctcId":1808,"ctcDifficulty":"HARD","title":"Foggy Whisper Loop","author":"yttrio","rules":"Normal Sudoku rules apply. Digits in a cage must not repeat and must sum to the small clue in the top left corner of the cage. Digits separated by a white dot are consecutive. Not all dots are given. Draw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally. The loop must enter every cell of every cage. The loop acts as a German Whispers line (i.e., adjacent digits on the loop must have a difference of at least 5). Additionally the grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells, possibly revealing more clues.","solution":"382564791967183254154279368615742839793618542248395617531927486476831925829456173","fogLight":"R1C1,R8C8","constraints":["cage","custom","fog","german-whispers","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop of orthogonally connected cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"38RpDFhqDm","ctcId":1809,"ctcDifficulty":"MEDIUM","title":"Polarity Loop","author":"yttrio","rules":"Normal sudoku rules apply. Digits in cages cannot repeat and must sum to the small clue given in the upper left corner of the cage. Cells separated by a white dot contain consecutive digits.  Not all dots are necessarily given. Draw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally. The loop must occupy all cells of all given cages. Adjacent digits on the loop must alternate polarity (low [1234] vs high [6789]).","solution":"618352749432798651957461328374519286896274513125683497761825934283947165549136872","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The loop may not touch itself, not even diagonally. The loop must occupy all cells of all given cages. Adjacent digits on the loop must alternate polarity (low [1234] vs high [6789]).","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"RDQq2T2rpG","ctcId":1810,"ctcDifficulty":"MEDIUM","title":"Whisper Loop-de-Loop","author":"yttrio","rules":"Normal sudoku rules apply. Digits in a cage must not repeat and must sum to the number in the top left corner of the cage. Draw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally. The loop must enter at least one cell of each cage. Numbers on the loop count as double their value when calculating cage sums. For example, a 2-cell cage summing to 10 may contain a 2 on the loop and a 6 not on the loop. The loop acts as a German Whispers line (i.e., adjacent digits on the loop must have a difference of at least 5). The original, undoubled value of the digit is always used for the purposes of the German Whispers constraint.","solution":"659173824431928675827645319285416793746392158193857462968231547374569281512784936","constraints":["cage","custom","german-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a cage must not repeat and must sum to the number in the top left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop of orthogonally connected cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"9fweqd0qeq","ctcId":1811,"ctcDifficulty":"MEDIUM","title":"Parity Islands","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nOrthogonally connected cells of the same parity (odd vs. even) are parity islands. A digit in a circle indicates the size of the island.","rulesClarified":"Normal Sudoku rules apply.\n\nTwo orthogonally connected cells of the same parity (both odd or both even) belong to the same parity island. An island is a whole connected group of cells of one parity.\n\nA circled digit gives the size of the island that contains the circled cell. The circled cell counts as one of the cells of that island. A circled 3 means that island has exactly three cells.\n\nAn island with no circle gives no information about its size.","solution":"124763958693584271857291634241637895968145723735829416389412567516978342472356189","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Orthogonally connected cells of the same parity (odd vs. even) are parity islands.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"nuf4q68voj","ctcId":1812,"ctcDifficulty":"MEDIUM","title":"Mad Mod Quad Loop","author":"carabet/yttrio","rules":"Normal Sudoku rules apply.\n\nCells separated by a white dot are consecutive. Cells separated by a black dot have a 2:1 ratio. Not all possible dots are necessarily given.\n\nDigits in a circle must appear in at least one of the four surrounding cells.\n\nDraw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally.\n\n  -- The loop must enter exactly one of the four cells surrounding each given quad clue.\n\n  -- The loop acts as a modular line. Each set of three adjacent digits along the loop must be one each from the sets [147], [258], and [369].","solution":"837416259241958763695723481974182536358674912126539847563897124712345698489261375","constraints":["custom","kropki","modular-line","quadruple"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop of orthogonally connected cells. -- The loop must enter exactly one of the four cells surrounding each given quad clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"D4n4GJB7Jf","ctcId":1815,"ctcDifficulty":"MEDIUM","title":"Build Your Own Between Lines","author":"Knickolas","rules":"Normal sudoku rules apply. Each pair of circles of the same colour are connected by a hidden Between Line. Each Between Line may not branch, move diagonally, or take up a full 2x2 area. Separate Between Lines may not overlap. Cells along a Between Line must have values between those in the circles at the ends of that line.","solution":"386712594291485637457369218179856423863241975542937861638124759724593186915678342","constraints":["between-line"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"H26FG6Bnjp","ctcId":1816,"ctcDifficulty":"HARD","title":"Galactic Whispers","author":"Knickolas","rules":"Normal sudoku rules apply. The dots given in the grid are the centres of rotationally symmetric “galaxies” (non-overlapping sets of orthogonally connected cells). Adjacent digits in the same galaxy must have a difference of at least 5. Caged cells are part of a galaxy with a given centre.","solution":"418295376675438291923716854182953647764182935359674182247369518591827463836541729","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The dots given in the grid are the centres of rotationally symmetric “galaxies” (non-overlapping sets of orthogonally connected cells). Adjacent digits in the same galaxy must have a difference of at least 5. Caged cells are part of a galaxy with a given centre.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]}]},{"id":"dh9t3PnBQ4","ctcId":1817,"ctcDifficulty":"MEDIUM","title":"Babbling Brook","author":"Knickolas","rules":"Normal sudoku rules apply. Shade the grid using two colours, such that all instances of each colour are orthogonally connected, and no 2x2 area is completely one colour. Blue lines must have an equal sum N within each colour they pass through. If a blue line passes through a colour multiple times, each individual pass sums to N. (N can be different for different lines). All lines must cross colours at least once. Cells separated by an X contain digits summing to 10.","solution":"187563942935412678642879135823194567516387294479625381254938716791246853368751429","constraints":["XV","custom","yin-yang"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Blue lines must have an equal sum N within each colour they pass through.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"F9fHgrQqQF","ctcId":1818,"ctcDifficulty":"VERY HARD","title":"Doppler Effect","author":"Knickolas","rules":"Normal sudoku rules apply. The grid contains two “galaxies”.  A galaxy is a collection of orthogonally-connected cells which exhibits 180 degree rotational symmetry around the central cell of the grid. Eg If r2c4 is in a galaxy then r8c6 must also be in that galaxy. All cells must be part of a galaxy and the two galaxies may only ever overlap in one cell - the central cell of the grid. No 2x2 area may be fully part of one galaxy. One of the galaxies is “redshifted” and cells in it have a value of one greater than their digit. The other galaxy is “blueshifted” and cells in it have a value of one less than their digit. Values along an arrow sum to the value in that arrow’s circle. Values in a cage sum to the given total. Digits may not repeat in a cage, but values may.","solution":"673125849154839627298674135831297456967548312542361978319782564425916783786453291","constraints":["arrow","cage","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Values along an arrow sum to the value in that arrow’s circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Values in a cage sum to the given total.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The grid contains two “galaxies”. One of the galaxies is “redshifted” and cells in it have a value of one greater than their digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7"]}]},{"id":"55e6o5g53o","ctcId":1820,"ctcDifficulty":"HARD","title":"World, a Tuning Fork","author":"Philipp Blume, aka glum_hippo","rules":"Normal Sudoku rules apply.\n\nBattenburg: Wherever a 2x2 area consists of two odd and two even digits in a checkerboard pattern, a little checkerboard symbol is marked.\n\nZipperlines: Digits in cells that are an equal number of steps from the midpoint of a lavender line must sum to the digit on the midpoint (marked by a lavender dot).","solution":"361825947259647183487913265912736458875294316643158729738461592594382671126579834","constraints":["custom","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Battenburg: Wherever a 2x2 area consists of two odd and two even digits in a checkerboard pattern, a little checkerboard symbol is marked.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"RHQ6GJGg3r","ctcId":1821,"ctcDifficulty":"MEDIUM","title":"Wayfinder","author":"Nordy","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in the corresponding circle. Digits joined by an X sum to 10.","solution":"486315297359726814721849536698571342174283965235964781913657428562438179847192653","constraints":["XV","arrow"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9zyrpmw0lb","ctcId":1824,"ctcDifficulty":"MEDIUM","title":"The Gallery","author":"Riffclown","rules":"Irregular Sudoku rules apply.\nDigits on a wide purple Renban line form a set of consecutive digits in any order.\nDigits on a thin blue region sum line have the same total for each region the line enters. Different lines may have different totals.\nDigits on a gold Nabner line may not repeat. if a digit appears on the line then digits consecutive with it must not appear on that line","solution":"428196735536974812681723549372549681945317268194862357867235194219658473753481926","constraints":["nabner-line","region-sum-line","renban"],"constraintFacts":[{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"17rhp0owyb","ctcId":1825,"ctcDifficulty":"MEDIUM","title":"Difference Fences","author":"RockyRoer","rules":"Normal sudoku rules apply.\n\nDigits in the circles must appear in the surrounding four cells.  \n\nThe white segments represent 'Difference Fences'.  Each segment has a value equal to the difference between the cells they separate. On a fence, no two segments can have the same value.  Each fence has a total value equal to the sum of all the segments, and this total value is given in the attached quad.  Some total values will need to be deduced.","solution":"483571926915628374672394815256839741194762583738415692547286139821953467369147258","constraints":["custom","quadruple"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The white segments represent 'Difference Fences'.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6D6Lrqt7p7","ctcId":1826,"ctcDifficulty":"MEDIUM","title":"Not Your Average Thermo Puzzle","author":"Scojo","rules":"Normal sudoku rules apply. Along a thermometer, digits increase from bulb to tip. Digits along an orange arrow average exactly to the digit in that arrow's circle. Multiple arrows extending from the same circle are treated as different arrows each averaging to the circled digit. For example, a circled 3 could have 15 on one of its arrows, and 24 on the other, because both arrows would average to 3. For clarity, 'average' in this puzzle refers to the arithmetic mean.","solution":"657921843942835761381476529126547938593682174874193256265318497438759612719264385","constraints":["arrow","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits along an orange arrow average exactly to the digit in that arrow's circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"67rr7DMJDh","ctcId":1827,"ctcDifficulty":"MEDIUM","title":"121","author":"Dorlir","rules":"Normal sudoku rules apply. The digits within a cage must sum to the small clue in the top-left corner of that cage. The inequality sign points to the smaller digit.","solution":"345687912687912345912345687234568791568791234791234568456879123879123456123456879","constraints":["cage","inequality"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"82gfkhwo9b","ctcId":1828,"ctcDifficulty":"MEDIUM","title":"DUNE 2","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nBox borders divide each blue line into segments with the same sum.\n\nNeighbouring digits on the green line have a difference of at least 5.\n\nDigits joined by an X sum to 10. Digits joined by a V sum to 5. Not all Xs and Vs are given.\n\nDigits joined by a white dot are consecutive. Not all dots are given.","solution":"541826397972314856386795412235461789418579623697283541123658974754932168869147235","constraints":["XV","german-whispers","kropki","region-sum-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"i7ze05evyv","ctcId":1829,"ctcDifficulty":"MEDIUM","title":"Symphony","author":"Playmaker6174","rules":"Normal Sudoku rules apply.\n\nAn X connects two digits that sum to 10. Not all Xes are given.\n\nDigits along an arrow sum to the digit in the circle cell attached to that arrow.\n\nAlong a green line, two adjacent digits have the difference of at least 5.\n\nAlong a pink line, digits form a set of non-repeating consecutive digits that can be in any order.","solution":"327648915481952367659371284873126459296584731514739826168493572742815693935267148","constraints":["XV","arrow","german-whispers","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits along an arrow sum to the digit in the circle cell attached to that arrow.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"y23lun2exp","ctcId":1830,"ctcDifficulty":"MEDIUM","title":"Parity Snakes","author":"Malrog","rules":"Normal sudoku rules apply.\nDigits separated by a white dot must be consecutive (not all dots are given).\nA digit in a grey square must be even.\nEach cell containing a circle is the head of a parity snake, whose length is the digit in the circle. A parity snake is a non-branching one-cell-wide path of orthogonally connected cells of the same parity, which may not orthogonally touch itself or other cells of matching parity. A snake may not have two heads, and may be a single cell.","solution":"691527348748963251352814967263741589179658423584392176927436815436185792815279634","constraints":["custom","even","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each cell containing a circle is the head of a parity snake, whose length is the digit in the circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"uyakkp4064","ctcId":1831,"ctcDifficulty":"MEDIUM","title":"Product Distribution Network","author":"Oddlyeven","rules":"Rules: Normal Sudoku rules apply. Put the digits 1 to 9 once each in each row, column and box.\nProduction Lines: Digits along a line sum to the product of the digits in the squares at either end of the line (if it is the same square, multiply that digit with itself). The sum does not include the digits in the squares. Digits may repeat on a line if permitted by the other rules.","solution":"963725841752148369481639257829351674576482193134976528647213985218594736395867412","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Production Lines: Digits along a line sum to the product of the digits in the squares at either end of the line (if it is the same square, multiply that digit with itself).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"8851i50p1d","ctcId":1833,"ctcDifficulty":"MEDIUM","title":"ZipBan!","author":"FullDeck and Missing a Few Cards","rules":"- Normal sudoku rules apply.\n- All lines are both Renban AND Zipper lines. Centres of Zipper lines are marked by small circles.\n- Along Renban lines, digits for a non-repeating set of consecutive digits in some order.\n- Along Zipper lines, pairs of digits equidistant from the center have the same sum. For odd length Zipper lines, that sum is the value in the center cell of the line.","solution":"317869245268435971954127683793248516681953427542716398876394152425681739139572864","constraints":["renban","zipper-line"],"constraintFacts":[{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"x8uuju3q3e","ctcId":1834,"ctcDifficulty":"VERY HARD","title":"River Crossing","author":"IcyFruit","rules":"Normal sudoku rules apply.\nDivide the grid into 3 orthogonally connected sections such that each pair of sections shares an edge and no 2x2 square in the grid belongs to a single section. \nA digit in a circle indicates the number of circles in its section.\nOn section-sum lines, all adjacent groups of digits along the line which are part of the same section have the same sum. No line can be entirely in one section.","solution":"783921654654783291921456783418632975276195438539874162165349827397218546842567319","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into 3 orthogonally connected sections such that each pair of sections shares an edge and no 2x2 square in the grid belongs to a single section. A digit in a circle indicates the number of circles in its section. On section-sum lines, all adjacent groups of digits along the line which are part of the same section have the same sum.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]}]},{"id":"qB6JNbFQqL","ctcId":1835,"ctcDifficulty":"HARD","title":"Double Self-Referral","author":"Aad van de Wetering","rules":"Place the digits 1-9, once each, in every row, column and marked region. When digit z is in cell (x, y) then digit y is in cell (x, z) and digit x is in cell (z, y).","solution":"754328169586913724469172583391654872217546398832465917175839246628791435943287651","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"When digit z is in cell (x, y) then digit y is in cell (x, z) and digit x is in cell (z, y).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"cjjw4ss931","ctcId":1836,"ctcDifficulty":"VERY HARD","title":"Pause the video.... Congrats","author":"apiyo","rules":"Normal Sudoku rules apply.\n\nDigits separated by a chess Knight's move must be different. Digits on a grey thermometer increase from its circle end. Digits along a purple Renban line must be chosen from a consecutive set, in any order.\n\nThe sum of the digits in two orange circles is equal to the sum of the digits along the line joining them.\n\nThe word Agadmator appears along the diagonal of the grid. Each instance of a given letter represents the same digit, and no two different letters represent the same digit. The M positioned on a corner is the difference between R6C6 and R7C7.","solution":"921846735635927814847513926512684397396275481784391562178432659469158273253769148","constraints":["antiknight","custom","renban","thermometer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits in two orange circles is equal to the sum of the digits along the line joining them. The word Agadmator appears along the diagonal of the grid. The M positioned on a corner is the difference between R6C6 and R7C7.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c8"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"D7HLp6nQB6","ctcId":1837,"ctcDifficulty":"MEDIUM","title":"Diamond In The Rough","author":"fjam","rules":"Normal sudoku rules apply.  Box borders divide each blue line into segments with the same sum. Cells separated by a black dot must contain digits with a ratio of 1:2. Not all dots are given.","solution":"712596384594238716638147592125874963349652178876319425483921657967485231251763849","constraints":["kropki","region-sum-line"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"4ev7ufnh17","ctcId":1838,"ctcDifficulty":"VERY HARD","title":"Modular Region Sum Lines","author":"Phistomefel","rules":"1. Normal Sudoku rules apply.\n2. Draw in lines that move orthogonally from cell to cell. Two circles of the same colour are start and end of a line. Lines may not intersect themselves or other lines.\n3. The lines drawn in the grid act both as a Region Sum Line and a Modular Line. Additionally, digits CANNOT repeat on a line.\n\nFurther explanation:\nRegion Sum Line: Digits on a line have the same sum in each region the line passes through. If a line passes through a region multiple times, each individual segment sums separately.\nModular Line: Every set of three sequential digits along a line must contain a complete set of residues modulo 3, i.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}.","solution":"594682371836471295712593846325947618641328957978165423257834169489716532163259784","constraints":["custom","modular-line","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"3. The lines drawn in the grid act both as a Region Sum Line and a Modular Line. Additionally, digits CANNOT repeat on a line. 2. Draw in lines that move orthogonally from cell to cell. Two circles of the same colour are start and end of a line. Lines may not intersect themselves or other lines.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"twacfrsxbk","ctcId":1839,"ctcDifficulty":"VERY HARD","title":"Segue Ursa","author":"Dorlir","rules":"- Normal sudoku rules apply.\n- It must be determined whether each white dot is a kropki dot or the centre of a galaxy.\n- KROPKI: The two digits joined by a white kropki dot have a difference indicated by the number on the kropki dot.\n- GALAXIES: A galaxy is a group of orthogonally connected cells, that has the white dot at its centre and is rotationally symmetrical through 180 degrees.\n- The number on the central dot of a galaxy indicates the number of cells (N) in the galaxy. This galaxy must contain all the digits from 1 to N.\n- Galaxies cannot share cells with any other galaxies or cells joined by a kropki dot.\n- Galaxies also function similarly to region sum lines; digits within each 3x3 box sum to the same amount if they are within the same galaxy. This region sum may be different for different galaxies.","solution":"523147986768923451194658372875234169239761845641589237312875694456392718987416523","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- GALAXIES: A galaxy is a group of orthogonally connected cells, that has the white dot at its centre and is rotationally symmetrical through 180 degrees.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"- KROPKI: The two digits joined by a white kropki dot have a difference indicated by the number on the kropki dot.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"68jb7y05c9","ctcId":1840,"ctcDifficulty":"HARD","title":"March of the Palindromes","author":"Eric Rathbun","rules":"Normal sudoku rules apply. A clue outside the grid gives the sum of the digits along the indicated diagonal. Digits separated by a black dot are in a 1:2 ratio. Gray lines are palindromes that read the same in both directions. Digits cannot repeat along the marked diagonal.","solution":"245361978713598624986247135452139786371856492869724351524913867138675249697482513","constraints":["diagonal","kropki","little-killer","palindrome"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"ucrlbqbg94","ctcId":1842,"ctcDifficulty":"MEDIUM","title":"Hypertension","author":"Michael Lefkowitz","rules":"Normal sudoku rules apply.\n\nSILENT KILLER\nDigits in a cage sum to the number in the cell pointed at by the cage's northwest corner. Digits cannot repeat in a cage.\nExample: row 1 column 2 shows the sum of the upper-leftmost cage.\n\nSILENT LITTLE KILLER\nA cell with an arrow shows the sum of the digits on the arrow's diagonal.","solution":"381625794972184356645937218427591683598362147163748925814273569236459871759816432","constraints":["cage","little-killer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"little-killer","type":"little-killer","variant":"modified","modifiers":[],"params":null,"note":"A cell with an arrow shows the sum of the digits on the arrow's diagonal.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]}]},{"id":"912ee99op9","ctcId":1843,"ctcDifficulty":"HARD","title":"Inner Circles","author":"Michael Lefkowitz","rules":"Normal sudoku rules apply. Also, fog covers the grid. Correctly placing digits clears the fog. No guessing is required (or allowed).\n\n- A black dot in a cell indicate its value has a 2-to-1 ratio with that of some (orthogonal) neighbor.\n- A white dot indicates its value is adjacent to some neighbor's.\n- A grey dot indicates its value and some neighbor's value sum to 5.\n\nAll possible dots have been given. Where multiple dots could apply, one has been chosen at random.","solution":"752913864319468527864725193527394618193856472648271935475639281931582746286147359","fogLight":"R1C1,R1C2,R2C1,R2C2,R2C3,R3C2,R4C5,R4C7,R4C8,R5C7,R5C8,R5C9,R6C8,R7C4,R8C4,R9C4","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- A black dot in a cell indicate its value has a 2-to-1 ratio with that of some (orthogonal) neighbor. - A white dot indicates its value is adjacent to some neighbor's. - A grey dot indicates its value and some neighbor's value sum to 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c7"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"2g4pswdpxz","ctcId":1844,"ctcDifficulty":"HARD","title":"Setter's Day Off","author":"Michael Lefkowitz","rules":"I need a break from setting sudokus. Could you set one for me please?\n\nI'd like for my sudoku to have five straight lines (and nothing else):\n- A horizontal Arrow pointing east (with a one-cell circle)\n- A horizontal Thermometer\n- A horizontal German Whispers line\n- A vertical German Whispers line\n- A vertical Zipper line\n\nEach should be as long as it is possible to make orthogonal straight lines of that variety in a sudoku. Put them wherever, just not in the cells with my signature please.\n\nI'd also like some sort of anti-chess constraint: anti-knight, anti-king, or anti-bishop (up to you, whichever works).\n\nOh, and make sure the solution has a 3 in the corner, won't you?","solution":"561728394432569178978134526354682917817945632296317845745893261123456789689271453","constraints":[],"constraintFacts":[]},{"id":"P4h9q6HtRH","ctcId":1845,"ctcDifficulty":"VERY HARD","title":"Rubik's Cube","author":"Michael Lefkowitz","rules":"Normal sudoku rules apply. The white dot separates digits with consecutive values. Cells in the same position in two 3x3 boxes may not contain the same digit. (So eg, r1c1 and r4c4 cannot contain the same digit as these are both in the top left corner of their 3x3 boxes.) 'XYZ' means 'Row X Col Y is digit Z.' If XYZ is true, YZX is also true.","solution":"672591483348267159915834726726915834483672591159348267267159348834726915591483672","constraints":["custom","disjoint-groups","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"'XYZ' means 'Row X Col Y is digit Z.' If XYZ is true, YZX is also true.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"zmgcavpoxu","ctcId":1846,"ctcDifficulty":"MEDIUM","title":"Tangram Killer","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply.\n\nDigits in a cage sum to the number in its corner. Cells that half-appear in a cage only contribute half their value to its sum. Digits appear at most once in the same cage (half-appearing twice counts as appearing once).","solution":"461259378758431269932786415276895134514673982893124756645917823327548691189362547","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a cage sum to the number in its corner.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"D9fpjbmHRn","ctcId":1848,"ctcDifficulty":"MEDIUM","title":"Only even … or even only odd?","author":"sujoyku","rules":"Normal sudoku rules apply. A clue outside the grid indicates the value of the sum of all even or all odd digits on the indicated diagonal. If the even digits are counted, no odd digit contributes to the sum and vice versa. Digits in a cage do not repeat, and the clue in a cage indicates the sum of all even digits or of all odd digits which are contained in that cage.","rulesClarified":"Normal sudoku rules apply.\n\nDigits in a cage do not repeat.\n\nThe clue in a cage is the sum of all its even digits or of all its odd digits. The clue does not say which parity it counts, so work that out from the digits.\n\nWhen the even digits are counted, odd digits contribute nothing to the sum, and when the odd digits are counted, even digits contribute nothing.\n\nA clue outside the grid indicates the sum of all even digits or all odd digits on the indicated diagonal. The clue does not say which parity it counts.","solution":"859316274267459183134287695543172968782965341691834527978521436325648719416793852","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A clue outside the grid indicates the value of the sum of all even or all odd digits on the indicated diagonal. Digits in a cage do not repeat, and the clue in a cage indicates the sum of all even digits or of all odd digits which are contained in that cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"DQJ3QHr6gN","ctcId":1849,"ctcDifficulty":"VERY HARD","title":"Minmax Mosaic","author":"sujoyku","rules":"Normal sudoku rules apply. All cages are minmax killer cages. Digits in a minmax killer cage do not repeat. The clue in the top left indicates the sum of the smallest and the largest digit that are contained in the cage. For example, a cage containing the digits 1, 3, 6 and 8 would have the minmax killer clue 9=1+8. On the main diagonals digits do not repeat.","solution":"671829543984573216253164879592437681836951724147682935769348152325716498418295367","constraints":["custom","diagonal"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All cages are minmax killer cages.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"oepolnj5ur","ctcId":1850,"ctcDifficulty":"MEDIUM","title":"Fraction party","author":"sujoyku","rules":"Normal sudoku rules apply. All given cages are divisor killer cages. Digits in a divisor killer cage do not repeat. Each cage contains one divisor digit (which has to be determined by the solver). The clue in the top left indicates the value of the sum of all other digits in that cage divided by the divisor digit. For example, a 3-cell divisor killer cage containing the digits 1, 2 and 3 may have a valid clue of either 5=(2+3)/1, 2=(1+3)/2 or 1=(1+2)/3.","solution":"543176298928435167617928534285743916194652783736819452862594371479381625351267849","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All given cages are divisor killer cages.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"1kvw0r00vd","ctcId":1853,"ctcDifficulty":"MEDIUM","title":"Four Leaf Renban","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nDigits connected by an X or V sum to 10 or 5, respectively. Not every X and V is given.\n\nEach pink line contains a set of consecutive, non-repeating digits, in any order.","solution":"128965734693742851475381629736194285981256347542873916367418592254639178819527463","constraints":["XV","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"2i3vnmx1ye","ctcId":1854,"ctcDifficulty":"HARD","title":"Border Square Sums","author":"Phistomefel","rules":"1. Normal Sudoku rules apply.\n2. The digits in each 2x2-square that crosses at least one box border sum to a multiple of eight - except for the square marked in grey.\n3. The digits on an arrow sum to the digit in the circle.","solution":"427359186536814279918276453152438697643792815789561342361945728875123964294687531","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"2. The digits in each 2x2-square that crosses at least one box border sum to a multiple of eight - except for the square marked in grey.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"5060viuw2v","ctcId":1855,"ctcDifficulty":"VERY HARD","title":"Counting Castles","author":"Marty Sears","rules":"• Divide the grid into 9 kingdoms of orthogonally connected cells.\n• Fill the grid with the digits 1-9 so that each digit appears once in each row, column and kingdom.\n• A digit on a castle indicates exactly how many castles contain that digit.\n• Every kingdom has a score, representing how powerful it is. It is calculated by adding the number of castles the kingdom contains to the number of neighbouring kingdoms it borders. (Two kingdoms are considered neighbours if they share at least one orthogonal edge.)\n• A digit in a blue square indicates its kingdom's score. No two kingdoms have the same score.\n• A bridge connects two digits in different kingdoms, and they will either sum to 5, sum to 10, or be in a 1:2 ratio.","solution":"159724368698431257382567149561843792724196835236958471973285614415372986847619523","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• A digit on a castle indicates exactly how many castles contain that digit. • Every kingdom has a score, representing how powerful it is. It is calculated by adding the number of castles the kingdom contains to the number of neighbouring kingdoms it borders. (Two kingdoms are considered neighbours if they share at least one orthogonal edge.) • A bridge connects two digits in different kingdoms, and they will either sum to 5, sum to 10, or be in a 1:2 ratio.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c6"]}]},{"id":"wg95d01p88","ctcId":1857,"ctcDifficulty":"MEDIUM","title":"InBetween Snack","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits along each line have values which lie between those of the digits in the circles at either end of that line. Moreover, for the three brown lines, the digit in one of the circles is the sum of the remaining digits including the digit in the other circle.","solution":"587139624614725398329486157742963581968517243153248769271694835896351472435872916","constraints":["between-line","custom"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Moreover, for the three brown lines, the digit in one of the circles is the sum of the remaining digits including the digit in the other circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"giuk6t4rfg","ctcId":1858,"ctcDifficulty":"MEDIUM","title":"Event Horizon","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply. The value of a digit inside the black dot (i.e. box 5) is double its normal value.\n\nKILLER - Digits in a cage do not repeat, and their values sum to the number in the cage's upper left corner.\nLITTLE KILLER - Values on indicated diagonals sum to the number by the arrow.\nRENBAN - Values on a pink line form a consecutive non-repeating set.","solution":"136847952892635714754129386415763298283914675679258143341576829967482531528391467","constraints":["cage","custom","little-killer","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"KILLER - Digits in a cage do not repeat, and their values sum to the number in the cage's upper left corner.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The value of a digit inside the black dot (i.e. box 5) is double its normal value.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"RENBAN - Values on a pink line form a consecutive non-repeating set.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"tl5phvto7f","ctcId":1860,"ctcDifficulty":"HARD","title":"Sashigane Whispers","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nSashigane: Divide the grid into regions of orthogonally connected cells.  Each region must be an L shape with a width of one cell.\n-- Digits cannot repeat within a region.\n-- Arrows must lie at one end of an L and point toward the bend.  The digit on an arrow must contain the number of cells along that leg of that region, including the bend and arrow cells.\n-- Circles must lie at the bend of an L.  Digits in a circle must contain the total number of cells in the region, including the circled cell.\n\nAny Sashigane region that contains either a circle or arrow clue must act as a German Whispers line (i.e., adjacent digits within such a region must have a difference of at least 5).  A Sashigane region without a circle or arrow clue has no such restriction.","solution":"395716428871942653624358179287563914436179285159824736713695842948231567562487391","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Sashigane: Divide the grid into regions of orthogonally connected cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"9zsl8s2gjl","ctcId":1861,"ctcDifficulty":"MEDIUM","title":"Slinky","author":"Blobz","rules":"Normal sudoku rules apply.\n\nAlong SLOW thermometers, digits either stay the same or they increase as they move away from the bulb.","solution":"374568291195724863826391745287439156631852974459176328563917482742683519918245637","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"1weh2nwtje","ctcId":1862,"ctcDifficulty":"MEDIUM","title":"Solver, there's a fly on my Sudoku!","author":"IcyFruit","rules":"Normal sudoku rules apply. Digits separated by a white Kropki dot must be consecutive. Digits separated by a black Kropki dot must have a ratio of 1:2.\n\nA fly has flown across the page, in orthogonal lines. It always went north from a cell containing a 2, east from a 4, south from a 6, and west from an 8. On odd digits, it kept going in a straight line. The fly entered the grid heading west at the arrow, and exited heading east at the bottom right of the grid. It did not leave and re-enter the grid at any point. The fly may have crossed its own path, but it never flew directly across a Kropki dot.","solution":"291678345745132968368459172687943251954261837123785496412596783539817624876324519","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A fly has flown across the page, in orthogonal lines.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"TLG44bqNgH","ctcId":1863,"ctcDifficulty":"HARD","title":"The Green Machine","author":"James Kopp","rules":"Normal sudoku rules apply. Adjacent digits along the green lines have a difference of at least five.","solution":"138657249624319875759824361415238697963475182287961534371546928596782413842193756","constraints":["german-whispers"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"rnj2zdy7zu","ctcId":1865,"ctcDifficulty":"HARD","title":"Across the Lines","author":"Michael Lefkowitz","rules":"Normal sudoku rules apply.\nWhites live between digits with consecutive values. Blacks live between digits in a 2:1 ratio. Not all possible dots are given.\nConnect the $ symbols with a single meandering Redline. The Redline moves along cell edges and never touches itself. It cannot cross a dot or the train tracks. The regions created by the Redline never contain both high values (6789) and low values (1234).\nThe words in the grid can be ignored.","solution":"342178965961254873758963421287691354496835712135427698829546137513789246674312589","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Connect the $ symbols with a single meandering Redline. It cannot cross a dot or the train tracks. The regions created by the Redline never contain both high values (6789) and low values (1234).","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c7","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"NrrMdpBTh9","ctcId":1868,"ctcDifficulty":"MEDIUM","title":"Sherlock's advice to the good Dr. Watson","author":"HalfBakedLunatic","rules":"Sherlock said to Watson: Eliminate the impossible and whatever remains - however improbable - must be the truth. (The trick, of course, is finding out what's impossible.) \n\nNormal sudoku rules apply.\n\nDigits along palindrome lines read the same forwards or backwards.\n\nThe digits in a cage must sum to the small clue in the top-left corner of the cage.\n\nOrthogonally adjacent cells do not sum to either 5 or 10.","solution":"429317658875426931361895247136958724542671893987243165698134572254789316713562489","constraints":["cage","custom","palindrome"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Orthogonally adjacent cells do not sum to either 5 or 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"2T2f9JmnpR","ctcId":1869,"ctcDifficulty":"MEDIUM","title":"Ziplock","author":"HalfBakedLunatic (David Workman)","rules":"• Normal sudoku rules apply. Cells an equal distance from the center of the Zipper lines must sum to the cell in the center of the line. Digits in cages must sum to the number in the corner of the cage.","solution":"249658731681347295357291486574132869812769543963485127426573918195826374738914652","constraints":["cage","zipper-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"Q7Bf3BHbfP","ctcId":1870,"ctcDifficulty":"MEDIUM","title":"Dune: The Mentat's Diversion","author":"HalfBakedLunatic","rules":"Normal sudoku rules apply.  Digits cannot repeat in cages which sum to the total shown.  Digits along a Sapho Juice colored thermometer must increase from the bulb end. Digits in cells separated by a black dot must be in a 2:1 ratio.","solution":"365917824427368195189542763671834952592671348843295671756123489938456217214789536","constraints":["cage","kropki","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"3a0z38vzgq","ctcId":1871,"ctcDifficulty":"MEDIUM","title":"A Few Glasses O' Bubbly","author":"HalfBakedLunatic","rules":"• Normal Sudoku Rules Apply\n• Digits along a Green Champagne Flute must differ by at least 5\n• Digits along an Orange Champagne Flute Line must differ by at least 4\n• Box borders divide the Blue Champagne Flute into segments with the same sum\n• The Purple base of the glasses must be a contiguous set of digits in any order\n• Cells separated by a Champagne bubble must contain adjacent digits\n• Quad circles show the digits that are in the four cells","solution":"943127658567894132182563947639275481421638795875941326216459873354786219798312564","constraints":["dutch-whispers","german-whispers","kropki","quadruple","region-sum-line","renban"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"4xlxw5wmad","ctcId":1873,"ctcDifficulty":"VERY HARD","title":"Under Pressure","author":"FullDeck and Missing a Few Cards","rules":"- Normal sudoku rules apply.\n- Low Pressure Gauges: Numbers inside a BLUE low pressure gauge indicate how many digits STRICTLY GREATER than that number appear in the up to 8 cells surrounding the gauge.\n- High Pressure Gauges: Numbers inside a RED high pressure gauge indicate how many digits STRICTLY SMALLER than that number appear in the up to 8 cells surrounding the gauge.","rulesClarified":"Normal sudoku rules apply.\n\nEach gauge sits in one cell. The gauge's own cell is not counted. The cells that count are the up to 8 cells touching the gauge's cell, including diagonal neighbours. A gauge on an edge or corner has fewer than 8.\n\nA blue low pressure gauge shows a number. That number is how many of the counted cells contain a digit strictly greater than it.\n\nA red high pressure gauge shows a number. That number is how many of the counted cells contain a digit strictly smaller than it.\n\nEach counted cell counts once.","solution":"912364578574128639386795214123547896768932145459681327297853461831476952645219783","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Low Pressure Gauges: Numbers inside a BLUE low pressure gauge indicate how many digits STRICTLY GREATER than that number appear in the up to 8 cells surrounding the gauge. - High Pressure Gauges: Numbers inside a RED high pressure gauge indicate how many digits STRICTLY SMALLER than that number appear in the up to 8 cells surrounding the gauge.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"8jdTTqGbgR","ctcId":1877,"ctcDifficulty":"HARD","title":"Knighten","author":"Testarossa","rules":"Normal sudoku rules apply. Cells separated by a knight's move (in chess) cannot contain the same digit. In each cage, digits cannot repeat and must sum to 10.","solution":"179364582365289471284571936591637824632148759847952163456893217728416395913725648","constraints":["antiknight","cage"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"n4qHMLbtTd","ctcId":1879,"ctcDifficulty":"MEDIUM","title":"Limbo","author":"Testarossa","rules":"1) Shikaku:\nDivide the grid into rectangular or square pieces. Each piece must contain exactly one digit, that shows its area.\n2) Star battle:\nPlace stars into the grid, so that each shikaku rectangle/square has one, and each row/column/3x3 box contains two of them. Stars can't be adjacent, even diagonally.\n3) Masyu:\nStars from star battle act as masyu circles - if it has a digit in the same cell, it is black; if not - it's white.\nDraw the single non-branching non-intersecting loop.\nThe loop should pass through all circles in such a way that:\nWhite circles must be passed through in a straight line, but the loop must turn in the previous and/or the next cell.\nBlack circles must be turned upon and the loop must travel straight through the next and the previous cell.\n4) Killer sudoku:\nNormal sudoku rules apply.\nGroups of cells not visited by the masyu loop act as killer cages.\nThose groups and killer cages already drawn in the grid must all sum to the same total.","solution":"618729534495361278723548196986257341154983627372416985849635712267194853531872469","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c16"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into rectangular or square pieces. Place stars into the grid, so that each shikaku rectangle/square has one, and each row/column/3x3 box contains two of them. Draw the single non-branching non-intersecting loop. Groups of cells not visited by the masyu loop act as killer cages.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c9","c15"]}]},{"id":"iutvqv1ht8","ctcId":1880,"ctcDifficulty":"HARD","title":"My First Soduko","author":"Marty and Nordy (aged 5)","rules":"Normal soduko rules apply. We have drawed a lot of clues, to mak it a really good puzzle. We have even put some red clues outside the grid. All clues are telling the truth accept for 5 of them, which are lying.  (if a clue doesnt completly work like it should, then it is lying.) Can you find the 5 lying clues?\n\nAll the clues are standdard rules:\n\nA pink line is a rembam, this means that all the digits on there are in a seqeunce, maybe like 4567, but they dont repeat and the seqeunce can be in a diffrent order like 5746.\n\nGreen means a German Shhhhh line. All of ajaxent digits on green lines must be at least 5 diffrent from eachother. Like 6 and 1 is ok but 4 and 2 is not ok.\n\nRed CLues outside the grid pointing inwards diloganly give the sum of the digits on that dialagonal.\n\nIf there is a dashed line cage then this is a KILLER! cage. anythign you rite in there cant repeat, and must sum to what the small number in the corner says.\n\nDigits along the light grey thermomometer must increase as you move away from the end with the blub.\n\nDitgits on a light blue arrow sum to whats in the circle.\n\nDark grey lines are Ten Lines which is an idea we stole from zetamaths. A ten line is made of groups of adjaxent digits which do'nt overlap and each group sums to 10. EG: 28532 can be split into two groops which sum to 10.\n\nDigits with white dot means they are consticutive like 3 and 4 are.\n\nA little purple arrow sits between two digits and points at the smaller one. Eg: 2 is smaller than 8.\n\nDigits with an X sum to 10. Eg: 3 and 7.\n\nFinaly! There is some caracters we drawed outside the grid. What they are saying (in red) counts as clues too, so remember thjey might be lying! lol","solution":"697258143824139657135476892916827534482563971753941268378615429261794385549382716","constraints":["XV","arrow","cage","custom","german-whispers","inequality","kropki","little-killer","renban","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c21"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All clues are telling the truth accept for 5 of them, which are lying.  (if a clue doesnt completly work like it should, then it is lying.) A ten line is made of groups of adjaxent digits which do'nt overlap and each group sums to 10. What they are saying (in red) counts as clues too, so remember thjey might be lying! lol","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c16","c25"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c19"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c18"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]}]},{"id":"myxmj3f1g9","ctcId":1882,"ctcDifficulty":"HARD","title":"Copycat","author":"Phistomefel","rules":"1. Normal Sudoku rules apply.\n2. Lines: The grey line is a palindrome, the lavender line is a Zipper line.\n3. Copycat: The two lines have the same composition of digits. E.g. if one line has two 3s, five 4s and a 9, then so does the other. The order of the digits is not necessarily the same on the two lines.\n4. Kropki: A white dot between two cells indicates that their values differ by 1. A black dot between two cells indicates that their values are in a 2:1 ratio. Not necessarily all dots are drawn in.\n5. Palindrome line: The digits on a palindrome line read the same in both directions.\n6. Zipper line: Digits an equal distance from the center of a zipper line must sum to the digit in the middle of that line.","solution":"276941358495238167138765249329486571547312986861597432983174625654829713712653894","constraints":["custom","kropki","palindrome","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"3. Copycat: The two lines have the same composition of digits. E.g. if one line has two 3s, five 4s and a 9, then so does the other. The order of the digits is not necessarily the same on the two lines.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"JDjq4DqQb3","ctcId":1883,"ctcDifficulty":"MEDIUM","title":"Jewelled Band","author":"99% Sneaky","rules":"Normal sudoku rules apply. Digits in a cage cannot repeat and must sum to the small clue in the top left corner of the cage. Digits in a white circle must appear at least once in the four cells touching the circle.","solution":"751923486863417259249658713917546832485132967326879541138795624594261378672384195","constraints":["cage","quadruple"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"b2qP7TL9D3","ctcId":1884,"ctcDifficulty":"MEDIUM","title":"Mishaps 1: Amplification","author":"99% Sneaky","rules":"Normal sudoku rules apply. Digits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. The sum of the digits on the 7 colored 3-cell lines is equal to double the sum of the digits along the white line in row 7. The prism (grey line) is cosmetic and does not affect the puzzle.","solution":"321645897946781523875923416489312675563497281217856349798564132632178954154239768","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits on the 7 colored 3-cell lines is equal to double the sum of the digits along the white line in row 7.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"TL9FdFpj3d","ctcId":1885,"ctcDifficulty":"MEDIUM","title":"Lilliputian Arrows","author":"99% Sneaky","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in the attached circle. Cages show their sums.","solution":"316458729587293164249671853935847612864125397172936485728514936693782541451369278","constraints":["arrow","cage"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"MbhjHdTD4D","ctcId":1886,"ctcDifficulty":"MEDIUM","title":"Mountaineering","author":"99% Sneaky","rules":"Normal sudoku rules apply. Digits may not repeat along the marked diagonal. Cells that share the same relative position in 3x3 boxes may not contain the same digit (eg if there is a 1 in the top left cell of Box 1 there may not be a 1 in the top left cell of any other 3x3 box.) Digits in cages sum to the small clue in the top-left corner of the cage.","solution":"413928576872635419965174328391857642748296153256413897184769235527381964639542781","constraints":["cage","diagonal","disjoint-groups"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"mvuj15iimm","ctcId":1887,"ctcDifficulty":"MEDIUM","title":"The Positive Diagonal","author":"99% Sneaky","rules":"Normal sudoku rules apply.\n\nDigits along an arrow sum to the digit in the attached circle. Arrows do not branch or overlap. Digits along a green line must have a difference of at least 5.\n\nDigits separated by a black dot are in a 1:2 ratio (i.e. one is double the other). Digits separated by a white dot are consecutive. Not all dots are necessarily given. \n\nDigits may not repeat along the marked diagonal.\n\nBoxes 1 and 9 are clones, meaning each digit is in the same relative position in both boxes (i.e. if R1C1 is 8, R7C7 must also be 8).\n\nAdditionally the grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells, possibly revealing more clues.","solution":"253179648716854392489263571374691825968527134521348967197486253842935716635712489","fogLight":"R1C1,R1C2,R2C1,R8C9,R9C8,R9C9","constraints":["arrow","clone","diagonal","fog","german-whispers","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"vsuh3lbq7r","ctcId":1888,"ctcDifficulty":"MEDIUM","title":"Giant's Deep","author":"99%Sneaky","rules":"Normal Sudoku rules apply. \nDigits along arrows sum to the digit in the attached circle. \nDigits in a grey square are even. Digits in grey circles are odd.\nDigits in cages sum to the number in the top-left corner of the cage. \nDigits along thermometers strictly increase from the bulb end. \nDigits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio (re: one is double the other). Not all dots (for both colors) are given.","solution":"593261847164758923872439516715892364426375189938614275649123758257986431381547692","constraints":["arrow","cage","even","kropki","odd","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7","c8"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"aae5b3ci1m","ctcId":1890,"ctcDifficulty":"HARD","title":"Fillomino sudoku","author":"Aron Lidé (Aspartagcus)","rules":"Sudoku: Fill each row, column and 3x3 box with the digits 1-9.\nFillomino: Divide the grid into regions of orthogonally connected cells. Two regions of the same size may not share an edge. Each region must contain at least one circle. Circles must contain the digit equal to the size of the regions they are in.","solution":"638954721197823564254761389582396147743512698961487253425178936376249815819635472","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Fillomino: Divide the grid into regions of orthogonally connected cells. Each region must contain at least one circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"t1fwee4bpz","ctcId":1891,"ctcDifficulty":"MEDIUM","title":"Crac-King the Easter Eggs","author":"olima","rules":"Normal Sudoku rules apply. Digits a King's move (in chess) apart must be different.\nAdjacent digits on a green line differ by at least 5.\nBlue lines have the same sum in each box they visit.\nBlack dot digits are in a 1:2 ratio, white dot digits are consecutive. Not all dots are necessarily given.","solution":"263814957947653218518279436639582174781436592425791863896345721172968345354127689","constraints":["antiking","german-whispers","kropki","region-sum-line"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"x2k2gvzqw4","ctcId":1892,"ctcDifficulty":"VERY HARD","title":"Seesaw","author":"Celery","rules":"Normal sudoku rules apply. \n\nDigits in a cage sum to the total in the top left corner (if given). Digits cannot repeat within a cage.","solution":"872153946693784521514629387326415798951378462748962153469837215135246879287591634","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"gomrgn0npb","ctcId":1893,"ctcDifficulty":"MEDIUM","title":"Doubling Loop","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nDigits along an arrow must sum to the digit in that arrow's bulb.\n\nDraw a one-cell-wide loop of orthogonally connected cells.  The loop may not touch itself, not even diagonally.\n\nDigits on the loop count as double their value for the purposes of arrows.","solution":"912354768683279154457186239174592386296843517835617942328765491769431825541928673","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits along an arrow must sum to the digit in that arrow's bulb.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally. Digits on the loop count as double their value for the purposes of arrows.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5"]}]},{"id":"2hw7t4w2lm","ctcId":1894,"ctcDifficulty":"MEDIUM","title":"Project Africa","author":"ThePedallingPianist","rules":"Normal sudoku rules apply; i.e. place the digits 1-9 once each in every row, column and 3x3 box.\n\nThe route (red line) is a German Whisper; i.e. adjacent digits on the line must differ by at least 5.\n\nOn land, \"hotter\" cells contain higher digits; i.e. orange cells contain larger digits than orthogonally adjacent yellow cells, which contain larger digits than orthogonally adjacent green cells.\n\nThe four cages must be filled with four important numbers from Russ Cook's journey, read left to right. The solver must decide which number goes in which cage:\n\n352 (days on mission);\n19 (million steps, at least);\n16 (countries/cells passed through);\n? (total no. of \"1s and 2s\" on the route*)\n\n(*\"1s and 2s\" is how Russ refers to left foot steps and right foot steps)","solution":"752164938138972546964835217529386471473251689681749352316597824295418763847623195","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On land, \"hotter\" cells contain higher digits; i.e. orange cells contain larger digits than orthogonally adjacent yellow cells, which contain larger digits than orthogonally adjacent green cells. The four cages must be filled with four important numbers from Russ Cook's journey, read left to right.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"magjthb2bw","ctcId":1896,"ctcDifficulty":"MEDIUM","title":"Assembly","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nDigits in a cage sum to the indicated total. Cells that half-appear in a cage only contribute half their value to its sum. Cells that quarter-appear in a cage only contribute a quarter of their value to its sum.\n\nDigits appear at most once in the same cage (half-appearing twice counts as appearing once).","solution":"612839754743152698958467213287943561594216837361785429479621385125378946836594172","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a cage sum to the indicated total.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells that half-appear in a cage only contribute half their value to its sum. Cells that quarter-appear in a cage only contribute a quarter of their value to its sum.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"nwvlk5shkh","ctcId":1897,"ctcDifficulty":"MEDIUM","title":"Circuit 8","author":"Riffclown","rules":"• Normal Sudoku rules apply.\n• Thermo: Digits on thermos must increase from the bulb to the tip.","solution":"819364725572189436463527981356912847724853169198746253941638572235471698687295314","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"48bg9rh8jm","ctcId":1902,"ctcDifficulty":"HARD","title":"Who's the man in the mirror ?","author":"Christounet","rules":"Normal sudoku rules apply. The values of the cells in a cage must sum to the small clue in the top left corner pf the cage. Digits may not repeat in cages (but values may repeat). In every row, column and 3x3 box, is a “mirrored digit”. It takes the value opposite to its own value on the 1-9 scale. (In other words, 1 takes the value of 9, 2 the value of 8... 9 the value of 1.) Each digit 1-9 is mirrored once.","solution":"635497812129583647874261395951738426463152978782946153518374269296815734347629581","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The values of the cells in a cage must sum to the small clue in the top left corner pf the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"ay6r6mmu5w","ctcId":1905,"ctcDifficulty":"HARD","title":"Close Enough","author":"IcyFruit","rules":"Normal sudoku rules apply. \nDigits may not repeat within a cage. Cage clues show the sum of the digits in that cage, rounded to the nearest multiple of 5.","rulesClarified":"Normal sudoku rules apply.\n\nDigits may not repeat within a cage.\n\nEach cage clue is the total of the digits in that cage, rounded to the nearest multiple of 5. The exact totals are not given, so each clue gives a range. A clue of 15 means the total is 13, 14, 15, 16 or 17. A clue of 5 means the total is 3, 4, 5, 6 or 7.","solution":"693157842857243169124698537715486923368972415249531678932864751481725396576319284","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Cage clues show the sum of the digits in that cage, rounded to the nearest multiple of 5.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"pn2nbdselm","ctcId":1909,"ctcDifficulty":"MEDIUM","title":"Transmission","author":"Qodec","rules":"- Sudoku: Each row, column, and region indicated by thick borders in the grid must contain the digits 1 to 9 once each.\n- Parity counter lines: The digit on one endpoint of a blue line indicates the number of even digits on the line while the digit on the other end indicates the number of odd digits on the line. This includes digits on the endpoints.\n- Consecutive pairs: A white dot between two cells means that the values of those cells must be consecutive. Not all dots are necessarily given.","solution":"734895216982163457156724389417932568398516724625478193873259641269341875541687932","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Parity counter lines: The digit on one endpoint of a blue line indicates the number of even digits on the line while the digit on the other end indicates the number of odd digits on the line. This includes digits on the endpoints.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"4qt4n1bnz3","ctcId":1910,"ctcDifficulty":"MEDIUM","title":"Murder on the Zipline Express","author":"FullDeck and Missing a Few Cards","rules":"- Standard sudoku rules apply: The digits 1 through 9 appear in every row, column, and box.\n- Cages: Digits in cages cannot repeat and must sum to the value shown in the upper left corner of the cage.\n- Zipper Line: Along Zipper lines, pairs of digits equidistant from the center of the line have the same sum. For Zipper lines of odd length, that sum is the central digit on the line.","solution":"612743859597182634438596721943267185256418973871359462329871546185624397764935218","constraints":["cage","zipper-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"4rd0wbkq84","ctcId":1912,"ctcDifficulty":"EASY","title":"Caged Arrows 2","author":"Eric Rathbun","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. Digits cannot repeat within a cage. Cells separated by a white dot contain consecutive digits. Cells separated by a black dot contain digits in a 1:2 ratio (ie one digit will be double the other). Not all possible dots are given.","rulesClarified":"Normal sudoku rules apply.\n\nDigits along an arrow must sum to the digit in that arrow's circle.\n\nDigits cannot repeat within a cage.\n\nA white dot sits on the edge between two neighbouring cells. The two digits it joins are consecutive (one is exactly one more than the other).\n\nA black dot sits on the edge between two neighbouring cells. The two digits it joins are in a 1:2 ratio: one digit is double the other.\n\nNot every possible dot is drawn. A pair of neighbouring cells with no dot between them has no dot rule.","solution":"243586971965271834781439526159627348827354619436918752618743295392165487574892163","constraints":["arrow","cage","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]}]},{"id":"PH9RM439TG","ctcId":1913,"ctcDifficulty":"MEDIUM","title":"Record Highs","author":"ViKingPrime","rules":"Normal sudoku rules apply. Along thermometers, digits must increase from the bulb end; however the digit 1 may be considered as having the value of 1 or 10.","solution":"359628147148537926267941835936152784825479613714386592683295471592714368471863259","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Along thermometers, digits must increase from the bulb end; however the digit 1 may be considered as having the value of 1 or 10.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"h6Mddj29b8","ctcId":1914,"ctcDifficulty":"HARD","title":"Bloodcursed Arrows","author":"ViKingPrime","rules":"Normal sudoku rules apply. Digits along an arrow sum to the value in its circle. There are 9 Vampire cells contained within the grid which are a set of the digits from 1-to-9. Each row, column and box contains exactly one Vampire cell. 9 Prey cells in the grid follow the same rules as the Vampire cells. A cell may have only one of these roles. For Arrows/Circles: Prey cells contribute no value; Vampire cells contribute the sum of the digits in the Vampire cell and the Prey cell within the same box.","solution":"627483915138569472549721368864152793752936841391874256973215684416398527285647139","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits along an arrow sum to the value in its circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There are 9 Vampire cells contained within the grid which are a set of the digits from 1-to-9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9pdTNMfMPF","ctcId":1915,"ctcDifficulty":"HARD","title":"Reversing Valve","author":"ViKingPrime","rules":"The value of digits within a cage must sum to the small clue in the top-left corner of the cage. Digits must not repeat within a cage (but values may repeat). The value of digits along a thermometer must increase from the bulb to the tip. There are 9 Hot cells contained within the grid comprised of a set of the digits 1-to-9. Each row, column and box contains exactly one Hot cell. There are nine 9 Cold cells contained within the grid following the same rules as the Hot cells. A cell may have only one of these roles. For cages and thermometer values, Hot cells increase the value of the contained digit by 1; and Cold cells decrease the value of the contained digit by 1.","rulesClarified":"Each cell is either Hot, Cold, or neither. A cell may have only one of these roles.\n\nThere are 9 Hot cells. Their digits are the digits 1 to 9, each used once. Each row, column and box contains exactly one Hot cell.\n\nThere are 9 Cold cells. They follow the same rules as the Hot cells: their digits are the digits 1 to 9, each used once, and each row, column and box contains exactly one Cold cell.\n\nHot and Cold cells change the value of their digit wherever a value is used, which is in cages and on thermometers. A Hot cell adds 1 to its digit. A Cold cell takes 1 away from its digit. Any other cell's value is just its digit.\n\nCages: the values in a cage must add up to the small clue in its top-left corner. Digits in a cage must not repeat, though values may.\n\nThermometers: the values along a thermometer must increase from the bulb (the circle at its start) to the tip.","solution":"389426715254317986671895324532984167148763592796251438965142873413678259827539641","constraints":["cage","custom","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The value of digits within a cage must sum to the small clue in the top-left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c1"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There are 9 Hot cells contained within the grid comprised of a set of the digits 1-to-9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"The value of digits along a thermometer must increase from the bulb to the tip.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"bgDhfmrfN4","ctcId":1916,"ctcDifficulty":"MEDIUM","title":"Trick Play","author":"ViKingPrime","rules":"Normal sudoku rules apply. Each of the following standard clue types occurs exactly three times in the grid: Arrow, Circle, Dots, Odd/Even, X/V and Zipper . For each of those clue types, exactly two of the appearances of that clue are correct and the other is incorrect. The 'standard' clue types mentioned above are as follows: White dots: Cells separated by a white dot must contain consecutive digits. Black dots: Cells separated by a black dot must be in the ratio of 1:2 (so one digit must be double the other). Arrow: Digits on an arrow must sum to the digit in that arrow's grey circle. Xs: Cells separated by an X must contain digits summing to 10. Vs: Cells separated by a V must contain digits summing to 5. Odds: Cells containing an opaque grey circle must contain an odd digit. Evens: Cells containing an opaque grey square must contain an even digit. Circle: A digit in a purple circle indicates exactly how many purple circles contain that digit. Zipper: digits an equal distance from the centre of a blue line must sum to the digit in the middle of that line.","solution":"485693721732415869619782435261839574954176382378524916523967148897241653146358297","constraints":["XV","arrow","custom","even","kropki","odd","zipper-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"Xs: Cells separated by an X must contain digits summing to 10. Vs: Cells separated by a V must contain digits summing to 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7","c8"]},{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Arrow: Digits on an arrow must sum to the digit in that arrow's grey circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Circle: A digit in a purple circle indicates exactly how many purple circles contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"even","type":"even","variant":"modified","modifiers":[],"params":null,"note":"Evens: Cells containing an opaque grey square must contain an even digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"The 'standard' clue types mentioned above are as follows: White dots: Cells separated by a white dot must contain consecutive digits. Black dots: Cells separated by a black dot must be in the ratio of 1:2 (so one digit must be double the other).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4","c5"]},{"slug":"odd","type":"odd","variant":"modified","modifiers":[],"params":null,"note":"Odds: Cells containing an opaque grey circle must contain an odd digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"zipper-line","type":"zipper-line","variant":"modified","modifiers":[],"params":null,"note":"Zipper: digits an equal distance from the centre of a blue line must sum to the digit in the middle of that line.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]}]},{"id":"7m8l0f0m4a","ctcId":1918,"ctcDifficulty":"VERY HARD","title":"Now the People Will Know We Were Here","author":"ViKingPrime","rules":"RULES:\n\nNormal Sudoku rules apply.\n\n• Kropki: White dots separate two cells containing consecutive values; Black dots separate two cells where one value is double the other [1:2].\n• Renban (pink): Values along a Renban line form a set of consecutive, non-repeating values in any order.\n• Nabner (gold): Values along a Nabner line form a set of non-consecutive, non-repeating values in any order (e.g. if a cell of value 3 appears on a Nabner line, then values of 2 and 4 cannot appear).\n\nMODIFIERS:\n\n• Hot/Cold: There are 9 Hot cells contained within the grid comprising a set of the digits from 1-to-9. Each row, column and box contains exactly one Hot cell. There are nine 9 Cold cells contained within the grid following the same rules as the Hot cells. A cell may have only one of these roles.\n\nfor Kropki/Renban/Nabner value(s)\nHot cells increase the value of the contained digit by 1.\nCold cells decrease the value of the contained digit by 1.","solution":"861735492392468751745192638138654279427319586956287143284971365513846927679523814","constraints":["kropki","nabner-line","renban"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"• Kropki: White dots separate two cells containing consecutive values; Black dots separate two cells where one value is double the other [1:2].","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"nabner-line","type":"nabner-line","variant":"modified","modifiers":[],"params":null,"note":"• Nabner (gold): Values along a Nabner line form a set of non-consecutive, non-repeating values in any order (e.g. if a cell of value 3 appears on a Nabner line, then values of 2 and 4 cannot appear).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"• Renban (pink): Values along a Renban line form a set of consecutive, non-repeating values in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"6QfQ4hB79q","ctcId":1919,"ctcDifficulty":"MEDIUM","title":"Anti Ratio Miracle","author":"Jobo","rules":"Normal sudoku rules apply. Any two orthogonally adjacent cells cannot contain digits in a 1:2, 1:3, 1:4 or 1:5 ratio. Every horizontal set of three orthogonally connected cells within any 3x3 box is a modular sequence (i.e. must contain one digit from [1 4 7], one digit from [2 5 8] and one digit from [3 6 9]). Every vertical set of three orthogonally connected cells within any 3x3 box is an entropic sequence (i.e. must contain one digit from [1 2 3], one digit from [4 5 6] and one digit from [7 8 9]). There are no 3's in a corner of the grid.","solution":"237198546546723891891654327189465273654372918723819465372981654465237189918546732","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any two orthogonally adjacent cells cannot contain digits in a 1:2, 1:3, 1:4 or 1:5 ratio. Every horizontal set of three orthogonally connected cells within any 3x3 box is a modular sequence (i.e. must contain one digit from [1 4 7], one digit from [2 5 8] and one digit from [3 6 9]). Every vertical set of three orthogonally connected cells within any 3x3 box is an entropic sequence (i.e. must contain one digit from [1 2 3], one digit from [4 5 6] and one digit from [7 8 9]). There are no 3's in a corner of the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]}]},{"id":"RD6TD6R2jj","ctcId":1920,"ctcDifficulty":"MEDIUM","title":"Barbed Wire","author":"Jobo","rules":"Normal sudoku rules apply. Digits cannot repeat on a marked diagonal. Digits along an arrow sum to the digit in the attached circle.","solution":"859237146731469528264851793643185279127694835985372461578923614316748952492516387","constraints":["arrow","diagonal"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"N4nH3m2ftL","ctcId":1921,"ctcDifficulty":"MEDIUM","title":"Ferris Wheel","author":"Jobo","rules":"Normal sudoku rules apply. Along thermometers, digits must increase from the bulb end. Digits on between lines must be between the digits in the attached circles. Adjacent digits along the green wheel (line) must differ by at least 5. Digits along a purple line are a set of consecutive, non-repeating digits in any order. Lines go straight where they cross. Digits separated by a white dot must be consecutive. Digits separated by an X must sum to 10.","solution":"593271486287643951614958237175834692429765813368129745741382569956417328832596174","constraints":["XV","between-line","german-whispers","kropki","renban","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"tGd8nT7R6P","ctcId":1922,"ctcDifficulty":"MEDIUM","title":"Radical Rainbow","author":"Jobo","rules":"Normal sudoku rules apply. Digits in thick bordered squares must be equal to the square root of the 2-digit number read from top to bottom in the corresponding cage. All squares must contain a different digit. Every square root sign also represents a different constraint. Parity line (red): Adjacent digits along the red line must alternate in parity (odd/even). Entropic line (orange): A set of three sequential cells along the orange line must contain a low [123], middle [456], and high [789] digit. German Whisper line (green): Adjacent digits along the green line must differ by at least 5. Renban (purple): Digits along the purple line are a set of consecutive, non-repeating digits in any order. Region Sum line (blue): Along a blue line, each line segment within a different 3x3 box must sum to the same total. Thermometer (grey): Digits along the thermometer must increase from the bulb to the tip (which are always at the ends of the line); which end is the bulb and which the tip must be deduced.","rulesClarified":"Normal sudoku rules apply. All squares must contain a different digit.\n\nDigits in thick bordered squares must equal the square root of the two-digit number read from top to bottom in the corresponding cage.\n\nEvery square root sign also represents a different constraint.\n\nParity line (red): adjacent digits along the red line alternate between odd and even.\n\nEntropic line (orange): every set of three sequential cells along the orange line contains a low digit (1, 2 or 3), a middle digit (4, 5 or 6) and a high digit (7, 8 or 9).\n\nGerman whisper line (green): adjacent digits along the green line differ by at least 5.\n\nRenban line (purple): digits along the purple line are consecutive and non-repeating, in any order.\n\nRegion sum line (blue): along the blue line, each line segment within a different 3x3 box must sum to the same total.\n\nThermometer (grey): digits increase from the bulb to the tip. The bulb and the tip are the two ends of the grey line; which end is which is for you to work out.","solution":"285174693714963285369582417942315876158697324673248159896451732521736948437829561","constraints":["custom","entropic-line","german-whispers","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in thick bordered squares must be equal to the square root of the 2-digit number read from top to bottom in the corresponding cage. All squares must contain a different digit. Parity line (red): Adjacent digits along the red line must alternate in parity (odd/even).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Thermometer (grey): Digits along the thermometer must increase from the bulb to the tip (which are always at the ends of the line); which end is the bulb and which the tip must be deduced.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]}]},{"id":"fy135l7its","ctcId":1923,"ctcDifficulty":"MEDIUM","title":"Fibonacci","author":"Jobo","rules":"Normal sudoku rules apply.\n\nDigits cannot repeat on either diagonal\n\nDigits separated by a white dot must be consecutive.\nDigits separated by a black dot must be in a 1:2 ratio.\nNot all dots are given.","solution":"681345792429687513375192486132456879846973251957821364763218945298564137514739628","constraints":["diagonal","kropki"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"HGGjr3NDm4","ctcId":1924,"ctcDifficulty":"MEDIUM","title":"Thermo Sum Lines","author":"Jobo","rules":"Normal sudoku rules apply. All thermometers are slow thermometers, as well as region sum lines. ie Digits along these thermometers must either stay the same or increase from the bulb end; and box borders divide each blue line into segments with the same sum. eg r8c2 + r7c3 = r6c4. Digits separated by a white dot must be consecutive. Not all dots are given.","solution":"859241673473658192126937845765329481942815736318764529284196357637582914591473268","constraints":["kropki","region-sum-line","thermometer"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7bprG39P87","ctcId":1926,"ctcDifficulty":"VERY HARD","title":"Crowd Control","author":"Allagem","rules":"Normal sudoku rules apply. Digits along grey lines between two circles must have values between those circles. Adjacent digits on a green line differ by 5 or more. Cells separated by the white dot must be consecutive. Cells separated by the black dot have a 1:2 ratio. The inequality sign points to the smaller cell.","solution":"318654297627193854945728361154237689836941572792586413583419726479862135261375948","constraints":["between-line","german-whispers","inequality","kropki"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]}]},{"id":"pjdTmP6JRt","ctcId":1927,"ctcDifficulty":"MEDIUM","title":"Eye of Agamotto","author":"Allagem","rules":"Normal sudoku rules apply. Adjacent digits along a green line must differ by at least 5. A digit in column 1 indicates the column in which the digit 1 appears in that row. Columns 5 and 9 have the same rule for the digits 5 and 9 respectively. (For example, an 8 in R7C1 tells you there's a 1 in R7C8. A 3 in R2C5 tells you there's a 5 in R2C3.)","solution":"728394165391865742654721398182479536936258471475136829217983654863542917549617283","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in column 1 indicates the column in which the digit 1 appears in that row.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"78hbnfQjPm","ctcId":1928,"ctcDifficulty":"MEDIUM","title":"Borromean Rings","author":"Allagem","rules":"Normal sudoku rules apply. Digits in cages sum to the clue in the corner of the cage. Adjacent digits on the red ring have different parity (odd/even). Adjacent digits on the green ring differ by at least 5. Digits on the blue line sum to the same value in each region the ring passes through.","solution":"318547962562891437947326185724619853136785249895234671271458396689173524453962718","constraints":["cage","custom","german-whispers","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent digits on the red ring have different parity (odd/even).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"MpdTnQ4TfP","ctcId":1929,"ctcDifficulty":"MEDIUM","title":"Pillboxes","author":"Allagem","rules":"Normal sudoku rules apply. Digits inside a cage do not repeat and sum to the small clue in the corner of the cage. All cages additionally act as fortresses – each digit inside a cage is greater than its orthogonally adjacent neighbors outside the cage.","solution":"869423157375916482421785369213549876648372915597168243782694531956831724134257698","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All cages additionally act as fortresses – each digit inside a cage is greater than its orthogonally adjacent neighbors outside the cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"fFBPDgBDFD","ctcId":1930,"ctcDifficulty":"MEDIUM","title":"Allergic Reaction","author":"Allagem","rules":"Normal sudoku rules apply. Digits on a thermometer increase from bulb to tip. The orange circle contains an odd digit. No orthogonally adjacent pair of digits sums to 10.","solution":"871294365496357218352618974615729483247836159938145726589472631763981542124563897","constraints":["custom","odd","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No orthogonally adjacent pair of digits sums to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"b7jGb3bhDJ","ctcId":1931,"ctcDifficulty":"MEDIUM","title":"Inner Harmony","author":"Allagem","rules":"Normal sudoku rules apply. Digits along a line must be strictly increasing in one direction or the other. Digits separated by the white dot are consecutive. Digits separated by the black dot are in a 2:1 ratio.","solution":"437612958869543721215897634398764215542189367671235489183976542754321896926458173","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits along a line must be strictly increasing in one direction or the other.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"gPdj8GrQrR","ctcId":1932,"ctcDifficulty":"MEDIUM","title":"Battle of Evermore","author":"kuraban","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow’s circle. Along a marked diagonal, digits cannot repeat. Cells separated by a single knight’s move (in chess) cannot contain the same digit.","solution":"946825137318796524257314698573281469482659371691473285769142853135968742824537916","constraints":["antiknight","arrow","diagonal"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"lbvymeu3as","ctcId":1933,"ctcDifficulty":"MEDIUM","title":"Earth Wurm","author":"Nordyttrio","rules":"Normal Sudoku rules apply.\n\nConstruct a one-cell-wide snake of orthogonally-connected cells whose two endpoints are given as circles. The snake cannot branch and cannot touch itself orthogonally, but may touch itself diagonally. Additionally:\n• All squares are on the snake.\n• A digit in a square gives the number of snake cells seen in all horizontal/vertical directions combined, including the cell with the square. Non-snake cells block the vision.\n• The snake acts as a German Whisper line—adjacent digits on the snake must have a difference of at least 5.","solution":"718439265253876194946251738361748952825193647497625381139587426684912573572364819","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Construct a one-cell-wide snake of orthogonally-connected cells whose two endpoints are given as circles. • A digit in a square gives the number of snake cells seen in all horizontal/vertical directions combined, including the cell with the square. Non-snake cells block the vision.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"seisxtsh0f","ctcId":1934,"ctcDifficulty":"HARD","title":"Killer Octopus","author":"ThePedallingPianist","rules":"Normal sudoku rules apply.\n\nDigits in a cage must sum to the given total.\n\nOctopus rules apply. I.e. draw 4 lines that must:\n- not cross or overlap anywhere except r5c5, where they all intersect;\n- have 180-degree rotational symmetry around r5c5;\n- visit exactly 2 cells on the edge of the grid, which are the beginning and end of the line;\n- all be the same length (in no. of cells passed through).\n\nThe 4 lines are \"Same Difference\" lines. I.e pairs of adjacent digits on a line must all have the same difference, though this difference may be different for different lines.","solution":"692173458543986172781425639265314897917258364438697521176542983329861745854739216","constraints":["cage","custom","same-difference-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Octopus rules apply.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"aem1ckhlvc","ctcId":1935,"ctcDifficulty":"HARD","title":"Cave of Killers","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nShade some cells so that the unshaded cells form a single orthogonally connected area, and each connected shaded region touches the grid boundary.\n\nA circle is always unshaded, and the digit in the circle equals the number of unshaded cells visible in a straight line from that cell, including the cell itself. Shaded cells obstruct the view.\n\nEach shaded region contains a corner clue which equals the sum of the digits in that region. Digits may not repeat in a shaded region, and the digit in the clued cell equals the size of the region.","rulesClarified":"Normal sudoku rules apply.\n\nShade some cells. The shaded cells must follow these rules:\n\nThe unshaded cells form one single area, connected edge to edge (orthogonally).\n\nEvery connected group of shaded cells touches the grid boundary.\n\nEach shaded region contains one corner clue. The clue is printed in one of the region's cells, and that cell is shaded. The clue equals the sum of all the digits in the region, including the digit in the clued cell. The digit in the clued cell equals the number of cells in the region. Digits may not repeat within a shaded region.\n\nCircles are never shaded. The digit in a circle equals the number of unshaded cells you can see from that circle along a straight line, counting the circle's own cell. A shaded cell blocks the view beyond it, and so does the edge of the grid.","solution":"215647839736289415489315276342578961597162348861934527953721684678453192124896753","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells so that the unshaded cells form a single orthogonally connected area, and each connected shaded region touches the grid boundary. A circle is always unshaded, and the digit in the circle equals the number of unshaded cells visible in a straight line from that cell, including the cell itself. Each shaded region contains a corner clue which equals the sum of the digits in that region. Digits may not repeat in a shaded region, and the digit in the clued cell equals the size of the region.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5","c6"]}]},{"id":"f0sif99oqy","ctcId":1936,"ctcDifficulty":"VERY HARD","title":"Double Date","author":"Malrog & Tallcat","rules":"Normal sudoku rules apply: place the digits 1-9 in each row, column and 3x3 region.\nNormal April 25th rules apply: two 2s, four 4s and five 5s are considered to have double their value, for the purposes of the following clues.\nNormal killer rules apply: digits must not repeat in cages, and the total sum of all values in the cage is given by the small number.\nNormal renban rules apply: digits along a purple line must form a set of consecutive non-repeating values.\nNormal arrow rules apply: values along an arrow sum to the value in the attached circle. Digits can repeat on arrows if allowed by other rules.","solution":"675839124843215796219674538768543912154928367392761845581496273437152689926387451","constraints":["arrow","cage","custom","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Normal arrow rules apply: values along an arrow sum to the value in the attached circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Normal killer rules apply: digits must not repeat in cages, and the total sum of all values in the cage is given by the small number.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Normal April 25th rules apply: two 2s, four 4s and five 5s are considered to have double their value, for the purposes of the following clues.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Normal renban rules apply: digits along a purple line must form a set of consecutive non-repeating values.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"NbqQ2HhP4P","ctcId":1938,"ctcDifficulty":"MEDIUM","title":"Miracle-Once Again","author":"Sumanta Mukherjee","rules":"Normal sudoku rules apply. (ie place the digits 1-9, once each, in every row, column & 3x3 box). A digit in a circle indicates how many circles contain that digit. Place some circles in the grid such that a box “m” contains exactly “m” number of circles. (Boxes are numbered in normal reading order so the top left box of the grid is box 1, the bottom right box is box 9, etc).  ie Box 1 should have 1 circle; box 3 should have 3 circles; etc. If a cell, eg R1C1, contains a circle then all the cells beneath it in the grid (8 cells in this case) must contain circles. No two 9s in the grid can be separated by a single Chess King’s or single Chess Knight’s move; but every 9 must share a diagonal with at least one other 9.","rulesClarified":"Normal sudoku rules apply: place the digits 1 to 9, once each, in every row, every column and every 3 by 3 box.\n\nBoxes are numbered in reading order, so the top left box is box 1 and the bottom right box is box 9.\n\nPlace some circles in the grid so that every box m contains exactly m circles. Box 1 has one circle, box 3 has three, and so on.\n\nIf a cell has a circle, then every cell below it in the same column must also have a circle. For example, a circle in R1C1 means all 8 cells beneath it in column 1 are circled.\n\nA digit in a circle tells you how many circles contain that digit.\n\nNo two 9s in the grid may be a single chess king's move or a single chess knight's move apart. Every 9 must share a diagonal with at least one other 9.","solution":"852741639741639528639528417528417396417396285396285174285174963174963852963852741","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle indicates how many circles contain that digit. Place some circles in the grid such that a box “m” contains exactly “m” number of circles. (Boxes are numbered in normal reading order so the top left box of the grid is box 1, the bottom right box is box 9, etc).  ie Box 1 should have 1 circle; box 3 should have 3 circles; etc. If a cell, eg R1C1, contains a circle then all the cells beneath it in the grid (8 cells in this case) must contain circles. No two 9s in the grid can be separated by a single Chess King’s or single Chess Knight’s move; but every 9 must share a diagonal with at least one other 9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]}]},{"id":"nn9ohqnsnz","ctcId":1939,"ctcDifficulty":"HARD","title":"Gouge Away","author":"Math Pesto","rules":"Normal sudoku rules apply.\nKiller: Digits cannot repeat inside a cage.\nQuads: Digits in a white circle must appear at least once each in the four surrounding cells.\nDouble Arrows: Digits on a line must have the same sum as the sum of the circles on the line's ends.","solution":"798643125512798436436251798241375869653189247879462513965814372127536984384927651","constraints":["cage","custom","quadruple"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Double Arrows: Digits on a line must have the same sum as the sum of the circles on the line's ends.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"azp64ejj1v","ctcId":1941,"ctcDifficulty":"HARD","title":"Parroty Lines","author":"Michael Lefkowitz and Marty Sears","rules":"Normal Sudoku rules apply.\n\nPARROTY LINES - A 'word' is a non-repeating sequence of digits, like '365', '24', or '7' (but not '747'). Each white Parroty Line consists of one or more copies of the same word. The digit on a parrot indicates the length of the word the parrot is saying. (Example: a parrot with a 3 could be saying “486 486”).\n\nCAGES - Digits in a cage sum to the attached tag.","rulesClarified":"Normal Sudoku rules apply.\n\nParroty Lines: a 'word' is a sequence of digits in which no digit repeats, such as 365, 24 or 7, but not 747.\n\nEach white Parroty Line is made of one or more copies of the same word, written one after another in order along the line. The digit on a parrot tells you how many digits the word has. For example, a parrot showing 3 could be on a line saying 486 486: two copies of the three-digit word 486.\n\nCages: the digits in each cage add up to the tag attached to that cage. The tag is the cage's total.","solution":"164359782382741659579682431435918276926537814817264593698473125743125968251896347","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each white Parroty Line consists of one or more copies of the same word. The digit on a parrot indicates the length of the word the parrot is saying.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"FdDGGJQf7R","ctcId":1942,"ctcDifficulty":"MEDIUM","title":"Disjunction Function","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nDigits may not repeat in a cage, and each cage sums to one of four distinct totals, which must be determined. Cages that share an edge must have different sums, and no digit may appear in more than one cage with the same sum.","rulesClarified":"Normal sudoku rules apply. Cage totals are not given.\n\nDigits may not repeat in a cage. Each cage sums to one of four distinct totals, which you must determine.\n\nCages that share an edge must have different sums.\n\nNo digit may appear in more than one cage with the same sum.","solution":"369817425274395861815462739428173596936528174751946382597231648143689257682754913","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cages that share an edge must have different sums, and no digit may appear in more than one cage with the same sum.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"pqttdq9MbQ","ctcId":1943,"ctcDifficulty":"HARD","title":"Molino de huevos","author":"Glum Hippo","rules":"Normal sudoku rules apply. Draw a snake (a one-cell wide path) into the grid which does not touch itself orthogonally. Areas not covered by the snake form 8 separate regions, one of each size 1-8 ('eggs') which, in turn, may touch one another diagonally but not orthogonally. Adjacent cells on a green line must contain one snake cell and one egg cell AND these cells’ digits must differ in value by at least 5. If a circle is in an egg, it gives the count of cells in the egg. If a circle is on the snake, it gives the number of snake cells “seen” by that circle, including itself (ie the number of contiguous snake cells extending horizontally and vertically from that cell, including itself).","rulesClarified":"Normal sudoku rules apply.\n\nDraw a snake: a single path of cells, one cell wide, that does not touch itself orthogonally.\n\nThe cells not covered by the snake form eight separate regions, called eggs, one of each size from 1 to 8. Eggs may touch each other diagonally but not orthogonally.\n\nGreen lines: on each green line, each pair of consecutive cells has one snake cell and one egg cell, and their digits differ by at least 5.\n\nA circle in an egg gives the number of cells in that egg.\n\nA circle on the snake gives the number of snake cells it sees, including its own cell. Count the contiguous snake cells extending horizontally and vertically from it, including itself.","solution":"176459823893216754542738196765894231318527469429361578284673915937145682651982347","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a snake (a one-cell wide path) into the grid which does not touch itself orthogonally. Areas not covered by the snake form 8 separate regions, one of each size 1-8 ('eggs') which, in turn, may touch one another diagonally but not orthogonally. Adjacent cells on a green line must contain one snake cell and one egg cell AND these cells’ digits must differ in value by at least 5. If a circle is in an egg, it gives the count of cells in the egg. If a circle is on the snake, it gives the number of snake cells “seen” by that circle, including itself (ie the number of contiguous snake cells extending horizontally and vertically from that cell, including itself).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6"]}]},{"id":"4LhtN674Br","ctcId":1946,"ctcDifficulty":"HARD","title":"Kroopki Wonderland","author":"MicroStudy","rules":"Normal sudoku rules apply. Digits separated by a white Kropki dot must be consecutive. Digits separated by a black Kropki dot must have a ratio of 1:2. Sets of digits separated by a white Kroopki ‘doot’ (the long, ellipse-looking things) must have their respective sums be consecutive. Sets of digits separated by a black Kroopki doot must have their respective sums be in a 1:2 ratio.","solution":"391257486258416793764893125683174952945362817127985634479521368516738249832649571","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Sets of digits separated by a white Kroopki ‘doot’ (the long, ellipse-looking things) must have their respective sums be consecutive. Sets of digits separated by a black Kroopki doot must have their respective sums be in a 1:2 ratio.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"czdmvpnot8","ctcId":1950,"ctcDifficulty":"MEDIUM","title":"Postcodes","author":null,"rules":"Normal sudoku rules apply. Digits in tabs must be placed within three cells of the narrow end of the tab (in that direction) in that row or column. A purple line contains a set of consecutive digits, in any order.","solution":"516792834732864591984513267367148952158329476249657318871235649693481725425976183","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in tabs must be placed within three cells of the narrow end of the tab (in that direction) in that row or column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"t884uj5ock","ctcId":1953,"ctcDifficulty":"MEDIUM","title":"High Impact","author":"Playmaker6174","rules":"Normal Sudoku rules apply: Every row, column and 3x3 box contains digits from 1 to 9 each once. \n\nWithin a cage, digits don't repeat and they must sum to the small number written in the top left of that cage.","solution":"718396542364528791952174386483217965521639478697485123836941257279853614145762839","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"el9sus7p0o","ctcId":1955,"ctcDifficulty":"HARD","title":"Pseudo Cluedo","author":"Marty Sears","rules":"A murder has been committed in Grid Mansion! Dr Awkward has been found dead, and there are six suspects. Can you work out who did it? \n\nNormal sudoku rules apply: place the digits 1-9 once each in every row, column, and 3x3 room.\n\nFIND YOUR PATH:\n• Draw a line passing through the centres of some cells to represent your journey from room to room, as you interrogate suspects and look for clues.\n• Your path must start at one of the lettered cells  (these are initials labelling the six suspects and the victim.) The path must finish at another lettered cell, and visit all the other lettered cells along the way. \n• Your path may move orthogonally or diagonally between cells, but may not cross itself.\n• You may not pass through a thick black wall; you can only get from room to room by travelling through the CENTRE of a doorway. For some doorways this may mean you have to go through diagonally.\n• The value of digits along your path must constantly increase or stay the same (like a slow thermometer). You must never move from a higher value to a lower value.\n\nPSEUDO CELLS:\n• Every row, column and room has exactly one 'pseudo cell'. These 9 pseudo cells contain the digits 1-9 once each.\n• For the purposes of your path, and for the weapon, victim and suspect rules below, the value of a pseudo cell equals its room number (regardless of which digit appears in the cell.) Rooms are numbered from 1-9 in reading order. Eg: room 1 is in the top left, room 7 is in the bottom left.\n\nWEAPONS:\n• Some weapons have been found, at locations marked by an X. The values of the two cells separated by a weapon sum to 10.\n\nTHE VICTIM:\n• Dr Awkward's body was found lying awkwardly in the doorway between rooms 4 and 7. This has been marked by a white outline. All that's known about the victim is that the values of his cells form a palindrome, reading the same from either end.\n\nTHE SUSPECTS:\n• Digits do not repeat in a killer cage (although their values might.) Each suspect has a particular trait:\n\n• Miss Parity (red) - values of orthogonally adjacent cell have a different parity (one is odd, the other is even).\n• Mrs Summer (blue) - a doorway divides her cells into two distinct groups, whose values both have the same sum.\n• Miss Tenclumpz - (white) - her cells can be divided into smaller distinct groups of orthogonally connected cells, each of which sum to 10.\n• Colonel Nabner (yellow) - none of his cell's values are consecutive with (or the same as) each other.\n• Professor Zipworthy (purple) - cells an equal distance from his central spot sum to the digit on his central spot.\n• The Whispering Reverend (green) - adjacent cells must have values with a difference of at least 5.\n\nOne particular digit (not value) appears in all of the suspects' cages, except for the real killer. Who is it?","solution":"389467215516923784742185963425891637168372459973654128854219376297536841631748592","constraints":["XV","cage","custom","german-whispers","nabner-line","palindrome","thermometer","zipper-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c15"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c19"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Your path must start at one of the lettered cells  (these are initials labelling the six suspects and the victim.) The path must finish at another lettered cell, and visit all the other lettered cells along the way. • Every row, column and room has exactly one 'pseudo cell'. These 9 pseudo cells contain the digits 1-9 once each. • Miss Parity (red) - values of orthogonally adjacent cell have a different parity (one is odd, the other is even). • Mrs Summer (blue) - a doorway divides her cells into two distinct groups, whose values both have the same sum. • Miss Tenclumpz - (white) - her cells can be divided into smaller distinct groups of orthogonally connected cells, each of which sum to 10. One particular digit (not value) appears in all of the suspects' cages, except for the real killer.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c12","c20","c21","c22","c26"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"• The Whispering Reverend (green) - adjacent cells must have values with a difference of at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c25"]},{"slug":"nabner-line","type":"nabner-line","variant":"modified","modifiers":[],"params":null,"note":"• Colonel Nabner (yellow) - none of his cell's values are consecutive with (or the same as) each other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c23"]},{"slug":"palindrome","type":"palindrome","variant":"modified","modifiers":[],"params":null,"note":"• Dr Awkward's body was found lying awkwardly in the doorway between rooms 4 and 7. This has been marked by a white outline. All that's known about the victim is that the values of his cells form a palindrome, reading the same from either end.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c17"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"zipper-line","type":"zipper-line","variant":"modified","modifiers":[],"params":null,"note":"• Professor Zipworthy (purple) - cells an equal distance from his central spot sum to the digit on his central spot.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c24"]}]},{"id":"f2DNr9b4tb","ctcId":1956,"ctcDifficulty":"HARD","title":"Chocolate Banana Sandwiches","author":"Scojo","rules":"Normal sudoku rules apply. Shade some cells so that every orthogonally connected group of shaded cells is rectangular, and every orthogonally connected group of unshaded cells is non-rectangular. (For the avoidance of doubt, a square is a rectangle.) A digit in a circle represents the number of cells in its shaded or unshaded group. Clues above a column represent the sum of any SHADED cells between the 1 and 9 in that column. Clues to the left of a row represent the sum of any UNSHADED cells between the 1 and 9 in that row.","solution":"645819327318742659729536148574261893986354271231987564462178935157693482893425716","constraints":["custom","sandwich"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells so that every orthogonally connected group of shaded cells is rectangular, and every orthogonally connected group of unshaded cells is non-rectangular. A digit in a circle represents the number of cells in its shaded or unshaded group.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"LJqq7g8d8d","ctcId":1958,"ctcDifficulty":"HARD","title":"Zag","author":"zetamath","rules":"Normal sudoku rules apply. Digits along the orange line must be broken into one or more contiguous groups of cells that each sum to ten. Such groups cannot overlap. Digits may repeat within such sums if allowed by other rules. For example, 513173 is a valid fill for a length 6 line, because it can be broken into 5131 and 73, each of which sum to 10. Digits along an arrow sum to the digit in that arrow’s circle.","solution":"287361954653429781419578236892134675176285493534796128941857362368942517725613849","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits along the orange line must be broken into one or more contiguous groups of cells that each sum to ten.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"48jp7phsoy","ctcId":1959,"ctcDifficulty":"VERY HARD","title":"Think Inside The Box","author":null,"rules":"Normal sudoku rules apply. Adjacent digits along a green line have a difference of at least five. Box borders divide a blue line into segments with the same sum. Digits on the purple line must be a consecutive set of digits, in any order.","solution":"963415287582937146147628593276849315431256879859371624624193758798562431315784962","constraints":["german-whispers","region-sum-line","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"fhr7gQfm9G","ctcId":1961,"ctcDifficulty":"HARD","title":"Quadrangularly Sparse","author":"Kennet's Dad","rules":"Normal sudoku rules apply. Digits may not repeat within a cage, and sum to the number shown. The digits along each arrow must sum to the digit in the circled cell. Digits separated by a white dot must be consecutive.","solution":"967415283218963547534278619723549861649781352185632974451396728892157436376824195","constraints":["arrow","cage","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"MHHM4gJn2Q","ctcId":1962,"ctcDifficulty":"MEDIUM","title":"Reindeer","author":"Kennet's Dad","rules":"Normal sudoku rules apply. Along any individual line, each line segment within a different 3x3 box must sum to the same total. Different lines may have different totals. Additionally, along ALL these same lines, digits an equal distance from the centre of the line sum to the same total. For odd length lines, the total is the digit in the centre of the line. (In other words, the lines in this puzzle are simultaneously 'region sum' and 'zipper' lines.)","solution":"938425176526371894714698235182537469345962781679184523891246357467853912253719648","constraints":["region-sum-line","zipper-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"hwks8iml0a","ctcId":1963,"ctcDifficulty":"HARD","title":"'I can resist everything but temptation'","author":"Kennet's Dad","rules":"Normal sudoku rules apply. Digits in cells a knight's move apart in chess must not be the same digit. Any 2x2 area of cells in the grid must contain at least one digit from each modulo 3 set: 147, 258, 369. Digits in cells separated by a black dot must be in a 1:2 ratio. Digits along a thermometer must increase from the bulb end.","solution":"754319862319862754862754319543198627198627543627543198431986275986275431275431986","constraints":["antiknight","custom","kropki","thermometer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any 2x2 area of cells in the grid must contain at least one digit from each modulo 3 set: 147, 258, 369.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"kt1pesfm29","ctcId":1964,"ctcDifficulty":"VERY HARD","title":"Nuts and Bolts","author":"Kennet's Dad","rules":"Normal sudoku rules apply. Box borders divide each line into segments with the same sum. Digits in a cage sum to the number in the top left corner of that cage.   One digit is double the other in cells separated by a black dot.","solution":"875461392629835741341792586752943168418657923963218457587124639236579814194386275","constraints":["cage","kropki","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Box borders divide each line into segments with the same sum.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"3blhorinlx","ctcId":1965,"ctcDifficulty":"HARD","title":"MOMs Day","author":"Kennet's Dad","rules":"For all the Moms...\n\nNormal sudoku rules apply. Digits along an arrow sum to the digit in that arrow's circle. On the pink line there must be a set of non-repeating consecutive digits in any order. Adjacent digits on a green line must have a difference of at least five. Any set of three adjacent digits on an orange line must have one digit from each of the following sets: 123, 456, 789. Digits on a red line must have a value between the values of the digits in that line's circles. Box borders divide a blue line into segments with equal sums. Digits joined by an X sum to 10; digits joined by a V sum to 5. Digits joined by a white dot must be consecutive; digits joined by a black dot must be in a 2:1 ratio. Not all Xs, Vs, or dots are necessarily given.","solution":"926813574371542968485976123142387659637159482859624731264731895593468217718295346","constraints":["XV","arrow","between-line","entropic-line","german-whispers","kropki","region-sum-line","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"ih1mkn7vk1","ctcId":1967,"ctcDifficulty":"MEDIUM","title":"Group Sum Renban Hybrid #8","author":null,"rules":"Normal sudoku rules apply. Numbers inside a circle indicate the sum of the digits in the four cells covered by the corresponding circle, which may include repeat digits. Each purple line contains a set of consecutive digits, in any order, without repeats.","solution":"279465813148973625563821479951384267432617598687592341794238156826159734315746982","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Numbers inside a circle indicate the sum of the digits in the four cells covered by the corresponding circle, which may include repeat digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9557h2w0uy","ctcId":1968,"ctcDifficulty":"HARD","title":"Far Far Away","author":"Agent","rules":"Normal sudoku rules apply.\n\nDoublers: Nine cells (one per row/column/box) are doublers, and have values equal to double their digit. Each digit appears in exactly one doubler.\n\nRemote Sums: A value X in a cage points to a second value Y located X cells away vertically or horizontally. The number in the top left corner of the cage indicates the sum of X+Y.","solution":"271359684459681723683724915842193576516847239937562841798435162365218497124976358","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Remote Sums: A value X in a cage points to a second value Y located X cells away vertically or horizontally.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"NHRrNJb98h","ctcId":1970,"ctcDifficulty":"HARD","title":"Electrostatic Discharge","author":"Allagem","rules":"Normal sudoku rules apply. Box borders divide blue Region Sum lines into segments with equal sums. Digits on a gold Nabner line do not repeat and are not consecutive with any other digits on the line.","solution":"384612759297358461615479823738524196159836274462197538576981342921743685843265917","constraints":["nabner-line","region-sum-line"],"constraintFacts":[{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"pn5mirfnyl","ctcId":1972,"ctcDifficulty":"HARD","title":"Is V Greater Than, Less Than, or Equal to 5?","author":"HalfBakedLunatic","rules":"Normal Sudoku Rules Apply\n\n\"V\" can be either \"inequality\" (arrow points to smaller digit) or \"two digits sum to 5\" or both. If the two digits do sum to 5, the \"V\" can be in any orientation and does not necessarily indicate greater than/less than.\n\nDigits must not repeat in cells that are a chess knight's move apart.\n\nThe digits in a cage must sum to the number printed in its corner.\n\nEntering a correct digit will clear the fog from around that cell.\n\nExported from sudokulab.net","solution":"789163452345972168216548973163289547954317286827456319472895631598631724631724895","fogLight":"R1C1,R2C1,R3C1,R3C2,R2C2,R1C6,R2C6,R3C5,R1C7,R2C7,R4C2,R5C3,R6C3,R5C4,R6C4,R5C5,R6C6,R4C8,R5C7,R6C7,R6C8,R9C1,R7C3,R7C1,R9C4,R9C5,R9C6,R8C6,R8C5,R7C7,R7C8,R7C9,R8C9,R8C8,R8C4,R6C5,R4C5,R3C4,R3C3,R1C5,R9C2,R9C3,R1C2,R7C2,R6C2,R3C8,R4C3,R4C4,R4C1,R5C2,R1C9,R3C9,R4C9","constraints":["antiknight","cage","custom","fog"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"\"V\" can be either \"inequality\" (arrow points to smaller digit) or \"two digits sum to 5\" or both.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"6ul7danidn","ctcId":1974,"ctcDifficulty":"MEDIUM","title":"Kingsroad","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nAnti-king: Cells touching diagonally cannot contain the same digit.\n\nLines in the grid act as both Region Sum Lines and Parity Lines.\n\nAs Region Sum Lines: Region borders divide a line into segments with equal totals. Different lines may have different totals.\n\nAs Parity Lines: Digits along a line must alternate between even and odd.","solution":"379452816456781392218936475793625184682147953145893627521368749864579231937214568","constraints":["antiking","custom","region-sum-line"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Lines in the grid act as both Region Sum Lines and Parity Lines.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"4swipiexba","ctcId":1975,"ctcDifficulty":"MEDIUM","title":"A Bit Of A Stretch","author":"gdc","rules":"Normal Sudoku rules apply.\nDigits an equal distance from the circled center of a  zipper line sum to the central digit.","solution":"628937154517648293439512867386721945294385671175496382963154728841279536752863419","constraints":["zipper-line"],"constraintFacts":[{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"51lxch73sn","ctcId":1976,"ctcDifficulty":"HARD","title":"Quadrarrows","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nThe sum of digits on an arrow must equal one of the digits in the four cells surrounding the connected circle. If more than one arrow on the same circle have the same sum, then said sum must appear at least that many times in the cells surrounding the circle.","solution":"639481275451726938287539641942653817168947523573812496324165789715298364896374152","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of digits on an arrow must equal one of the digits in the four cells surrounding the connected circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"x56ymej4lq","ctcId":1978,"ctcDifficulty":"HARD","title":"Fakes in the Fog","author":"Marty Sears","rules":"• Normal sudoku rules apply.\n• Enter correct digits to clear fog. No guessing is necessary.\n• In every row, column and box, there is exactly one 'pseudo cell'. The digits 1-9 each appear once in a pseudo cell.\n• The real value of a pseudo cell is calculated by adding its row number to its column number. Eg: if there is a pseudo cell in r8c5, it has the value of 13, regardless of which digit is in that cell.\n• On a lavender 'zipper' line, the values of any pair of cells that are an equal distance from the central spot  always sum to the value on that central spot.\n• On a turquoise 'same difference' line, the values of adjacent cells always have the same difference (but this difference may be different for different turquoise lines.)\n• Values joined by a V sum to 5.","solution":"768239514129645873534178962287364195496851237315792648941583726652417389873926451","fogLight":"R4C7,R4C8,R4C9,R5C7,R5C8,R5C9,R6C7,R6C8,R6C9","constraints":["XV","custom","fog","same-difference-line","zipper-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• In every row, column and box, there is exactly one 'pseudo cell'. The digits 1-9 each appear once in a pseudo cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"zipper-line","type":"zipper-line","variant":"modified","modifiers":[],"params":null,"note":"• On a lavender 'zipper' line, the values of any pair of cells that are an equal distance from the central spot  always sum to the value on that central spot.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"xkbz6iw8mm","ctcId":1979,"ctcDifficulty":"HARD","title":"Shima Yuteki","author":"rockratzero","rules":"Normal sudoku rules apply.\nShimaguni rules apply. Shade an orthogonally connected group of cells within each dashed cage. Two shaded cells may not share a cage border. No two orthogonally touching cages may contain the same number of shaded cells.\n-Circles are unshaded and contain the count of shaded cells in their cage.\n-Small values in the top left of cages (if given) sum the digits in shaded cells in the cage. Digits may not repeat in shaded cells in the cage (no restriction on unshaded cells).\n-Digits in cells joined by a black dot are in a 2:1 ratio.","solution":"314798265598162437672534198783649521459321786261875349845913672936257814127486953","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shimaguni rules apply. -Circles are unshaded and contain the count of shaded cells in their cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"q6kayoiu83","ctcId":1981,"ctcDifficulty":"HARD","title":"Mountain and Valley","author":null,"rules":"Normal sudoku rules apply. For every coloured cell, the digits in all orthogonal neighbours (ie those sharing an edge with that cell) are either all greater or all less than the digit in the cell. A digit cannot repeat along a main diagonal (marked in green).","solution":"419582637385746192627391548152978364973465821846123759594617283738254916261839475","constraints":["custom","diagonal"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For every coloured cell, the digits in all orthogonal neighbours (ie those sharing an edge with that cell) are either all greater or all less than the digit in the cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"dLgJ4RDG3j","ctcId":1982,"ctcDifficulty":"HARD","title":"Border Square Diagonals","author":"Phistomefel","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow’s circle. A border square is a 2x2 square that crosses at least one box border. For all border squares except for the four marked in grey, its two diagonals sum to the same number. The diagonals of different border squares may sum to different numbers.","solution":"476829135895731246132456798687912354921345687354678921243567819719284563568193472","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For all border squares except for the four marked in grey, its two diagonals sum to the same number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"6guvv1za0z","ctcId":1983,"ctcDifficulty":"MEDIUM","title":"±1","author":"Math Pesto","rules":"Normal sudoku rules apply. Values along a purple line comprise a set of non-repeating, consecutive numbers (in any order). A black dot joins two values in a 1:2 ratio. \nThere is exactly one 'knapp daneben' cell in each row, column, and box. A digit in a knapp daneben cell has its value either increased or decreased by exactly 1 (e.g. a 3 becomes either 2 or 4). Each digit appears in a knapp daneben cell exactly once. (However, it is permissible for two digits to become modified to the same value, such as both 5 and 7 becoming 6.)","solution":"273645981894371562651829374985134627167298435432756819319487256748562193526913748","constraints":["custom","kropki","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There is exactly one 'knapp daneben' cell in each row, column, and box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"A black dot joins two values in a 1:2 ratio.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Values along a purple line comprise a set of non-repeating, consecutive numbers (in any order).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"b193jegg4x","ctcId":1984,"ctcDifficulty":"MEDIUM","title":"Chess Lines","author":"gdc","rules":"Normal Sudoku rules apply.\nAdjacent digits on a line must form a valid chess move by the indicated piece on a 3x3 numpad.\nFor example, a 1 on a knight line may only have the numbers 6 and 8 next to it so 6-1-8-1 would be valid.\nPawns can only move exactly one cell up or one cell down, so 2-5-8-5 would be a valid pawn line.","solution":"136479258524863971879125346392586417457291863618347529981654732243718695765932184","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent digits on a line must form a valid chess move by the indicated piece on a 3x3 numpad.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"NRqTD93pf7","ctcId":1985,"ctcDifficulty":"HARD","title":"Polygons","author":"James Kopp","rules":"Normal sudoku rules apply. Adjacent digits along an orange line have a difference of at least four. Box borders break a blue line into segments with the same sum. Digits inside a cage do not repeat and sum to the total indicated.","solution":"847352691192864357536917482613528749289741563475639218321485976958276134764193825","constraints":["cage","dutch-whispers","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"qvjh329nc0","ctcId":1986,"ctcDifficulty":"HARD","title":"Taron","author":"IcyFruit","rules":"Normal fog of war sudoku rules apply.\nLines travel orthogonally or diagonally through the centers of cells. They do not branch and do not cross themselves or each other. All given lines are a different colour. A grey dot may hide part of a line.\nLines are region-subset lines: Box borders divide lines into segments. If a digit appears in a segment of length N, it must appear in all segments of length N or greater on that line. All lines have at least two segments.\nIn addition, a digit on a line indicates the number of times that digit appears on that line.","solution":"412385796597621348683749125971456832856293471234178569328567914149832657765914283","fogLight":"R1C6,R3C7,R3C2,R4C4,R6C8","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Lines are region-subset lines: Box borders divide lines into segments. In addition, a digit on a line indicates the number of times that digit appears on that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c9"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"7kov2n4lrz","ctcId":1987,"ctcDifficulty":"HARD","title":"Zippery When Wet","author":"Marty Sears","rules":"• Normal sudoku rules apply.\n\nYIN-YANG:\n• Each cell is either land or water.\n• All cells of the same type must be orthogonally connected.\n• No 2x2 area may be entirely land or entirely water.\n\nLINE TYPES:\n• Renban (pink) - Digits on a pink line don't repeat, and form a consecutive sequence, but these can be arranged in any order along the line.\n• Nabner (yellow) - A digit on a yellow line cannot be consecutive with (or the same as) any other digit anywhere on the line.\n• German Whisper (green) - Adjacent digits on a green line must have a difference of at least 5.\n• Region Sum (blue) - Digits along a blue line must have the same total within each 3x3 box.\n• Parity (red) - Digits along a red line must alternate between odd and even.\n• Entropic (orange) - Any group of 3 adjacent digits on an orange line must contain a low digit (1, 2 or 3), a medium digit (4, 5 or 6), and a high digit (7, 8 or 9).\n• Palindrome (grey) - A grey line must read the same in either direction.\n• Same Difference (turquoise) - Each pair of adjacent digits along a turquoise line must have the same difference.\n\nZIPPERY WHEN WET:\n• Any line that is completely wet (only enters water cells) loses the property of its presenting colour, and instead becomes a zipper line. Along a zipper line, each pair of digits that are the same distance from the line's central cell, sum to the digit in that centre cell.\n• Any line that is completely dry (only enters land cells) behaves normally, as described in the list above. It does not behave like a zipper line.\n• If a line is partly dry and partly wet, it retains its presenting property, but it is ALSO a zipper line as well.","solution":"826593714139764258547128963291847536475236891683915472752681349914372685368459127","constraints":["custom","entropic-line","german-whispers","nabner-line","palindrome","region-sum-line","renban","same-difference-line","yin-yang","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Parity (red) - Digits along a red line must alternate between odd and even. • Any line that is completely dry (only enters land cells) behaves normally, as described in the list above. It does not behave like a zipper line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c11","c17"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"• German Whisper (green) - Adjacent digits on a green line must have a difference of at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"nabner-line","type":"nabner-line","variant":"modified","modifiers":[],"params":null,"note":"• Nabner (yellow) - A digit on a yellow line cannot be consecutive with (or the same as) any other digit anywhere on the line.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"palindrome","type":"palindrome","variant":"modified","modifiers":[],"params":null,"note":"• Palindrome (grey) - A grey line must read the same in either direction.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c13"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"• Region Sum (blue) - Digits along a blue line must have the same total within each 3x3 box.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c16","c18"]}]},{"id":"lc3vr050ng","ctcId":1988,"ctcDifficulty":"VERY HARD","title":"Where does it all end?","author":"apetersen","rules":"Normal Sudoku rules apply.\nThe grid is covered in fog. Correctly entered digits remove fog in surrounding cells.\nCells with a grey square contain an even digit.\nEach line has a distinct color.\nLines do not branch or cross and only move orthogonally.\nAll lines have a length of 3 or more.\nThe box location of each line's ends determine its type(s):\n1: Ten Line\n2: Renban\n3: German Whisper\n4: Same Difference\n5: Between\n6: Modular\n7: Nabner\n8: Region Sum\n9: Entropic\ne.g. yellow has one end at r3c5 and the other at r7c5. It is both Renban (box 2) and Region Sum (box 8).\n\nTen Line: The line can be broken into segments such that each sums to 10.\nRenban: The line contains a set of non-repeating consecutive digits, in any order.\nGerman Whisper: Adjacent digits along this line must differ by at least 5.\nSame Difference: Adjacent digits along this line have the same difference for all pairs.\nBetween: All other digits along the line have values that fall strictly between those of the ends.\nModular: Every group of 3 consecutive cells along the line contains a full set of remainders modulo 3: one from (1,4,7), one from (2,5,8), and one from (3,6,9).\nNabner: None of the digits on the line repeat, nor are consecutive with any other digit along the line.\nRegion Sum: Box borders break the line into segments with the same sum.\nEntropic: Every group of 3 consecutive cells along the line must contain a low (1,2,3), mid (4,5,6), and high (7,8,9) digit.","solution":"368917254419285736725463981871346529593721468246598173934672815152834697687159342","fogLight":"R3C5,R4C6,R7C5","constraints":["between-line","custom","entropic-line","even","fog","german-whispers","modular-line","nabner-line","region-sum-line","renban","same-difference-line"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c24"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The box location of each line's ends determine its type(s): Ten Line: The line can be broken into segments such that each sums to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c8","c20"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c28"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c22"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c25"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c26"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c27"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c21"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c23"]}]},{"id":"rghovwpref","ctcId":1990,"ctcDifficulty":"MEDIUM","title":"Killer Sudoku Storm","author":"Jeremy Butler (quarterthru)","rules":"Normal Sudoku rules apply.\n\nCages must sum to the given total in the cage.","solution":"935284716746319258812765934169542387384971625527836149671453892258197463493628571","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"meq4crszcg","ctcId":1992,"ctcDifficulty":"HARD","title":"Counting Calories","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nDivide the grid into yellow regions and brown regions. Each region must consist of orthogonally connected cells, and two regions of the same colour may not share an orthogonal edge.\n\nBrown regions (chocolate bars) must be rectangular (squares are ok too).\n\nYellows regions (bananas) must NOT be square / rectangular.\n\nDigits may repeat within regions.\n\nA digit in a banana cell indicates exactly how many banana cells contain that digit.\n\nA digit in a brown diamond belongs to a chocolate bar and indicates the size of that chocolate bar. Every chocolate bar has a different size.\n\nA digit on an arrow cell indicates the total sum of the closest (neighbouring) cells in each of the indicated directions.","rulesClarified":"Normal sudoku rules apply. Digits may repeat within a region.\n\nEvery cell belongs to either a yellow region (a banana) or a brown region (a chocolate bar). Each region is made of orthogonally connected cells. Two regions of the same colour may not share an orthogonal edge.\n\nBrown regions must be rectangles, squares included. Yellow regions must not be rectangles or squares.\n\nEach brown diamond marks a cell in a chocolate bar. The digit in a brown diamond is the number of cells in that bar. Every chocolate bar has a different size.\n\nA digit in a yellow cell (a banana) is exactly the number of yellow cells in the grid that contain that digit. The banana cell itself counts.\n\nAn arrow points from its cell to the nearest cell in one direction. A digit in an arrow cell is the sum of the nearest cells in the directions its arrows point, one cell per direction.","solution":"864219573915743826372568941237681459149325768586497312651934287423876195798152634","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into yellow regions and brown regions. A digit in a banana cell indicates exactly how many banana cells contain that digit. A digit in a brown diamond belongs to a chocolate bar and indicates the size of that chocolate bar. A digit on an arrow cell indicates the total sum of the closest (neighbouring) cells in each of the indicated directions.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7","c8","c10"]}]},{"id":"qy2dyyfrcg","ctcId":1994,"ctcDifficulty":"EASY","title":"Rainbow Trout","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply.\n\nFISHING LINES - Adjacent digits on a grey line (including the the hook) differ by exactly N, where N is the digit on the corresponding fish.","solution":"536148297128397564947526831289735146361984752475261983892473615753619428614852379","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"FISHING LINES - Adjacent digits on a grey line (including the the hook) differ by exactly N, where N is the digit on the corresponding fish.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"flh8lr4syy","ctcId":1996,"ctcDifficulty":"HARD","title":"Flying Dutchmen","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along an orange line have a difference of at least four.\nCells separated by a \"6 ball” sum to six.","solution":"573819264219645378468327951951486732834572196726193485197258643345961827682734519","constraints":["custom","dutch-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells separated by a \"6 ball” sum to six.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"Td2qPdqdHj","ctcId":1997,"ctcDifficulty":"HARD","title":"How Bizarre","author":"Nahileon","rules":"Normal sudoku rules apply. The circled cell contains an odd digit. Divide each grey line into at least two non-overlapping segments. The digits on each segment of a line sum to the same total. (Different lines may have different totals.) Additionally each segment individually forms a set of non-repeating consecutive digits in any order.","solution":"278319564463258197519467283836194752721583946945726318397845621154632879682971435","constraints":["custom","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digits on each segment of a line sum to the same total. Additionally each segment individually forms a set of non-repeating consecutive digits in any order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c6"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"n8GBhrHDhf","ctcId":1998,"ctcDifficulty":"MEDIUM","title":"Emergence","author":"Jay Dyer","rules":"Normal sudoku rules apply. The 3x3 box borders divide a blue line into segments.  The sum of the digits along each segment is the same for that line. Different lines may have different segment sums. Eg r4c7+r4c8 = r1c6+r2c6+r3c6 = r1c7+r2c8+r3c9+r3c8","solution":"517284369398651427246739518174923685852476931963518274621845793735192846489367152","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"5ol2he9bbw","ctcId":1999,"ctcDifficulty":"EASY","title":"Pressure Zone","author":"Riffclown","rules":"• Normal Sudoku rules apply. Place the digits 1-9 in each row, column and box without repetition.\n• Thermo: Digits on grey thermos must increase from the bulb to the tip.","solution":"356497812297138654841625937918573426532964178674281395463712589785349261129856743","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"q3ik3a630w","ctcId":2004,"ctcDifficulty":"EASY","title":"Tulip","author":null,"rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle.","solution":"731465289254891367689237541875942136196573428342186975468359712513728694927614853","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"TtPpQdrH4n","ctcId":2006,"ctcDifficulty":"MEDIUM","title":"That's all the X's","author":"rockratzero","rules":"Normal sudoku rules apply. No digit repeats along a marked diagonal. Digits in cages sum to the indicated value.  Digits on a purple line (each ‘line’ in this puzzle contains 5 cells) form a set of consecutive digits in any order. Digits in cells connected by 'X' sum to 10.","solution":"438562917216739584759184632561273849927458163384916725692847351845391276173625498","constraints":["XV","cage","diagonal","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Digits on a purple line (each ‘line’ in this puzzle contains 5 cells) form a set of consecutive digits in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"zdmnz4qx5m","ctcId":2007,"ctcDifficulty":"MEDIUM","title":"Circles in the Mist","author":"Oddlyeven","rules":"Rules: Normal Sudoku rules apply.\nArrows: Digits on an arrow sum to the digit in that arrow's circle. Arrows do not branch, cross or share cells (including circles) with other arrows.\nCircles: A digit in a circle gives how many times that digit appears in circles. Arrow circles count as circles for this rule.\nFog: The grid is partially covered in fog. Entering a correct digit in the grid will clear the fog around that digit.","rulesClarified":"Rules: normal sudoku rules apply.\n\nArrows: digits on an arrow sum to the digit in that arrow's circle. The circle itself is not part of the sum. Arrows do not branch, cross or share cells (including circles) with other arrows.\n\nCircles: a digit in a circle gives how many times that digit appears in circles. Every circle in the grid counts, including the circle an arrow starts from. A circle's own digit counts itself: a circle showing 3 means exactly three circles in the grid, its own included, contain a 3.\n\nFog: the grid is partially covered in fog. Entering a correct digit in the grid will clear the fog around that digit.","solution":"861752439259431687437689512573864921692317854184295376746528193928143765315976248","fogLight":"R1C1,R1C2,R1C3,R2C1,R2C2,R2C3,R3C1,R3C2,R3C3,R7C1,R7C2,R7C3,R8C1,R8C2,R8C3,R9C1,R9C2,R9C3","constraints":["arrow","custom","fog"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Circles: A digit in a circle gives how many times that digit appears in circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"3D64nRR387","ctcId":2014,"ctcDifficulty":"MEDIUM","title":"Kropki Cave","author":"Ben Needham","rules":"Normal sudoku rules apply. Shade some cells (walls) such that they form orthogonally connected regions that must touch an edge of the grid. Similarly, leave some cells unshaded (tunnel) to form a single orthogonally connected path, which may not touch itself diagonally and does not branch. No 2x2 area of the grid may be completely shaded or unshaded. Cells marked with a square indicate how many cells (including themselves) they see orthogonally (walls block their view, but they may themselves be walls). White dots indicate consecutive digits along the path (all white dots are shown). Black dots indicate that cells are in a 1:2 ratio within the wall (all black dots are shown). Note that dots do not disclose relationships between shaded and unshaded cells.","solution":"837965412246781953591243687683192574972534168415678239368419725759826341124357896","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells (walls) such that they form orthogonally connected regions that must touch an edge of the grid. Similarly, leave some cells unshaded (tunnel) to form a single orthogonally connected path, which may not touch itself diagonally and does not branch. No 2x2 area of the grid may be completely shaded or unshaded. Cells marked with a square indicate how many cells (including themselves) they see orthogonally (walls block their view, but they may themselves be walls).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7"]}]},{"id":"q7nxdos135","ctcId":2015,"ctcDifficulty":"MEDIUM","title":"Pi","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Within a 3x3 box, cells a single knight's move apart (in chess) cannot contain consecutive digits.","solution":"593284176627159384184376295415932867932867451876541932769423518251798643348615729","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Within a 3x3 box, cells a single knight's move apart (in chess) cannot contain consecutive digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"e65gt211wt","ctcId":2020,"ctcDifficulty":"HARD","title":"Knightmare on Mount Pleasant Avenue","author":"HalfBakedLunatic (aka David Workman)","rules":"• Normal Sudoku Rules Apply\n• Digits in a cage must sum to the number in the corner of the cage\n• Cells separated by Black dots must in a 2:1 ratio, white dots must be consecutive digits\n• Knightmare rules apply - digits a 'knights move' apart can not sum to 5 or 15","solution":"961782354574693821823541769786934512219857643345126978698415237437269185152378496","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Knightmare rules apply - digits a 'knights move' apart can not sum to 5 or 15","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"RJtrMfLmBq","ctcId":2021,"ctcDifficulty":"MEDIUM","title":"Square Numbered Fog Totals","author":"RockyRoer","rules":"Normal sudoku rules apply.  Placing correct digits will remove fog from surrounding cells to reveal more clues. Somewhere in the fog are 9 marked cells - one in every row, column and 3x3 box.  These cells must contain the digits 1-9 once each.  For each marked cell, the sum of ALL the digits in the cells up to and including that marked cell, (top to bottom, left to right, as one might read) must always sum to a square number. For example, if R4C2 is a marked cell, then the sum of all the digits in row 1, row 2, row 3, R4C1, and R4C2 must be a square number.","solution":"625487319814639527379251684982543761136972845457168293761324958243895176598716432","fogLight":"R1C5,R1C6,R1C7,R2C5,R2C6,R2C7,R3C5,R3C6,R3C7","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Somewhere in the fog are 9 marked cells - one in every row, column and 3x3 box. For each marked cell, the sum of ALL the digits in the cells up to and including that marked cell, (top to bottom, left to right, as one might read) must always sum to a square number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ghBJJQ3L4g","ctcId":2022,"ctcDifficulty":"HARD","title":"Blackjack","author":"Blashyrkh","rules":"Normal sudoku rules apply. Digits in cages do not repeat and sum to the number indicated.","solution":"624385179983167542517429863132576498468931257759248631345892716871653924296714385","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"gTJqhL2TFb","ctcId":2023,"ctcDifficulty":"MEDIUM","title":"Sharing Economy","author":"Blashyrkh","rules":"Normal sudoku rules apply.\n\nDigits along thermometers increase from the bulb end.\n\nDigits do not repeat along the indicated diagonal.","solution":"847352169369148752215976348953214687786593214124867593631789425578421936492635871","constraints":["diagonal","thermometer"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"gp6TDtR6RN","ctcId":2025,"ctcDifficulty":"MEDIUM","title":"Diagonal Skyscrapers","author":"Blashyrkh","rules":"Normal sudoku rules apply.\n\nSkyscraper: Each digit should be viewed as a skyscraper with height equal to its value. Clues outside the grid indicate how many digits are 'seen' along that diagonal, with higher digits blocking lower or identical digits from view.","solution":"168573924924618357753294168596481273837952641241736895685149732419327586372865419","constraints":["skyscraper"],"constraintFacts":[{"slug":"skyscraper","type":"skyscraper","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"dowo5gsiqj","ctcId":2026,"ctcDifficulty":"MEDIUM","title":"Club 27","author":"Blashyrkh","rules":"Normal sudoku rules apply.\n\nDigits along a thermometer strictly increase from the bulb to the tip.","solution":"512687439964315278837429651476193582398256714251748963649531827723864195185972346","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"gfjgpqtw7z","ctcId":2028,"ctcDifficulty":"MEDIUM","title":"Projected Differences","author":"ThePedallingPianist","rules":"X Sudoku: Place digits from 1-9 in every cell such that digits do not repeat in a row, column, box or along a marked blue diagonal.\n\nProjected Differences: A diamond clue shows that there exist two digits N steps away from the diamond in an orthogonal direction that have a difference of N, where N is the digit in the diamond. Not all diamonds are necessarily given.\n\n(For example, if r6c4 is a 3, then at least one pair of digits from the set of digits in r3c4, r6c7, r9c4 and r6c1 must have a difference of 3)","solution":"184962357725438916693175248246783195958241673371596824439817562567329481812654739","constraints":["custom","diagonal"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Projected Differences: A diamond clue shows that there exist two digits N steps away from the diamond in an orthogonal direction that have a difference of N, where N is the digit in the diamond.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"5b1du6ra7d","ctcId":2030,"ctcDifficulty":"MEDIUM","title":"RAT RUN 3: Double Dutch","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path will be a snaking line that passes through the centres of cells, without visiting any cell more than once, crossing itself or passing through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through the rounded end / corner of a wall.\n\nBLACKCURRANTS: Cells connected by a blackcurrant have a 1:2 ratio (one is double the other.) Not all possible blackcurrants have been given.\n\nTEST CONSTRAINT: In this experiment, the correct path will be a valid Dutch Whisper line - ie: adjacent digits along the path must have a difference of at least 4.","solution":"192475638378261594564938271239784165685312749417659382853196427926547813741823956","constraints":["custom","dutch-whispers","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"j3hwgi98hr","ctcId":2031,"ctcDifficulty":"HARD","title":"Copycat Collaboration","author":"Scojo & Chat","rules":"Normal sudoku rules apply: Place the digits 1-9 once each into every row, column, and 3x3 box.\n\nCopycat Cells: Place 9 Copycat Cells into the grid so that there is exactly one Copycat Cell in each row, column, and 3x3 box. Each Copycat Cell must contain a different digit. The value of a Copycat Cell is the digit in the cell rotationally opposite itself in the grid (180° rotation about the center of the grid). For example, if r2c3 is a Copycat Cell containing the digit 5, and r8c7 contains the digit 9, the value of r2c3 is the digit in r8c7, which is 9.\n\nZippers: Values an equal distance from the center of a lavender line sum to the value in the center of the line (which is marked with a small circle).\n\nOdd Lots: A value in a yellow circle counts the number of odd values on the attached line.","solution":"796512384534768129182493567379824615241657893865931472617349258428175936953286741","constraints":["custom","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Copycat Cells: Place 9 Copycat Cells into the grid so that there is exactly one Copycat Cell in each row, column, and 3x3 box. Odd Lots: A value in a yellow circle counts the number of odd values on the attached line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7"]},{"slug":"zipper-line","type":"zipper-line","variant":"modified","modifiers":[],"params":null,"note":"Zippers: Values an equal distance from the center of a lavender line sum to the value in the center of the line (which is marked with a small circle).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]}]},{"id":"f5vq2fborp","ctcId":2032,"ctcDifficulty":"MEDIUM","title":"Lots Of Lavender","author":"gdc","rules":"Normal Sudoku rules apply.\nThe grid is covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area.\nDigits an equal distance to the circled center of a lavender zipper line sum to the central digit.\nA digit in a yellow circle counts the number of odd digits on the attached line (including itself and the central cell).\nA digit in a blue square counts the number of even digits on the attached line (including itself and the central cell).\nZipper lines only move orthogonally and don't share cells with other zipper lines.","solution":"912675348763184295584923176831259764675348912429761853396512487247896531158437629","fogLight":"R3C5,R3C6,R3C7","constraints":["custom","fog","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a yellow circle counts the number of odd digits on the attached line (including itself and the central cell). A digit in a blue square counts the number of even digits on the attached line (including itself and the central cell).","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"5c6uuvchca","ctcId":2033,"ctcDifficulty":"HARD","title":"21","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along the green lines have a difference of at least five.\nThe clues outside the grid show the sum of the first X digits from that direction, where X is the first of those digits.","solution":"729354618143687592658912347536128974897546231214793856472839165965271483381465729","constraints":["german-whispers","x-sum"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"xgmmht4odf","ctcId":2034,"ctcDifficulty":"HARD","title":"The Buddy System","author":"Allagem","rules":"Normal Sudoku rules apply. A digit in a circle indicates how many circles contain that digit. Digits along a grey line form a palindrome, i.e. they read the same forwards and backwards. Digits on a blue line between two circles have values between the digits in those circles. Digits separated by a black dot are in a 2:1 ratio.","solution":"563879241479312856281654397836125479712498635945763128394581762658237914127946583","constraints":["between-line","custom","kropki","palindrome"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle indicates how many circles contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"qeyblnue96","ctcId":2035,"ctcDifficulty":"HARD","title":"Don't Fence Me In","author":"HalfBakedLunatic (aka David Workman)","rules":"• Normal Sudoku Rules Apply\n• Digits touching the outside of a Blue cage on all orthogonal edges (but not touching diagonally) must sum to the indicated total\n• Digits touching the outside corners of a Green cage (diagonally, but not touching the cage orthogonally) must sum to the indicated total\n• Digits touching the outside of a Red cage both orthogonally and diagonally must sum to the indicated total\n• No repeats are allowed in the digits making up the totals","solution":"491378562528461739673925184316859427857234916942716853265197348734582691189643275","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Digits touching the outside of a Blue cage on all orthogonal edges (but not touching diagonally) must sum to the indicated total • Digits touching the outside corners of a Green cage (diagonally, but not touching the cage orthogonally) must sum to the indicated total • Digits touching the outside of a Red cage both orthogonally and diagonally must sum to the indicated total","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]}]},{"id":"9hLjJRdRpd","ctcId":2039,"ctcDifficulty":"MEDIUM","title":"Dots and Stripes","author":"GBPack","rules":"Normal sudoku rules apply. Digits along thermometers increase from the bulb end. Cells separated by a white dot contain consecutive digits. Cells separated by a black dot contain digits in a 1:2 ratio (ie one digit is double the other). Not all possible black or white dots are given.","solution":"542897361319526847876143952751389426964712538238654179123965784695478213487231695","constraints":["kropki","thermometer"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"wv8l8x67dy","ctcId":2042,"ctcDifficulty":"MEDIUM","title":"RAT RUN 4: Borderline","author":"Marty Sears","rules":"Normal sudoku rules apply: place the digits 1-9 once each in every row, column, and 3x3 box (marked with dotted lines.)\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze (the path will be a snaking line that passes through the centres of cells, without visiting any cell more than once, crossing itself or passing through any thick maze walls.) Diagonal moves are not possible in this maze.\n\nBLACKCURRANTS: Cells connected by a blackcurrant have a 1:2 ratio (one is double the other.) Not all possible blackcurrants have been given.\n\nONE-WAY DOORS: Finkz may only pass directly through a purple arrow if moving in the direction the arrow is pointing. An arrow always points to the smaller of the two digits it sits between.\n\nTEST CONSTRAINT: In this experiment, the correct path will be a valid Region Sum line - ie: box borders (dotted lines) will divide the path into segments which each have the same sum.","solution":"163874592879526431245319786394251867517968243628743915736492158951687324482135679","constraints":["custom","inequality","kropki","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze (the path will be a snaking line that passes through the centres of cells, without visiting any cell more than once, crossing itself or passing through any thick maze walls.) ONE-WAY DOORS: Finkz may only pass directly through a purple arrow if moving in the direction the arrow is pointing.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"7fapjms0yv","ctcId":2044,"ctcDifficulty":"MEDIUM","title":"Dovetail","author":"zetamath & friends","rules":"Normal sudoku rules apply. Additionally, in this puzzle digits cannot repeat on a line. Digits along a grey line can be broken into non-overlapping segments whose digits sum to ten. Eg 71246 is a valid fill for a length 5 line, because it can be broken into 712 and 46, each of which sum to 10. Along a green line, adjacent digits must differ by at least 5. Along a blue line, the 3x3 box borders divide the line into segments; each segment’s digits have the same sum. (Different lines can have different sums.) eg r5c2+r4c2 = r3c2+r3c3+r2c3 = r2c4+r2c5+r2c6. The sum of the digits along a line connecting two circles is equal to the sum of the digits in the circles. In this puzzle, digits can't repeat in any of these five cells. Any three adjacent digits along a teal line must include one digit from 147, one from 258, and one from 369. Any three adjacent digits along a peach line must include one digit from 123, one from 456, and one from 789. Along red lines, each pair of adjacent digits must have one even and one odd digit.","solution":"584167329931248765276935841758491236493826517162573984845712693629354178317689452","constraints":["custom","entropic-line","german-whispers","modular-line","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Additionally, in this puzzle digits cannot repeat on a line. Digits along a grey line can be broken into non-overlapping segments whose digits sum to ten. The sum of the digits along a line connecting two circles is equal to the sum of the digits in the circles. Along red lines, each pair of adjacent digits must have one even and one odd digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c8","c12"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"cj8grmrtes","ctcId":2045,"ctcDifficulty":"HARD","title":"Stepping Stones","author":"grkles","rules":"Fill the grid such that each row, column, and orthogonally-connected 9-cell region contains each of the digits 1-9 with no repeats. Region borders must be deduced (though one is given).\n\nClues outside the grid give the sum of the first digit seen in each successive region in that row or column. **The summed digits always appear in increasing order.**","rulesClarified":"Fill the grid such that each row, column, and orthogonally-connected 9-cell region contains each of the digits 1-9 with no repeats.\n\nRegion borders must be deduced (though one is given).\n\nClues sit outside the grid, at the start of a row or column. A clue at the top of a column reads downwards; a clue at the bottom reads upwards; a clue to the left of a row reads rightwards; a clue to the right reads leftwards.\n\nA clue gives the sum of the first digit seen in each successive region along its line. For each region the line passes through, take the first digit you meet in that region, and the clue is the sum of those digits.\n\nThe summed digits always appear in increasing order.","solution":"346518927123795648972486315685923174418237569739841256591672483864159732257364891","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Region borders must be deduced (though one is given). Clues outside the grid give the sum of the first digit seen in each successive region in that row or column. **The summed digits always appear in increasing order.**","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"mqrdnrGFb3","ctcId":2046,"ctcDifficulty":"MEDIUM","title":"Half the Digits","author":"Cane_Puzzles","rules":"Normal sudoku rules apply. In a cage, digits cannot repeat and the digits must sum to the small clue in the top left corner of the cage.","solution":"378245196612379458945618732487963521531482967269157843156834279824796315793521684","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"bjD8gPPjqG","ctcId":2047,"ctcDifficulty":"VERY HARD","title":"Glyphs #5","author":"damasosos92","rules":"Normal sudoku rules apply. Draw a single line connecting 29 different cells in the grid that starts and ends with the two given digits. The line can reach a cell in the border of the grid only at the start or at the end of its path. The line cannot intersect itself and cannot branch. No 2x2 in the grid can be entirely covered by the line or entirely not-reached. Adjacent digits on the line must be consecutive. In cages, the digits on the line sum to the cage total.","rulesClarified":"Normal sudoku rules apply.\n\nDraw a single line through 29 different cells of the grid. The line starts and ends with the two given digits.\n\nThe line cannot branch and cannot cross itself.\n\nThe line can reach a border cell only at its start or its end.\n\nNo 2x2 block of cells may be entirely covered by the line, or entirely not covered by it.\n\nDigits next to each other along the line must be consecutive, meaning they differ by exactly 1.\n\nEach killer cage's total is the sum of the digits the line passes through inside that cage. Cells the line does not pass through do not count toward the total.","solution":"658279134124385679739641582546817293972563841381924756297138465865492317413756928","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single line connecting 29 different cells in the grid that starts and ends with the two given digits. In cages, the digits on the line sum to the cage total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7"]}]},{"id":"mBJDRbQLTj","ctcId":2048,"ctcDifficulty":"MEDIUM","title":"A Wonderful Discovery","author":"damasosos92","rules":"Every little circle is the center of a 3x3 box. Fill the grid with the numbers from 1 to 9 so that in each row, column, and aforementioned box each digit occurs exactly once.\n\nAdjacent digits along green lines must differ by at least 5. Digits along an indicated diagonal must sum to the given total. The value of 'x' has to be determined by the solver.","solution":"453682719127834596794126835836597124682719453541978362965341278378265941219453687","constraints":["german-whispers","little-killer","region"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"hf4Jjm3H3J","ctcId":2049,"ctcDifficulty":"VERY HARD","title":"The Song of the Serpent and the Wanderer","author":"Damasosos92","rules":"The Sudokuland: Divide the grid into regions, each consisting of nine orthogonally connected cells. Each row, column and region must contain the digits 1 to 9 once each.\n\nThe King's Palace: The shown region is the king's palace. It is one of the regions in which the grid has to be divided, and so it contains the digits 1 to 9 once each.\n\nThe Serpent: Some cells must be shaded to form a single snake that is one cell wide that does not branch and cannot touch itself, not even diagonally. The snake must contain only odd digits.\n\nThe Watchtowers: The digit in a watchtower (the squared cells) says how many snake cells are a knight's move away from that cell. Those snake cells sum to the number placed in the top-left corner of the watchtower. There is a watchtower in every region of the grid, and the snake cannot pass through any watchtower.\n\nThe Spell: Each region of the grid must contain exactly the same number of snake cells.","solution":"391584762742863195826157439514936287465729813239641578657318924178295346983472651","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The Sudokuland: Divide the grid into regions, each consisting of nine orthogonally connected cells. The King's Palace: The shown region is the king's palace. The Serpent: Some cells must be shaded to form a single snake that is one cell wide that does not branch and cannot touch itself, not even diagonally. The Watchtowers: The digit in a watchtower (the squared cells) says how many snake cells are a knight's move away from that cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c3","c5","c7"]}]},{"id":"in3a5cg87s","ctcId":2051,"ctcDifficulty":"MEDIUM","title":"P = NP","author":"damasosos92","rules":"Normal sudoku rules apply.\n\nEvery cage in the grid is either a P pentomino or a N pentomino. Every pentomino is completely filled by either a renban line or a thermometer, hidden behind the pentomino. Cells along a renban line contain a set of consecutive, non-repeating digits in any order. Digits on a thermometer must strictly increase as they move away from the bulb. The position of the bulb has to be deduced by the solver. Thermometers only make vertical or horizontal turns inside the pentominous and don't branch.\n\nAll the cages of the same shape hide the same constraint: the solver has to deduce which constraint is hidden behind each shape.","solution":"367589241218674539459123768732861954546932817891457623184295376923746185675318492","constraints":["custom","renban","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every cage in the grid is either a P pentomino or a N pentomino. Every pentomino is completely filled by either a renban line or a thermometer, hidden behind the pentomino. All the cages of the same shape hide the same constraint: the solver has to deduce which constraint is hidden behind each shape.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c8"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"fb3Hh9r7r4","ctcId":2054,"ctcDifficulty":"MEDIUM","title":"Rolling Wave","author":"Lizzy01","rules":"Normal sudoku rules apply. The 3x3 box borders divide a blue line into segments, each of which has the same sum. eg r4c8+r4c9 = r3c9+r2c8+r1c8. Different lines may have different sums. Along a thermometer, digits must increase from the bulb end.","solution":"958146732742593816136278549621937485495812673387465291863751924579324168214689357","constraints":["region-sum-line","thermometer"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"txsylemoy3","ctcId":2055,"ctcDifficulty":"MEDIUM","title":"Hooked On Sudoku","author":"Blashyrkh","rules":"Normal sudoku rules apply.\n\nDigits along a thermometer strictly increase from the bulb end.","solution":"678913452539824617421567389284179563763258941915436728192345876347682195856791234","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"wdzu2e0qne","ctcId":2057,"ctcDifficulty":"MEDIUM","title":"Six Rules Four Clues","author":"99%Sneaky","rules":"1) Normal sudoku rules apply. \n2) Digits along the thermometer must increase from the bulb to the tips.\n3) Digits along arrows sum to the digit in the attached circle.\n4) The digits in the cage sum to the small number printed in the corner. Digits may not repeat in the cage.\n5) Along the blue line thick box boarders divide the line into segments with equal sums. When the line re-enters a box a new segment is formed.\n6) Cells separated by a knight's move in chess may not contain the same digit.","solution":"643781952185923467279465381367849215958312746412657839821574693734196528596238174","constraints":["antiknight","arrow","cage","region-sum-line","thermometer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"cd0mh5vccv","ctcId":2059,"ctcDifficulty":"MEDIUM","title":"Roman Circus","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nUsing red, green, and blue, color in all circles such that:\n-Orthogonally adjacent circles are different colors.\n-The digit inside a circle appears that many times in circles of that color.\n\nDigits connected by an X or V sum to 10 or 5, respectively. Not every X or V is given.","rulesClarified":"Normal Sudoku rules apply.\n\nColour every circle red, green or blue, so that:\n- Two circles that touch orthogonally have different colours.\n- The digit inside a circle appears that many times in circles of that colour.\n\nA V sits on the border between two cells. The two digits on either side of a V sum to 5.\n\nAn X sits on the border between two cells. The two digits on either side of an X sum to 10.\n\nNot every X or V is given. An edge with no marker gives no information about its two digits.","solution":"397815624865249731412376958583724196729651483641938572174582369958163247236497815","constraints":["XV","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"-Orthogonally adjacent circles are different colors. -The digit inside a circle appears that many times in circles of that color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"fosir7x3ud","ctcId":2060,"ctcDifficulty":"EASY","title":"Weird Arrow Man","author":"Adem Jaziri","rules":"Normal sudoku rules apply.\n\nArrows : Digits on an arrow sum to the digit in the attached circle. Digits may repeat on an arrow if allowed by other rules.\n\nKropki white dots : Cells separated by a white dot contain consecutive digits. Not all dots are necessarily given.","solution":"348675219562913784719248563691357428825491637437826951184569372276134895953782146","constraints":["arrow","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"f338uqc57l","ctcId":2062,"ctcDifficulty":"MEDIUM","title":"123","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along a green line have a difference of at least five.","solution":"573962841184573962296184573357296184418357296629418357735629418841735629962841735","constraints":["german-whispers"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"DmdGJNbj22","ctcId":2063,"ctcDifficulty":"MEDIUM","title":"Bricked In","author":"Arbitrary","rules":"Normal sudoku rules apply. Digits separated by white dots are consecutive. If a region of cells is enclosed by a section of orange line, then the sum of digits in the area enclosed by the line is equal to the sum of the digits along the perimeter line section. Digits may repeat on area sum lines if permitted by other rules. Area sum regions have orange lines running around them, but not through them.","solution":"125638479376491825894527163569283714741956382238174956653819247487362591912745638","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If a region of cells is enclosed by a section of orange line, then the sum of digits in the area enclosed by the line is equal to the sum of the digits along the perimeter line section.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"TB93qrfhjq","ctcId":2064,"ctcDifficulty":"MEDIUM","title":"Around the block","author":"Arbitrary","rules":"Normal sudoku rules apply. Digits along an arrow sum to the value in the connected circle. Neighbouring digits on a green line have a difference of at least 5.","solution":"265478319948361572173952864692834157317295648854617293726543981581729436439186725","constraints":["arrow","german-whispers"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"q80drlpksu","ctcId":2065,"ctcDifficulty":"HARD","title":"Things in common","author":"Arbitrary","rules":"Normal sudoku rules apply.\n\nRenban lines: Digits along pink lines are a consecutive set without repeats.\n\nKiller cages:  Digits within cages do not repeat and sum to the indicated value (if given).","solution":"642831975571249368398567421915682734437195682286473519124756893863914257759328146","constraints":["cage","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"f3hfvcu3xz","ctcId":2066,"ctcDifficulty":"HARD","title":"A puzzle of two halves","author":"Arbitrary","rules":"Normal sudoku rules apply.\n\nRenban lines:  Digits along pink lines are a consecutive set without repeats.\n\nArrows: Digits along arrows sum to the value in the connected circle.\n\nQuads:  Digits within small circles must be in at least one of the surrounding cells.  Within quad clues, digits are represented by unique letters which must be determined by the solver.","solution":"248763159136952478975481263653278941789134625412695387321847596597326814864519732","constraints":["arrow","custom","quadruple","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Within quad clues, digits are represented by unique letters which must be determined by the solver.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qh4zzpbcow","ctcId":2067,"ctcDifficulty":"HARD","title":"Traces","author":"Arbitrary","rules":"Normal sudoku rules apply.\n\nRegion sum lines: Box borders divide blue lines into sections of equal sum. Different lines may have different region sums.\n\nQuads: Digits in small circles must appear in at least one of the surrounding cells.","solution":"197645328453928167268137945719456283542783619836291574325814796974362851681579432","constraints":["quadruple","region-sum-line"],"constraintFacts":[{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Region sum lines: Box borders divide blue lines into sections of equal sum.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"rdb3z3k51d","ctcId":2068,"ctcDifficulty":"MEDIUM","title":"One Trick Pony","author":"Arbitrary","rules":"Normal sudoku rules apply.\n\nDigits in cages sum to the indicated value.\n\nDigits along arrows sum to the value in the connected circle.","solution":"274953168863217954519684327738461592426795831195328476351876249682549713947132685","constraints":["arrow","cage"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"r00yffw1w7","ctcId":2070,"ctcDifficulty":"MEDIUM","title":"Gold","author":null,"rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in the attached circle. In cages, digits cannot repeat and must sum to the small clue in the top left corner of the cage. Grey lines are palindromes and must read the same forwards and backwards.","solution":"249687315138945726657132894476823951893561472521794638714358269362419587985276143","constraints":["arrow","cage","palindrome"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"wv01avmfs9","ctcId":2071,"ctcDifficulty":"HARD","title":"RAT RUN 5: Disparity","author":"Marty Sears","rules":"Normal sudoku rules apply: place the digits 1-9 in each row, column, and 3x3 box (marked with dotted lines.)\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path will be a snaking line that passes through the centres of cells, without visiting any cell more than once, crossing itself or passing through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass through a rounded corner / end of a wall.\n\nONE-WAY DOORS: Finkz may only pass directly through a purple arrow if moving in the direction the arrow is pointing. An arrow always points to the smaller of the two values it sits between.\n\nBLACKCURRANTS: Cells connected by a blackcurrant are in a 1:2 ratio (one is double the other.) Not all possible blackcurrants have been given.\n\nTEST CONSTRAINT: In this experiment, the correct path will be a valid alternating parity line - ie: any pair of adjacent cells along the path must contain one even digit and one odd digit.","solution":"734165298528934167691782534183697425275348916469251873952876341347519682816423759","constraints":["custom","inequality","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The path will be a snaking line that passes through the centres of cells, without visiting any cell more than once, crossing itself or passing through any thick maze walls. ONE-WAY DOORS: Finkz may only pass directly through a purple arrow if moving in the direction the arrow is pointing. TEST CONSTRAINT: In this experiment, the correct path will be a valid alternating parity line - ie: any pair of adjacent cells along the path must contain one even digit and one odd digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5","c9"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"x48q45yg2r","ctcId":2073,"ctcDifficulty":"HARD","title":"Square Dance","author":"Jay Dyer","rules":"Normal sudoku rules apply. Digits in a cage may not repeat, and sum to the indicated total.","solution":"728649531345718692961532874487926153159483267632157489573261948294875316816394725","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"2p1an6oilw","ctcId":2074,"ctcDifficulty":"MEDIUM","title":"Zodiac Project: Ponta Delgada","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nThe nine cells containing a clue form an extra region, i.e. they contain the digits 1-9 without repetition.\n\nModified Nurikabe\nShade some cells so that all of the following conditions are fulfilled:\n- All shaded cells form one orthogonally connected area (water).\n- Groups of orthogonally connected unshaded cells form islands. An island may consist of only one cell, and each island contains exactly one clue.\n- No 2x2 may be fully shaded or fully unshaded.\n\nThermal Killer\n- Each island acts as a killer cage, in which digits may not repeat and sum to the given clue (although for some of the cages the sum is unknown).\n- Within an island, digits must either all increase or all decrease in every direction, starting from the cell with the clue.","solution":"532197684487652193196843527845761932729538461613429875368214759971385246254976318","constraints":["cage","custom","region"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"- Each island acts as a killer cage, in which digits may not repeat and sum to the given clue (although for some of the cages the sum is unknown).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells so that all of the following conditions are fulfilled: - Within an island, digits must either all increase or all decrease in every direction, starting from the cell with the clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c10"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"3xa2x14bxe","ctcId":2075,"ctcDifficulty":"MEDIUM","title":"RAT RUN 6: Equilibrium","author":"Marty Sears","rules":"Normal sudoku rules apply: place the digits 1-9 in each row, column, and 3x3 box (marked with dotted lines.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nTELEPORTS: Entering a yellow teleport will cause Finkz to be instantly transported to the other teleport. From there she can continue her journey. The teleports contain the same digit.\n\nONE-WAY DOORS: Finkz may only pass directly through a purple arrow if moving in the direction the arrow is pointing. An arrow always points to the smaller of the two values it sits between.\n\nBLACKCURRANTS: Cells connected by a blackcurrant are in a 1:2 ratio (one is double the other.) Not all possible blackcurrants have been given.\n\nTEST CONSTRAINT: In this experiment, the sum of the digits on the path before teleporting must equal the sum of the digits on the path after teleporting.","solution":"512468739349257861786931542965783124134526978278149653427895316853612497691374285","constraints":["custom","inequality","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls. As well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. TELEPORTS: Entering a yellow teleport will cause Finkz to be instantly transported to the other teleport. The teleports contain the same digit. ONE-WAY DOORS: Finkz may only pass directly through a purple arrow if moving in the direction the arrow is pointing. TEST CONSTRAINT: In this experiment, the sum of the digits on the path before teleporting must equal the sum of the digits on the path after teleporting.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7","c8","c12"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"8h24l900cg","ctcId":2078,"ctcDifficulty":"MEDIUM","title":"Entanglement","author":"Jay Dyer","rules":"Normal sudoku rules apply. Digits in a cage may not repeat, and sum to the indicated total.","solution":"965231874873645192241978365516827943329164587784359216132786459497513628658492731","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"c8waymdam4","ctcId":2079,"ctcDifficulty":"MEDIUM","title":"Gegentakt","author":"Myxo","rules":"Sudoku: Place the digits 1-9 exactly once in each row, column and box.\n\nArrow: Digits along an arrow must sum to the number in the attached circle.\n\nRenban: Each pink line contains a sequence of consecutive digits in any order.","solution":"276419538893275164154863927637528419481396275529741683918634752745182396362957841","constraints":["arrow","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"86p8y4m9kl","ctcId":2080,"ctcDifficulty":"VERY HARD","title":"Repeat Prescription","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nThe digits on a line form a consecutive set, but may be in any order. Digits may repeat on a line, and the digit on the dot equals the number of distinct digits on that line.","solution":"124587639357926814698341572263718945745693128819254763482165397571439286936872451","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits may repeat on a line, and the digit on the dot equals the number of distinct digits on that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"The digits on a line form a consecutive set, but may be in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"DhFTHL63t7","ctcId":2081,"ctcDifficulty":"MEDIUM","title":"Galapagos","author":"Niverio","rules":"Normal sudoku rules apply. Shade some cells such that all shaded cells are orthogonally connected (without creating a 2x2 area) which divides the unshaded cells into blocks of unshaded cells (islands). Each island contains exactly one clue (the small numbers in the grid), and that clue gives the sum of the digits on the island. All clues (except the given 4, whose shading is unknown) are part of the islands. Digits do not repeat on an island. No island is contained within a single 3x3 box, and an island’s cells must have the same sum within each box that island enters. Different visits to a box DO NOT count separately. (Example: A 36 clue island may have cells in 4 boxes that all sum to 9; or 3 boxes with all summing to 12; or 2 boxes with each box's digits summing to 18.)","solution":"613892745752134689849657321531768294978245163264319578426583917195476832387921456","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells such that all shaded cells are orthogonally connected (without creating a 2x2 area) which divides the unshaded cells into blocks of unshaded cells (islands).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"bo63al9pzv","ctcId":2082,"ctcDifficulty":"MEDIUM","title":"Zip Zag","author":null,"rules":"Normal sudoku rules apply: Place the digits 1 to 9 once each in every row, column, and box.\n\nZipper lines: Cells on a lavender zipper line at an equal distance to the center, which is marked with a dot, sum to the digit at the center.","solution":"925483671386175429714269385863512947241897563579634218692758134438921756157346892","constraints":["zipper-line"],"constraintFacts":[{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"wa9fbfdl75","ctcId":2083,"ctcDifficulty":"MEDIUM","title":"Alarm Clock","author":"Jobo","rules":"Normal sudoku rules apply.\n\nAdjacent digits along the red line must alternate in parity (odd/even).\n\nGrey lines are thermometers. Digits along thermometers must increase from the bulb to the tip, which can be on either end and are to be deduced.\n\nDigits separated by a white dot must be consecutive.\nDigits separated by an X must sum to 10.\nNot all dots and X are given.\n\nCells in the same position within two 3x3 boxes cannot contain the same digit (disjoint sets).","solution":"491623758328715496765498123812967534943852671657341982189276345534189267276534819","constraints":["XV","custom","disjoint-groups","kropki","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent digits along the red line must alternate in parity (odd/even).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Grey lines are thermometers.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"F28G66PTLg","ctcId":2084,"ctcDifficulty":"HARD","title":"Fare thee well, Miss Carousel","author":"Phistomefel","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle.  A dot in the centre of a 2x2 square indicates that the two digits in its positive diagonal have the same difference as the two digits in its negative diagonal. This difference is not necessarily the same for different 2x2 squares with dots. Not necessarily all such dots are given.","solution":"321879546547236819869145372492568731756391284183724965615987423938412657274653198","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A dot in the centre of a 2x2 square indicates that the two digits in its positive diagonal have the same difference as the two digits in its negative diagonal.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"Pbh6rNGPdg","ctcId":2088,"ctcDifficulty":"VERY HARD","title":"Friendly Indexing Miracle","author":"thoughtbyte","rules":"Normal sudoku rules apply. A cell is 'friendly' if it contains its row, column, or 3x3 box number. [Boxes are numbered in normal reading order ie top left (box 1) through to bottom right (box 9).) All friendly cells are column and row indexers, and they must index at least one cell other than themselves. Column indexing: friendly digits in column X indicate the column in which the digit X appears in that row. Row indexing: Friendly digits in row X indicate the row in which the digit X appears in that column. Friendly indexer example: if r3c6 is a 2, then r3c2 is a 6 and r2c6 is a 3. Digits may not repeat along the indicated diagonal.","solution":"542713869361982754798465132654321987137698425829547613475136298213879546986254371","constraints":["custom","diagonal"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All friendly cells are column and row indexers, and they must index at least one cell other than themselves.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"dh722BmNdM","ctcId":2089,"ctcDifficulty":"MEDIUM","title":"Sum Foggy Quads","author":"thoughtbyte","rules":"Normal sudoku rules apply. Placing a correct digit in the grid will clear any fog in the surrounding cells. Digits along a blue region sum line have an equal sum within each 3x3 box the line passes through. Region sum lines do not branch. Each “quadruple clue” is a white circle containing four digits – these four digits must each appear once in the four surrounding cells.  The digits in each quadruple clue’s white circle are in ascending order from left to right, top to bottom.","solution":"435768912128594673967123458853472169641359287792816345584231796276945831319687524","fogLight":"R2C2,R2C8,R9C9,R9C1","constraints":["fog","quadruple","region-sum-line"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"1pcuk5mpn2","ctcId":2092,"ctcDifficulty":"MEDIUM","title":"Apologetic Airlines","author":"olima","rules":"Normal Sudoku rules apply.\nAdjacent digits on a green line differ by at least 5.\nDigits on purple lines are distinct, consecutive and in any order.\nBox borders divide blue lines into segments with equal sums.\nBlack dots indicate digits in a ratio of 1:2, white dots consecutive digits. Not all dots are necessarily shown.\nRed squares indicate the position of the 5 in that row.","solution":"489172563253869741671534298542698137937415826168723459896241375325987614714356982","constraints":["custom","german-whispers","kropki","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Red squares indicate the position of the 5 in that row.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"yp87tkg99m","ctcId":2093,"ctcDifficulty":"MEDIUM","title":"RAT RUN 7: Multiple Choice","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nTELEPORTS: Entering a teleport will cause Finkz to be instantly transported to the matching coloured teleport. From there she can continue her journey. Matching teleports always have identical digits, but teleports that don't match always have different digits.\n\nONE-WAY DOORS: Finkz may only pass directly through a purple arrow if moving in the direction the arrow is pointing. An arrow always points to the smaller of the two values it sits between.\n\nTEST CONSTRAINT: In this experiment, for any two adjacent digits along the correct path, one can be divided by the other to give an exact integer (ie; one is a multiple of the other.)","solution":"728136495164295738935748261387652149641987523259314876572863914416579382893421657","constraints":["custom","inequality"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls. Matching teleports always have identical digits, but teleports that don't match always have different digits. TEST CONSTRAINT: In this experiment, for any two adjacent digits along the correct path, one can be divided by the other to give an exact integer (ie; one is a multiple of the other.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c7","c10"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"slyjfc5x9r","ctcId":2094,"ctcDifficulty":"MEDIUM","title":"Swimming in the Reeds","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along a green line have a difference of at least five. \nAll digits along a blue line must sum to the same total in each 3x3 box the line visits.\nCells separated by a black dot are in the ratio 1 to 2. \nCells separated by a white dot are consecutive. \nNot all possible dots are given.","solution":"961738542243516798758492163136274859482359617579861324624183975897645231315927486","constraints":["german-whispers","kropki","region-sum-line"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"cbux5i6zv0","ctcId":2095,"ctcDifficulty":"MEDIUM","title":"Drop","author":"zetamath & friends","rules":"Normal sudoku rules apply. Within a cage digits do not repeat and must sum to the total given at the cage’s top left corner. Along green lines, adjacent digits must differ by at least 5. Digits on a purple line form a set of non-repeating, consecutive digits in any order. The sum of digits on a blue line is the same within each 3x3 box. Any three adjacent digits along a peach line must include one digit from 123, one from 456, and one from 789.","solution":"241537869568149723793682451852913647179864532634725918486291375915376284327458196","constraints":["cage","entropic-line","german-whispers","region-sum-line","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"9t76BmHtFp","ctcId":2096,"ctcDifficulty":"HARD","title":"These Aren't The Circles You're Looking For","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nShade some cells such that, if a digit N appears in a shaded cell, it appears in exactly N shaded cells. The digit in a circle equals the sum of the digits in all shaded cells in the 3x3 area centered on the circle. \n\nThe digit on the grey square is even.","solution":"476918253583462197219537846135879462827645931964123785648751329792386514351294678","constraints":["custom","even"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells such that, if a digit N appears in a shaded cell, it appears in exactly N shaded cells. The digit in a circle equals the sum of the digits in all shaded cells in the 3x3 area centered on the circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"cgqcfwnwmi","ctcId":2097,"ctcDifficulty":"MEDIUM","title":"Sir Bri Sudoku","author":"olima","rules":"Normal Sudoku rules apply.\nAdjacent digits on green lines differ by at least 5.\nOn purple lines digits are from a set of consecutive digits in any order.\nBlack dots indicate digits in a 1:2 ratio. \nNot all dots are necessarily given.","solution":"283175649716924538495368721641589372537241986928736154162857493879413265354692817","constraints":["german-whispers","kropki","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"ykl7sztkdv","ctcId":2098,"ctcDifficulty":"VERY HARD","title":"Clasp Locker","author":"Dorlir","rules":"Normal sudoku rules apply. Digits an equal distance from the center of the purple line must sum to the digit in the center of that purple line.","solution":"457618392312947586698523471586134729173289645924765138865472913241396857739851264","constraints":["zipper-line"],"constraintFacts":[{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"BtghmrqfDb","ctcId":2099,"ctcDifficulty":"MEDIUM","title":"Kropki DotS","author":"Nityant Agarwal","rules":"Normal sudoku rules apply. Adjacent digits along the green line differ by at least 5. A black dot joins digits with a 2:1 ratio. A white dot joins cells with consecutive digits.","solution":"542879631687231954319564872854613297761928543293745186138496725976352418425187369","constraints":["german-whispers","kropki"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"etuf5ak2y4","ctcId":2100,"ctcDifficulty":"HARD","title":"RAT RUN 8: Discontinuous","author":"Marty Sears","rules":"Normal sudoku rules apply: place the digits 1-9 in each row, column, and 3x3 box (marked with dotted lines.)\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nMODIFIER: There are 9 doubler cells to be located in the maze, one in each row, column and box, and each containing a different digit. The real value of a doubler cell is calculated by doubling the digit that appears in it.\n\nBLACKCURRANTS: The values of cells connected by a blackcurrant are in a 1:2 ratio (one is double the other.) Not all possible blackcurrants have been given.\n\nFORBIDDEN DOORS: The values of cells connected by a red X sum to 10. Finkz may never pass through a red X. Not all possible Xs have been given.\n\nTEST CONSTRAINT: In this experiment, dotted box borders divide the correct path into segments, each of which must be a valid 'nabner line'; no two cells anywhere on a path segment can have consecutive or equal values. Eg: if a path segment contains an 8, there may not be a 7, a 9, or a doubled 4 anywhere else on that segment.","solution":"635978412279145368481362957354781296162539784798426135846213579523697841917854623","constraints":["XV","custom","kropki","nabner-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"FORBIDDEN DOORS: The values of cells connected by a red X sum to 10.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls. As well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. MODIFIER: There are 9 doubler cells to be located in the maze, one in each row, column and box, and each containing a different digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"BLACKCURRANTS: The values of cells connected by a blackcurrant are in a 1:2 ratio (one is double the other.)","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]}]},{"id":"3jdlbq25sj","ctcId":2101,"ctcDifficulty":"MEDIUM","title":"Big Bang","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle.","solution":"148653927652497813973128546497836152386215479521749638714962385839571264265384791","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"by04qqkuna","ctcId":2102,"ctcDifficulty":"MEDIUM","title":"Weird Bug","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nDigits on a line may not repeat and form a consecutive set, but may be in any order.\n\nDigits connected by a black dot are in a 1:2 ratio.","solution":"852491763347628159169357248291836574683574921475219386524183697938762415716945832","constraints":["kropki","renban"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"RGM6Pt7qM7","ctcId":2105,"ctcDifficulty":"MEDIUM","title":"9 Hours, 9 Pins, 9 Doors","author":"Botaku","rules":"Normal sudoku rules apply. For each number 1-9, there must be at least one set of three identical digits in a straight line of adjacent cells somewhere in the grid.","solution":"475913628392685147816274539961837452284159763537426981153742896749368215628591374","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For each number 1-9, there must be at least one set of three identical digits in a straight line of adjacent cells somewhere in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"r433rBpLPG","ctcId":2107,"ctcDifficulty":"MEDIUM","title":"Euclidean Windmill","author":"Botaku","rules":"Normal sudoku rules apply. For any two instances of a digit N, if it takes X horizontal steps and Y vertical steps to go from one to the other, then X*X + Y*Y is at least N.","solution":"861543972547962813932817564716354298285796341394281756473625189658139427129478635","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For any two instances of a digit N, if it takes X horizontal steps and Y vertical steps to go from one to the other, then X*X + Y*Y is at least N.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hm38DDftrd","ctcId":2109,"ctcDifficulty":"MEDIUM","title":"This + This = That","author":"Eric Rathbun","rules":"Normal Sudoku Rules apply.\nNormal Arrow Rules apply.\nDigits separated by a white dot have a difference of one while digits separated by a black dot are in a 1:2 ratio. Not all dots are given.","solution":"513678942487295613692134587951827436276413895834956271745382169369541728128769354","constraints":["arrow","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"vlkzbme0k2","ctcId":2110,"ctcDifficulty":"HARD","title":"Zoom Out","author":"Myxo","rules":"Sudoku: Place the digits 1-9 exactly once in each row, column and box.\n\nThermometer: Digits along a grey thermometer form an increasing sequence in order, with the lowest digit in the bulb.\n\nGerman Whisper: Digits separated by a green line differ by at least 5.","solution":"361978254428516937975432681654197328293864715817325496149683572736251849582749163","constraints":["german-whispers","thermometer"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6G7Mj2Bdmm","ctcId":2111,"ctcDifficulty":"MEDIUM","title":"True Blue","author":"James Kopp","rules":"Normal sudoku rules apply. Box borders divide blue lines into segments with equal sums. Cells separated by a black dot are in the ratio 1 to 2. All possible black dots are given.","solution":"819526473675134928432789615347961852196258347528347196761892534954673281283415769","constraints":["kropki","region-sum-line"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Every marker is given","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"lkztmzmo88","ctcId":2112,"ctcDifficulty":"MEDIUM","title":"Mystery Product","author":"Oddlyeven","rules":"Rules: Normal Sudoku rules apply. Put the digits 1 to 9 once each in each row, column and box.\nFog: The grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells.\nProduct-Sum Lines: Digits along a line sum to the product of the digits in the squares at either end of the line (if it is the same square, multiply that digit with itself). Digits may repeat on a line if permitted by the other rules. Lines do not branch or cross, but they may share squares with other lines.","solution":"629851347875634219143297865532179486984562173716348592461923758357486921298715634","fogLight":"R1C1,R1C2,R1C3,R2C1,R2C2,R2C3,R3C1,R3C2","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Product-Sum Lines: Digits along a line sum to the product of the digits in the squares at either end of the line (if it is the same square, multiply that digit with itself).","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"zd0vryms8s","ctcId":2114,"ctcDifficulty":"MEDIUM","title":"Hooked","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nBox borders divide each blue line into segments with the same sum.","solution":"476289153319475826852163947265814379941732685783596412597341268138627594624958731","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"vaeya6u829","ctcId":2115,"ctcDifficulty":"MEDIUM","title":"RAT RUN 9: Shock Value","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nTELEPORTS: Entering a yellow teleport will cause Finkz to be instantly transported to the other teleport. From there she can continue her journey. The teleports contain the same digit.\n\nBLACKCURRANTS: Cells connected by a blackcurrant have a 1:2 ratio (one is double the other.) Not all possible blackcurrants have been given.\n\nCAGES: Digits don't repeat in a cage. Every cage has the same total, which is to be deduced. The digit on a cage's electricity symbol is its 'shock value'. Any cage with a shock value of 5 or more is switched on, and Finkz should not enter these for safety reasons. Cages with a shock value lower than 5 are switched off and therefore safe to enter.\n\nTEST CONSTRAINT: In this experiment, the correct path will be a valid Chinese Whisper line, ie; adjacent digits along the path must differ by at most 2.","solution":"765312489314985627892467135671853942528794361439621578253148796146279853987536214","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls. As well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. TELEPORTS: Entering a yellow teleport will cause Finkz to be instantly transported to the other teleport. The teleports contain the same digit. Any cage with a shock value of 5 or more is switched on, and Finkz should not enter these for safety reasons. TEST CONSTRAINT: In this experiment, the correct path will be a valid Chinese Whisper line, ie; adjacent digits along the path must differ by at most 2.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7","c13","c15"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"66g31006zr","ctcId":2117,"ctcDifficulty":"HARD","title":"Ghost Cages","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply.\n\nThe dashed lines are part of non-overlapping retangular cages hidden in the grid. Digits in a cage do not repeat, and sum to the number represented by one or more cells in its upper left corner (read from left to right).\n\nExample: If a cage summed to 27, its upper leftmost cell would have a 2, with a 7 to its right.","solution":"327548169658319724491672385132854976789136452564297813813425697945761238276983541","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"0m0zb2b86m","ctcId":2118,"ctcDifficulty":"MEDIUM","title":"Spread","author":"Kennet’s Dad","rules":"Double Arrows, Product Squares \n\n-Normal sudoku rules apply. \n-The sum of digits along a line between two circles is equal to the sum of the digits in those two circles (ie Double arrows).\n-An X in the center of a 2x2 region of cells, a “product square,” indicates that the two digits in the square’s positive diagonal have the same product as the two digits in its negative diagonal. The product is not necessarily the same for different product squares. Not all product squares are necessarily indicated.","solution":"245186397367429581198735624739562148586914273412378965924851736853697412671243859","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"-The sum of digits along a line between two circles is equal to the sum of the digits in those two circles (ie Double arrows). -An X in the center of a 2x2 region of cells, a “product square,” indicates that the two digits in the square’s positive diagonal have the same product as the two digits in its negative diagonal.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"hrsnhhdbno","ctcId":2120,"ctcDifficulty":"HARD","title":"Copycat Confusion","author":"Phistomefel","rules":"1. Normal Sudoku rules apply.\n2. Divide the four lines in the grid into two pairs. The lines in a pair are copycats of each other, i.e. they have the same composition of digits. E.g. if one line has two 3s, five 4s and a 9, then the other one also has two 3s, five 4s and a 9. The order of the digits is not necessarily the same on the two lines.\n3. The two lines in the grid with a circle on one end are an average arrow and a thermometer. The two lines without a circle are a region sum line and a german whispers line. The solver has to find out which line obeys to which rule.\n\nAverage Arrow: The digit in the circle is the average (exact, not rounded) of the digits on the line.\nThermometer: The digits have to increase along the thermometer, starting from its bulb.\nRegion Sum Line: The line is cut into multiple segments by the box borders, each summing to the same number.\nGerman Whisper: Two neighboring digits have a difference of 5 or more.","solution":"647852931925163487183947526219478365856319742734526819598231674372694158461785293","constraints":["custom","german-whispers","region-sum-line","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"2. Divide the four lines in the grid into two pairs. The lines in a pair are copycats of each other, i.e. they have the same composition of digits. E.g. if one line has two 3s, five 4s and a 9, then the other one also has two 3s, five 4s and a 9. The order of the digits is not necessarily the same on the two lines. Average Arrow: The digit in the circle is the average (exact, not rounded) of the digits on the line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"German Whisper: Two neighboring digits have a difference of 5 or more.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Region Sum Line: The line is cut into multiple segments by the box borders, each summing to the same number.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Thermometer: The digits have to increase along the thermometer, starting from its bulb.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"dxuvqdw2co","ctcId":2121,"ctcDifficulty":"HARD","title":"Mission Impossible","author":null,"rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. Cells separated by a single knight's move (in chess) cannot contain the same digit.","solution":"376152489259486137814937652637594821592618374148273965765849213921365748483721596","constraints":["antiknight","arrow"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"3nkifpknc6","ctcId":2123,"ctcDifficulty":"HARD","title":"Lief, the Univeres, and Everythign","author":"SSG","rules":"SSG is turning 42? That can't be rihgt.\n\nNormal sudoku rules apply; but, every clue is wrogn. Any clue that fully obeys one of the following rules is not wrogn.\n\nAmbiguous Thermos: Digits along a gray line must strictly increase from one end to the other.\n\nAscending Starters: A clue outside the grid applies to the sum of the first run of ascending digits from the position of the clue (i.e. the sum from the first digit encountered until digits are no longer ascending). This may be only a single digit.\n\nEntropic Lines: Along a peach line, every group of three consecutive cells must contain one low {1,2,3}, one medium {4,5,6}, and one high {7,8,9} digit.\n\nKiller: Digits in a cage may not repeat and must sum to the given total.\n\nModular Lines: Along a teal line, every run of three digits must all have different remainders under division by 3.\n\nNabner: No two cells on a yellow line may contain either the same digit or consecutive digits.\n\nParity Lines: Along a red line, adjacent digits may not have the same parity.\n\nRenban: Digits along a purple line form a non-repeating consecutive set.\n\nQuadruples: Every digit in a circle must appear at least once in the surrounding four cells.","solution":"784391265123456789569287413942138657678549132351762894296873541815924376437615928","constraints":["cage","custom","entropic-line","modular-line","nabner-line","quadruple","renban","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Killer: Digits in a cage may not repeat and must sum to the given total.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Ascending Starters: A clue outside the grid applies to the sum of the first run of ascending digits from the position of the clue (i.e. the sum from the first digit encountered until digits are no longer ascending). Parity Lines: Along a red line, adjacent digits may not have the same parity.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c12"]},{"slug":"entropic-line","type":"entropic-line","variant":"modified","modifiers":[],"params":null,"note":"Entropic Lines: Along a peach line, every group of three consecutive cells must contain one low {1,2,3}, one medium {4,5,6}, and one high {7,8,9} digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"modular-line","type":"modular-line","variant":"modified","modifiers":[],"params":null,"note":"Modular Lines: Along a teal line, every run of three digits must all have different remainders under division by 3.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"nabner-line","type":"nabner-line","variant":"modified","modifiers":[],"params":null,"note":"Nabner: No two cells on a yellow line may contain either the same digit or consecutive digits.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c11"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Renban: Digits along a purple line form a non-repeating consecutive set.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c13"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Ambiguous Thermos: Digits along a gray line must strictly increase from one end to the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"fjayk4klcz","ctcId":2124,"ctcDifficulty":"HARD","title":"RAT RUN 10: Sensored","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nFOG: The maze has been filled with fog. When correct digits are entered, the nearby fog will clear. No guessing is required.\n\nBLACKCURRANTS: Digits connected by a blackcurrant are in a 1:2 ratio (one is double the other.) Not all possible blackcurrants have been given.\n\nMOTION SENSORS: The digit on a pink motion sensor indicates how many of the (up to 9) cells immediately surrounding the sensor are visited by Finkz - ie; any cells neighbouring the sensor cell (diagonally or orthogonally), as well as the sensor cell itself, are counted, if they lie on the path.\n\nCAGES: Digits don't repeat in a cage. Every cage has an electricity symbol, which indicates its 'shock value'. Any cage with a shock value of 5 or higher should not be entered by Finkz. Cages with a shock value lower than 5 are safe to enter.\n\nTEST CONSTRAINT: In this experiment, the first cage that Finkz enters could have any total. After that, each subsequent cage she enters must have a total exactly one greater than the previous cage she entered. Cages not entered by Finkz can have any total.","solution":"248597631396821745175463289739286154862145397514739826923614578687952413451378962","fogLight":"R8C1,R8C2,R9C1,R9C2","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. CAGES: Digits don't repeat in a cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c11"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"ww029llseg","ctcId":2125,"ctcDifficulty":"MEDIUM","title":"No RePEAts","author":"sujoyku","rules":"Normal sudoku rules apply. The circles contain a complete set of the digits from 1 to 9. In other words, no two circles may contain identical digits. Pea Lines: The sum of the digits on a line strictly between two circles is equal to a concatenation of the two values in the circles, in some order. For instance, 3_346_1 could be a valid split pea line, as 3+4+6=13, which is 1 concatenated with 3.","solution":"279813456613459782854672931937268145128594367465731298386147529792385614541926873","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The circles contain a complete set of the digits from 1 to 9. Pea Lines: The sum of the digits on a line strictly between two circles is equal to a concatenation of the two values in the circles, in some order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"7xe7r6dwgb","ctcId":2129,"ctcDifficulty":"HARD","title":"Compression","author":"Jay Dyer","rules":"Normal sudoku rules apply. The 3x3 box borders divide each blue line into segments. Along a line, each segment’s digits sum to the same total. Different lines may have different sums for their segments.","solution":"387492615621853974459671832876129453193745268245386197762518349518934726934267581","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"B44HPbbdfn","ctcId":2131,"ctcDifficulty":"VERY HARD","title":"Modifier Mystery","author":"Mnasti2","rules":"Normal sudoku rules apply. One cell in each row, column, and box contains a modifier. Each of the digits 1-9 is modified once. A modifier affects the value of a cell for purposes of all clue types besides normal sudoku. Four of the modifiers double the digit in that cell. Four of the modifiers increase the digit in that cell by 1. One modifier is broken and leaves the digit in that cell unchanged. Values in cells joined by a white dot are consecutive. Values in cells joined by a black dot are in a 1:2 ratio. Values in cells separated by a V must sum to 5. A digit in a grey square is even. Values in the cage sum to the total given. Values along an arrow sum to the number in the attached circle. Values along a thermometer must strictly increase from bulb to tip. Neighbouring Values along a green line must differ by at least 5. Values along the orange line read the same forwards and backwards. Values along a purple line must form a set of consecutive values in any order.","solution":"493817265286945317175263894951734628837526941624189753362458179519372486748691532","constraints":["XV","arrow","cage","even","german-whispers","kropki","palindrome","renban","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Values along an arrow sum to the number in the attached circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c13"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Values in the cage sum to the total given.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c12"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Neighbouring Values along a green line must differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c15"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Values in cells joined by a black dot are in a 1:2 ratio.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8","c9"]},{"slug":"palindrome","type":"palindrome","variant":"modified","modifiers":[],"params":null,"note":"Values along the orange line read the same forwards and backwards.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c16"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Values along a purple line must form a set of consecutive values in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c17"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Values along a thermometer must strictly increase from bulb to tip.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c14"]}]},{"id":"GThfJTPqtL","ctcId":2133,"ctcDifficulty":"MEDIUM","title":"A (sling)Shot in the Dark","author":"mnasti2","rules":"Normal sudoku rules apply. A digit on a bent arrow shows how many cells away the digit in the cell from which the arrow originates appears in the direction of the arrow, e.g. if R1C4 was a 3, then whichever digit is in R2C4 would also be in R1C1. Under the fog, a double-headed arrow is two overlapping slingshots, and adjacent digits along a green line differ by at least 5.","solution":"294135867768492513513768294359276148471853629826914375645327981182549736937681452","fogLight":"R1C4,R1C5,R1C6,R3C7","constraints":["custom","fog","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit on a bent arrow shows how many cells away the digit in the cell from which the arrow originates appears in the direction of the arrow, e.g. if R1C4 was a 3, then whichever digit is in R2C4 would also be in R1C1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"8c67u7k14l","ctcId":2137,"ctcDifficulty":"HARD","title":"The Lizard Baby Disambiguation","author":"olima","rules":"Normal Sudoku rules apply. Adjacent digits on a green line differ by at least 5. White dots indicate consecutive digits, the black dot digits in a 1:2 ratio. Not all dots are necessarily given. Red squares show the position of their cell's column number in that row, e. g. a 3 in R2C1 would put a 1 in R2C3.","solution":"974586321685321947132497685729845163341762859856139472568973214413258796297614538","constraints":["custom","german-whispers","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Red squares show the position of their cell's column number in that row, e. g. a 3 in R2C1 would put a 1 in R2C3.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"ur2bt9j05l","ctcId":2139,"ctcDifficulty":"MEDIUM","title":"Center Clash","author":"Blashyrkh","rules":"Normal sudoku rules apply.\n\nDigits along a thermometer strictly increase from the bulb end.","solution":"179263854682549713534718962921387645746152389358694127465971238217835496893426571","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"fbqQB8jrhn","ctcId":2141,"ctcDifficulty":"HARD","title":"Double Fireworks","author":"Antiknight","rules":"Normal sudoku rules apply. The digits along each arrow must multiply to the digit in the circled cell. Nine cells in the grid (one per row, column and 3x3 box) are Doublers, which count as double their value on arrows. Each digit appears in exactly one Doubler. Doublers aren't necessarily on arrows. The value of the Doubler is counted if it appears on a one cell arrow. Eg if r7c6 is a 3 and a Doubler then r6c5 is a 6.","solution":"132496875957328461846157293473982516519634782268715349394271658625849137781563924","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"The digits along each arrow must multiply to the digit in the circled cell.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Nine cells in the grid (one per row, column and 3x3 box) are Doublers, which count as double their value on arrows.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"rqFff63jpm","ctcId":2143,"ctcDifficulty":"HARD","title":"Foggy Loop","author":"Antiknight","rules":"Normal sudoku rules apply. The digits along each arrow must sum to the digit in the circled cell. Arrows don't branch and don't overlap each other. Every arrow circle has exactly one arrow connected to it. Every cage in the puzzle is a 3x3 square cage. Digits cannot repeat within a cage. A black dot between cells indicates cell values with a 2:1 ratio. A white dot between cells indicates cells with consecutive values. Not all dots are given.","rulesClarified":"Normal sudoku rules apply.\n\nEach arrow starts at a circled cell. The digits along the arrow, not counting the circle, sum to the digit in that circle.\n\nArrows do not branch, and they do not overlap each other. Every arrow circle has exactly one arrow connected to it.\n\nEvery cage is one of the 3x3 square cages. Digits cannot repeat within a cage.\n\nA black dot between two cells means one digit is double the other (a 2:1 ratio).\n\nA white dot between two cells means their digits are consecutive.\n\nNot all dots are given. A pair of cells with no dot between them tells you nothing.","solution":"967123458541678329328945716273589641459261873186734592815496237692357184734812965","fogLight":"R8C7,R7C8,R8C3,R7C2,R3C2,R2C3,R2C7,R3C8","constraints":["arrow","cage","fog","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8"]}]},{"id":"qcccbe8xug","ctcId":2144,"ctcDifficulty":"MEDIUM","title":"5's live in Foggy Flats","author":"Antiknight","rules":"Normal sudoku rules apply. All 5's in the grid must strictly have EITHER; a '1' directly above it AND/OR a '9' directly below it. It may have both, but it doesn't need both. The digits along each arrow must sum to the digit in the circled cell. Digits may repeat along an arrow if permitted by other rules.  Adjacent digits along each German whisper line must have a difference of at least 5. Digits along each thermometer must increase starting from the bulb end. The grid is partially covered with fog. Correctly placed digits will clear the fog around that cell.","solution":"347825691182649375569173482428596137971234568635718924816957243754362819293481756","fogLight":"R9C2,R9C5,R9C7,R9C9","constraints":["arrow","custom","fog","german-whispers","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All 5's in the grid must strictly have EITHER; a '1' directly above it AND/OR a '9' directly below it.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"yjy08cqz6p","ctcId":2145,"ctcDifficulty":"MEDIUM","title":"∑ or μ","author":"Antiknight","rules":"Normal Sudoku rules apply. The digit in the circle is the exact average of the digits on the golden line. The digits along each grey line must sum to 10. The four cells surrounding the white circle in box 6 must contain consecutive digits in any order.","solution":"739824156641597382825613974517986243392471865486235791274368519153749628968152437","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digit in the circle is the exact average of the digits on the golden line. The digits along each grey line must sum to 10. The four cells surrounding the white circle in box 6 must contain consecutive digits in any order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]}]},{"id":"6gdihuldki","ctcId":2146,"ctcDifficulty":"VERY HARD","title":"The Hare And The Tortoise","author":"Marty Sears?","rules":"Normal sudoku rules apply: place the digits 1-9 once each in every row, column, and 3x3 box.\n\nRACE: The Hare and the Tortoise must race in orthogonal or diagonal steps, and must not enter ponds, or cross or overlap each other or themselves, apart from at the finish line, where they both end.\n\nHARE: The Hare must enter every box exactly once each (including box 9 - starting in box 9 does NOT count as entering it). The Hare's racing line will be a valid Super Fast Thermo - ie. digits along it increase by at least 3 at a time, but the Hare has a nap at every box border and the Thermo may begin again on any digit in the next cell.\n\nTORTOISE: The Tortoise's racing line will be a valid Slow Thermo - ie. digits along it may not decrease.\n\nFOX: The Fox declares the winner by displaying a digit that does NOT appear on the winner's racing line.\n\nDUCK: Digits separated by the Duck sum to 5.","solution":"186459327934217865572683194418935276297864513365172489823596741749321658651748932","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"RACE: The Hare and the Tortoise must race in orthogonal or diagonal steps, and must not enter ponds, or cross or overlap each other or themselves, apart from at the finish line, where they both end. HARE: The Hare must enter every box exactly once each (including box 9 - starting in box 9 does NOT count as entering it). FOX: The Fox declares the winner by displaying a digit that does NOT appear on the winner's racing line. DUCK: Digits separated by the Duck sum to 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c6","c7"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]}]},{"id":"0of52e2mjx","ctcId":2148,"ctcDifficulty":"VERY HARD","title":"Medieval Upheaval 4","author":"Nordy","rules":"Chaos Construction: Divide the grid into regions, each consisting of nine orthogonally-connected cells. Every row, column, and region must contain the digits 1 to 9 once each.\n\nRenbans: Digits along a pink line form a non-repeating consecutive set, but may be written in any order.\n\nChess Sums: A cell with a number in its top-left corner is a Chess Sums cell. The number in the top-left corner indicates the amount of Chess Sums satisfied by the digit in that cell. A digit in a Chess Sums cell gives one or more of the following:\n• The sum of all digits that share its region and are a king’s move away\n• The sum of all digits that share its region and are a knight’s move away\n• The sum of all digits that share its region and are a bishop’s move away\n\nClarifications:\n• Bishops can “see” past cells from other regions—cells from other regions do not block a bishop’s vision.\n• Each Chess Sum is calculated separately. For example, a cell with a “2” clue that contains a 7 can see 4 and 3 by king’s move, and can see 5 and 2 by knight’s move—the king’s move digits and the knight’s move digits each sum to 7 separately.","solution":"859137624716328459623714985395476812978561243184295367241859736462983571537642198","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Chess Sums: A cell with a number in its top-left corner is a Chess Sums cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"a6zbf6jui2","ctcId":2151,"ctcDifficulty":"VERY HARD","title":"The Goldilocks Zone","author":"Marty Sears","rules":"Normal sudoku rules apply\n\nDivide the grid into 3 zones. Each zone consists of a single group of orthogonally connected cells. No 2x2 area may be entirely within one zone.\n\nThe first zone is 'too hot'. Any cell in the hot zone has a value one greater than its digit.\n\nThe second zone is 'too cold'. Any cell in the cold zone has a value one less than its digit.\n\nThe third zone is 'just right'; this is the Goldilocks Zone. In this zone, a cell's value equals its digit, like normal.\n\nThe 9 objects (bowls, chairs and beds) all contain different digits, but each object of the same type has the same value.\n\nZone borders (NOT box borders) divide blue lines into segments, each of which has the same total (ie; the sum of its VALUES.) The two ends of a blue line always lie in different zones.","solution":"956182473718354962342697581687543129594271638231869745423916857879435216165728394","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into 3 zones. The 9 objects (bowls, chairs and beds) all contain different digits, but each object of the same type has the same value.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c11"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Zone borders (NOT box borders) divide blue lines into segments, each of which has the same total (ie; the sum of its VALUES.)","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]}]},{"id":"1eo6o1zoq2","ctcId":2152,"ctcDifficulty":"MEDIUM","title":"PalinPhisto","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Cells separated by a single knight's move (in chess) cannot contain the same digit.  The grey line in the grid is a palindrome (ie the string of digits along the line must read the same forwards and backwards.)","solution":"271589364689341572543672891456127983897453126132896457728914635964735218315268749","constraints":["antiknight","palindrome"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"510jy8hqjs","ctcId":2153,"ctcDifficulty":"MEDIUM","title":"A Night in the Entropics","author":"Walking Writer","rules":"Normal sudoku rules apply. Digits connected by a black dot have a 2 to 1 ratio. Digits connected by a white dot are consecutive. Not all black and white dots are shown. Cells separated by a chess king’s move cannot contain the same digit. Cells separated by a chess queen’s move cannot contain the same digit, but this rule applies only to digits 3, 6 and 9. Any three consecutive digits along a peach line must include a digit from the set (1, 2, 3), a digit from the set (4, 5, 6) and a digit from the set (7, 8, 9). All peach lines of length three MUST contain the digits 3, 6 and 9 in some order.","solution":"731852649842697531965431827513284796274965183698173254157348962329516478486729315","constraints":["antiking","custom","entropic-line","kropki"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells separated by a chess queen’s move cannot contain the same digit, but this rule applies only to digits 3, 6 and 9. All peach lines of length three MUST contain the digits 3, 6 and 9 in some order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c8"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"z01nexs74t","ctcId":2158,"ctcDifficulty":"MEDIUM","title":"Take the Low Road","author":"Chilly","rules":"Normal Sudoku rules apply.\nSome cells contain arrows. A digit in a cell with an arrow must be larger than all the other digits in the grid in the cells along the direction of the arrow.","solution":"791362845265847193438195627879653412543218976126479538984736251352981764617524389","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a cell with an arrow must be larger than all the other digits in the grid in the cells along the direction of the arrow.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"i0jnn0206n","ctcId":2159,"ctcDifficulty":"MEDIUM","title":"Paths Through the Mist","author":"Chilly","rules":"The grid is partially covered in fog. Placing correct digits will clear the fog, possibly revealing more clues. No guessing is required. Each row, column, and region contains the digits 1–9 exactly once each. A region is an orthogonally connected collection of cells, and regions are to be determined. The digit in a cell containing an arrow indicates the number of region borders in that direction. (If there is more than one arrow, the number of borders is the same in each direction eg a 4 in the cell with two arrows pointing East and North would indicate that there were 4 borders to the East AND 4 borders to the North). The outer edges of the grid do not count as borders. A digit in a circle equals the total number of cells seen horizontally and vertically that are in the same region as the digit, including itself. Borders obstruct vision.","rulesClarified":"The grid is partially covered in fog. Placing correct digits will clear the fog, possibly revealing more clues. No guessing is required.\n\nEach row, column and region contains the digits 1–9 exactly once each.\n\nA region is an orthogonally connected group of cells. The regions are to be determined by you.\n\nBorders obstruct vision. The outer edges of the grid do not count as borders.\n\nArrow clue: the digit in a cell containing an arrow is the number of region borders in the direction the arrow points. If a cell has more than one arrow, the same number applies to each direction. For example, a 4 in a cell with arrows pointing East and North means there are 4 borders to the East and 4 borders to the North.\n\nCircle clue: a digit in a circle equals the total number of cells seen horizontally and vertically that are in the same region as the circle's cell, including the circle's own cell. Looking outward in each of the four directions, the count stops at a border.","solution":"953816724278691435495782613587934162164325897829147356632578941316459278741263589","fogLight":"R4C5,R6C1,R7C3","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A region is an orthogonally connected collection of cells, and regions are to be determined. The digit in a cell containing an arrow indicates the number of region borders in that direction. A digit in a circle equals the total number of cells seen horizontally and vertically that are in the same region as the digit, including itself.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c9"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"bwevls7kjx","ctcId":2161,"ctcDifficulty":"VERY HARD","title":"Renban Circus","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nEach purple line contains a set of consecutive, non-repeating digits, which can appear in any order.\n\nUsing red, green, and blue, color in all circles such that:\n-Orthogonally adjacent circles are different colors.\n-Circles on the same purple line are the same color.\n-The digit inside a circle appears that many times in circles of that color.","solution":"956478321247315968318629475179842653682153794435796182894237516721564839563981247","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"-Orthogonally adjacent circles are different colors. -Circles on the same purple line are the same color. -The digit inside a circle appears that many times in circles of that color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"869hsb49kn","ctcId":2164,"ctcDifficulty":"MEDIUM","title":"Hazy Rellik","author":"gdc","rules":"𝗦𝘂𝗱𝗼𝗸𝘂: Normal Sudoku rules apply.\n𝗙𝗼𝗴: The grid is covered in fog. Placing correct digits reveals  clues in the surrounding 3x3 area.\n𝗥𝗲𝗹𝗹𝗶𝗸 𝗖𝗮𝗴𝗲𝘀: Any combination of one or more digits within a Cage CANNOT sum to the value in the top left. Digits may not repeat in a cage.\n𝗞𝗿𝗼𝗽𝗸𝗶 𝗣𝗮𝗶𝗿𝘀: Digits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. Not all dots are given.","solution":"438617592521938674769254831854791326392546718617382945945163287283475169176829453","fogLight":"R1C1,R1C2,R1C3,R2C1,R2C2,R2C3,R3C1,R3C2,R3C3","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"𝗥𝗲𝗹𝗹𝗶𝗸 𝗖𝗮𝗴𝗲𝘀: Any combination of one or more digits within a Cage CANNOT sum to the value in the top left.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"2susajautc","ctcId":2167,"ctcDifficulty":"HARD","title":"Galaxies Collide","author":"Marty Sears and Dorlir","rules":"• Normal sudoku rules apply.\n• Divide the grid into two galaxies. Every cell in the grid belongs to one of the two galaxies.\n• Each galaxy must consist of a region of orthogonally connected cells, and must have 180 degree rotational symmetry. (The central point around which a galaxy is symmetrical doesn't need to actually belong to that galaxy.)\n• No 2x2 area may belong entirely to one galaxy.\n• One of the two galaxies behaves like a German whisper; orthogonally adjacent cells in this galaxy must have a difference of at least 5.\n• An arrow cell counts how many cells in its own galaxy are being pointed at altogether by its arrow(s), and this combined total is displayed on the arrow cell (the arrow cell itself is not included in the count.) Vision is not obscured by the other galaxy's cells.","solution":"863249571127568943495317268349185726782436159516792834651823497238974615974651382","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Divide the grid into two galaxies. Every cell in the grid belongs to one of the two galaxies. • Each galaxy must consist of a region of orthogonally connected cells, and must have 180 degree rotational symmetry. (The central point around which a galaxy is symmetrical doesn't need to actually belong to that galaxy.) • No 2x2 area may belong entirely to one galaxy. • An arrow cell counts how many cells in its own galaxy are being pointed at altogether by its arrow(s), and this combined total is displayed on the arrow cell (the arrow cell itself is not included in the count.) Vision is not obscured by the other galaxy's cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"dk0wreok2y","ctcId":2169,"ctcDifficulty":"MEDIUM","title":"That’s 3 in the Corner","author":"James Kopp","rules":"Normal sudoku rules apply.\nWithin a 3x3 box, orthogonally connected cells must have a difference of at least 3.\nPlace an arrow in the grid with its (single cell) circle in box 1, with a straight shaft and the tip of its shaft in box 9. The circle plus the shaft is eight cells long. Digits on the shaft sum to the digit in the circle of that arrow.","rulesClarified":"Normal sudoku rules apply.\n\nWithin each 3x3 box, any two cells that are next to each other horizontally or vertically must differ by at least 3. Diagonal neighbours have no such rule.\n\nPlace one arrow in the grid. The arrow is not drawn; you must work out where it goes. Its circle is a single cell in box 1 (the top-left box). Its shaft is a straight line of seven cells that starts next to the circle, and its tip, the last cell of the shaft, lies in box 9 (the bottom-right box). The circle and the shaft together are eight cells long.\n\nThe digits on the seven shaft cells add up to the digit in the circle. The circle's own cell is not part of that sum.","solution":"594738261261495837837162594159627483483951726726384159948273615615849372372516948","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Within a 3x3 box, orthogonally connected cells must have a difference of at least 3.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qul8bqsp5c","ctcId":2170,"ctcDifficulty":"HARD","title":"Diaeresis 2.0","author":"Kennet's Dad","rules":"-Normal sudoku rules apply.\n-The grid is mostly covered in fog; placing a correct digit removes fog in the neighboring and surrounding cells.\n-A red \"X\" indicates a product square: a 2x2 region of cells where the product of the digits on the negative diagonal equals the product of the digits on the positive diagonal. \n-A blue \"X\" indicates a sum square: a 2x2 region of cells where the sum of the digits on the negative diagonal equals the sum of the digits on the positive diagonal. \n-Digits in cells separated by a white dot must be consecutive.\n-No rule is subject to a negative constraint.","solution":"975826413862413597431759862793148256528697134614235789286371945149562378357984621","fogLight":"R2C2","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"-A red \"X\" indicates a product square: a 2x2 region of cells where the product of the digits on the negative diagonal equals the product of the digits on the positive diagonal. -A blue \"X\" indicates a sum square: a 2x2 region of cells where the sum of the digits on the negative diagonal equals the sum of the digits on the positive diagonal.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"mqx8o45al4","ctcId":2171,"ctcDifficulty":"MEDIUM","title":"Zip-Pea","author":"sujoyku","rules":"Normal sudoku rules apply. Pea lines: The sum of the digits on a line strictly between two circles is equal to a concatenation of the two values in the circles, in some order. For instance, 3_346_1 could be a valid split pea line, as 3+4+6=13, which is 1 concatenated with 3. Zipper lines: Cells on a lavender line at an equal distance to the centre, which is marked with a dot, sum to the digit at the centre. (Note: The circles of pea lines are NOT part of the zipper lines. Ie the pea lines are green and lavender but the zipper lines are only the lavender parts.)","solution":"976234851254618937183957246529863714861745329347129685792581463418396572635472198","constraints":["custom","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Pea lines: The sum of the digits on a line strictly between two circles is equal to a concatenation of the two values in the circles, in some order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"fjllpp2awq","ctcId":2172,"ctcDifficulty":"MEDIUM","title":"Loopy Odysee","author":"gdc","rules":"Normal sudoku rules apply.\nDraw a one-cell-wide loop of orthogonally connected cells. The loop may touch itself diagonally, but not orthogonally.\nAdjacent digits on the loop differ by 5 or more.\nBox borders divide the loop into segments. Circles are on the loop and their digits count the number of cells in their segments.","rulesClarified":"Normal sudoku rules apply.\n\nDraw one loop through some cells. The loop is one cell wide: each cell on the loop is orthogonally connected to the two cells next to it along the loop, and the loop closes on itself.\n\nThe loop may touch itself diagonally, but two loop cells that share an edge must be next to each other along the loop.\n\nAny two cells that are next to each other along the loop have digits that differ by 5 or more.\n\nThe 3x3 box borders divide the loop into segments: each time the loop passes from one 3x3 box into another, a new segment begins.\n\nEach circle sits on a cell of the loop. Its digit is the number of cells in the segment that contains it, and that count includes the circle's own cell.","solution":"729154368164938257835267941386529174512473689497816532953741826271685493648392715","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop of orthogonally connected cells. Circles are on the loop and their digits count the number of cells in their segments.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"e0l316poog","ctcId":2173,"ctcDifficulty":"VERY HARD","title":"Bodysnatchers","author":"AnalyticalNinja and Kafkapharnaum","rules":"Normal Sudoku rules apply\n\nDOUBLERS\n– There is exactly one Doubler cell in every row, column, and 3x3 box. These cells contain a full set of the digits 1-9 and do not overlap with the Body Snatcher cells\n– A Doubler cell's value is twice the value of the digit in that cell\n\nBODY SNATCHERS\n–There is exactly one Body Snatcher cell in every row, column, and 3x3 box. These cells contain a full set of the digits 1-9 and do not overlap with the Doubler cells\n– Body snatcher cells count as exactly one higher, or one lower than the value of one of the cells they are orthogonally adjacent to, which cell must be in the same box as the Body Snatcher it's parasited by\n\nRENBANS\n– Each purple line contains a set of consecutive, non-repeating values, which can appear in any order\n– Digits can repeat on a renban as long as the value they take is never twice the same and no value ends up repeated on the renban","solution":"136745829497826531582319764359487612718962453264153978621594387975238146843671295","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"– There is exactly one Doubler cell in every row, column, and 3x3 box. These cells contain a full set of the digits 1-9 and do not overlap with the Body Snatcher cells –There is exactly one Body Snatcher cell in every row, column, and 3x3 box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c6"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"– Each purple line contains a set of consecutive, non-repeating values, which can appear in any order","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]}]},{"id":"j3j5t378kj","ctcId":2176,"ctcDifficulty":"EASY","title":"Climbing The Stairs","author":null,"rules":"Normal sudoku rules apply. Starting in a corner, along the grey stairs the difference between the first pair of digits is at least 2, the next pair at least 3, then at least 4 etc. Moreover the first and last digits are equal.","solution":"157483692928615347643927185784132956392756418561849723239561874475398261816274539","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Starting in a corner, along the grey stairs the difference between the first pair of digits is at least 2, the next pair at least 3, then at least 4 etc. Moreover the first and last digits are equal.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"3ma2z9n9lr","ctcId":2177,"ctcDifficulty":"MEDIUM","title":"Balance","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nBalance Cells: Identify 9 Balance Cells in the grid such that there is one Balance Cell in every row, column, and 3x3 box. Each Balance Cell must contain a different digit. The value of a Balance Cell is the arithmetic mean of the up to 4 digits orthogonally adjacent to itself, regardless of the digit in the Balance Cell.\n\nGlobal Balance: The sum of the values of every cell in the grid is 405.\n\nKiller: The values of cells in a cage must sum to the total in the top left corner. Digits may not repeat within a cage, but values may.","rulesClarified":"Normal sudoku rules apply: place the digits 1 to 9 once each in every row, column and 3x3 box.\n\nNine cells are balance cells. The grid does not mark them. You must choose them so that there is exactly one balance cell in every row, every column and every 3x3 box. Each balance cell must contain a different digit.\n\nThe value of a balance cell is the arithmetic mean of the digits in the orthogonally adjacent cells (above, below, left and right). Use only the neighbours that exist, so an edge cell has fewer than four. The balance cell's own digit does not count. A neighbour is used for its digit, even if the neighbour is itself a balance cell.\n\nThe value of any other cell is its digit.\n\nThe values of all 81 cells add up to 405.\n\nKiller cages: the values of the cells in a cage add up to the total in its top-left corner. Values are summed, not digits.\n\nWithin a cage, no two cells may have the same digit. Two cells in one cage may have the same value.","solution":"548629371361875942729143685284936517176582493935417268457361829692758134813294756","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Killer: The values of cells in a cage must sum to the total in the top left corner.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Balance Cells: Identify 9 Balance Cells in the grid such that there is one Balance Cell in every row, column, and 3x3 box. Each Balance Cell must contain a different digit. The value of a Balance Cell is the arithmetic mean of the up to 4 digits orthogonally adjacent to itself, regardless of the digit in the Balance Cell. Global Balance: The sum of the values of every cell in the grid is 405.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]}]},{"id":"urcfy6f7yx","ctcId":2178,"ctcDifficulty":"MEDIUM","title":"Is Zipper A Zodiac Sign?","author":"gdc","rules":"𝗦𝘂𝗱𝗼𝗸𝘂: Normal Sudoku rules apply.\n𝗙𝗼𝗴 𝗢𝗳 𝗪𝗮𝗿: The grid is covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area.\n𝗦𝗽𝗶𝗿𝗮𝗹 𝗚𝗮𝗹𝗮𝘅𝗶𝗲𝘀: Divide the grid into galaxies: orthogonally connected groups of cells that have 180 degree rotational symmetry about their centers (marked with a large circle). All cells must be part of a galaxy; no galaxies overlap.\n𝗡𝗼 𝗥𝗲𝗽𝗲𝗮𝘁𝘀: Digits may not repeat in a galaxy.\n𝗭𝗶𝗽𝗽𝗲𝗿 𝗚𝗮𝗹𝗮𝘅𝗶𝗲𝘀: A \"Z\" orbiting a galaxy center marks a zipper galaxy where each digit and the cell rotationally opposite to it sum to the circled digit.\n𝗚𝗮𝗹𝗮𝘅𝘆 𝗧𝗼𝘁𝗮𝗹𝘀: If given, a digit orbiting a galaxy center shows the sum of all digits in that galaxy.","solution":"451698327623574981879213564542187639938462175716935248395746812287351496164829753","fogLight":"R6C6","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"𝗦𝗽𝗶𝗿𝗮𝗹 𝗚𝗮𝗹𝗮𝘅𝗶𝗲𝘀: Divide the grid into galaxies: orthogonally connected groups of cells that have 180 degree rotational symmetry about their centers (marked with a large circle). 𝗡𝗼 𝗥𝗲𝗽𝗲𝗮𝘁𝘀: Digits may not repeat in a galaxy. 𝗭𝗶𝗽𝗽𝗲𝗿 𝗚𝗮𝗹𝗮𝘅𝗶𝗲𝘀: A \"Z\" orbiting a galaxy center marks a zipper galaxy where each digit and the cell rotationally opposite to it sum to the circled digit. 𝗚𝗮𝗹𝗮𝘅𝘆 𝗧𝗼𝘁𝗮𝗹𝘀: If given, a digit orbiting a galaxy center shows the sum of all digits in that galaxy.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c6","c7","c8"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"n5c2fyb55l","ctcId":2181,"ctcDifficulty":"MEDIUM","title":"Mission Impossible 2","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits along an arrow must sum to the digit in that arrow's circle. Digits may not repeat along a main diagonal (marked in blue). Cells separated by a (single) king's move (in chess) cannot contain the same digit.","solution":"254386791798142365163975428425619837837254619916837542642598173571423986389761254","constraints":["antiking","arrow","diagonal"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"d4qzz9umkk","ctcId":2183,"ctcDifficulty":"HARD","title":"Milestones","author":"Marty Sears","rules":"Normal sudoku rules apply\n\nDivide the grid into grey and orange regions. A region is a group of orthogonally connected cells of the same colour. No 2x2 area may be all one colour. Two regions of the same colour may not touch diagonally.\n\nMILESTONES:\nA digit on an arrow cell indicates how many cells you have to travel in the indicated direction until you reach a cell of the opposite colour. Eg: if an orange arrow cell contains a 1 then the neighbouring cell in the direction of the arrow would be grey.\n\nDUTCH WHISPERS:\nTwo orthogonally adjacent orange cells must have a difference of at least 4.\n\nREGION SIZE CLUES:\nA small clue indicates the number of cells in the region.\n\nBALANCED CAGES:\nIn a cage, the sum of orange digits must equal the sum of grey digits. Digits MAY repeat in a cage if allowed by sudoku.","solution":"627159384815463729934827516398674152742531968156298473561942837279385641483716295","constraints":["custom","dutch-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into grey and orange regions. No 2x2 area may be all one colour. Two regions of the same colour may not touch diagonally. A digit on an arrow cell indicates how many cells you have to travel in the indicated direction until you reach a cell of the opposite colour. A small clue indicates the number of cells in the region. In a cage, the sum of orange digits must equal the sum of grey digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c5","c7","c12","c14"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"0qxs14n4hl","ctcId":2184,"ctcDifficulty":"VERY HARD","title":"Runway","author":"Qodec","rules":"- Sudoku: Each row, column, and region indicated by thick borders in the grid must contain the digits 1 to 9 once each.\n- Arrows: Digits along an arrow sum to the digit in its attached circle. (Digits may repeat on an arrow if allowed by other rules.)\n- Maximum killer cages: An area surrounded by a dashed line is a killer cage. Digits in a cage cannot repeat. If a number is given in the upper left corner of a cage, the digits in that cage sum to that number, or less.","rulesClarified":"Normal sudoku rules apply: each row, column and thick-bordered region holds the digits 1 to 9 once each.\n\nArrows: each arrow starts at a circle. The digits along the arrow, not counting the circle, sum to the digit in that circle. Digits may repeat along an arrow if no other rule forbids it.\n\nKiller cages: a cage is an area drawn with a dashed line. Digits in a cage cannot repeat.\n\nA cage with a number in its top-left corner has digits that sum to that number or less. A cage without a number has no sum limit; only the no-repeat rule applies to it.","solution":"621483579573269148849517632736924815958136427412875963264398751397651284185742396","constraints":["arrow","cage"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"xqgzhq4bqn","ctcId":2185,"ctcDifficulty":"MEDIUM","title":"Pea Soup","author":"Oddlyeven","rules":"Rules: Normal Sudoku rules apply. Put the digits 1 to 9 once each into every row, column and 3x3 box.\nFog: The grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells.\nSplit-Pea Lines: The sum of the digits on a line strictly between two circles is equal to a concatenation of the two values in the circles, in some order. For instance, 4-347-1 could be a valid split pea line, as 3 + 4 + 7 = 14, which is 1 concatenated with 4. Digits may repeat on a line if allowed by the other rules. Lines do not cross, branch or share cells with other lines, but they may share circles.\nDots: Digits on a black dot are in a 1 to 2 ratio. Not all dots are given.","solution":"435812697817965324629374158798126543163549872542783916251438769986257431374691285","fogLight":"R1C1,R1C2,R1C3,R2C1,R2C2,R2C3,R3C1,R3C2,R3C3","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Split-Pea Lines: The sum of the digits on a line strictly between two circles is equal to a concatenation of the two values in the circles, in some order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"2iaiw4r5o5","ctcId":2186,"ctcDifficulty":"MEDIUM","title":"Restricted Access","author":"Kennet's Dad","rules":"Negative Diagonal, Fog of War, Odd/Even, X/V Pairs (neg. V), Kropki Pairs\n\nNormal sudoku rules apply. Digits along the blue 'negative' diagonal may not repeat; this diagonal begins in row 1 column 1 and crosses the grid to row 9 column 9. Some of the grid is covered in fog; placing a correct digit will remove the fog surrounding that digit. A cell filled with a blue square contains an even digit. Digits in cells joined by an X sum to 10; NOT all X clues are given. Digits in cells joined by a V sum to 5; ALL V clues are given and visible from the outset of the puzzle. One digit is double the other in cells joined by a black dot. Not all black dots are given.","solution":"175462839634978125289531476927814653361759284458326917893245761512697348746183592","fogLight":"R1C3,R9C7,R5C2,R6C3,R9C5,R5C8,R4C7,R1C5,R1C8,R2C7,R2C8,R3C6,R3C7,R4C5,R4C6,R5C5,R6C4,R6C5,R7C3,R7C4,R8C2,R8C3,R9C2,R1C1,R9C9","constraints":["XV","diagonal","even","fog","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"jx80un5ofh","ctcId":2187,"ctcDifficulty":"HARD","title":"Eureka!","author":"Michael Lefkowitz","rules":"Normal sudoku rules apply. Shade some additional cells grey ('walls') and leave some unshaded ('cave'). The cave is one orthogonally-connected group, and walls form orthogonally-connected groups that touch an edge of the grid. Draw a 1-cell wide loop that moves orthogonally, entering every cave cell (and no wall cells). Each digit on the loop in row N differs from its neighbours on the loop by at least N. Gold is found in wall cells with digits larger than their row number. All possible gold has been given. Digits separated by a white dot have consecutive values.","solution":"174598632826413795593762418957346281632851947418279356781924563269135874345687129","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some additional cells grey ('walls') and leave some unshaded ('cave'). The cave is one orthogonally-connected group, and walls form orthogonally-connected groups that touch an edge of the grid. Draw a 1-cell wide loop that moves orthogonally, entering every cave cell (and no wall cells). Each digit on the loop in row N differs from its neighbours on the loop by at least N. Gold is found in wall cells with digits larger than their row number. All possible gold has been given.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"0tzabtgceq","ctcId":2188,"ctcDifficulty":"MEDIUM","title":"Parity loop","author":"Lithium-Ion","rules":"Normal Sudoku rules apply. All even digits in the grid except the even digits in the center box form a single, closed loop that moves orthogonally through the centers of cells, and does not branch, overlap, or touch itself (not even diagonally). A digit in a circle indicates exactly how many circles contain that digit. Digits in a cage sum to the value in the top left corner. Digits in a thermometer must increase from the bulb end.","solution":"391468275784215693625973481259741368413689752867532914548397126932156847176824539","constraints":["cage","counting-circle","custom","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All even digits in the grid except the even digits in the center box form a single, closed loop that moves orthogonally through the centers of cells, and does not branch, overlap, or touch itself (not even diagonally).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"5ljgkj9tos","ctcId":2189,"ctcDifficulty":"MEDIUM","title":"Divide and conquer","author":"Lithium-Ion","rules":"Normal Sudoku rules apply. Orthogonally adjacent cells are not allowed to contain consecutive digits. The only digits that can be placed on a yellow divisor line have to be divisors of the maximum digit on the line. For example, if the maximum digit on a yellow divisor line is 8, one is only allowed to place the digits 1,2,4 and 8 on this line. Digits on a yellow divisor line may repeat if allowed by other rules.","solution":"573168429816492753249735186681357942924681375357924618795246831138579264462813597","constraints":["custom","non-consecutive"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The only digits that can be placed on a yellow divisor line have to be divisors of the maximum digit on the line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"f8ndB28nDT","ctcId":2190,"ctcDifficulty":"HARD","title":"Black mamba","author":"Lithium-Ion","rules":"Normal sudoku rules apply. Draw a one-cell wide snake, which starts in Box 5 and ends in Box 9, that moves orthogonally through the center of cells. The snake is not allowed to branch, intersect with itself or touch itself, even diagonally. Cells that are orthogonally adjacent along the snake have to contain consecutive digits. Within each box, the box number (1=top left, 2=top center, 3=top right, etc.) has to be part of the snake. Cells separated by a black dot contain digits that are in a 1:2 ratio. All black dots are given.","rulesClarified":"Normal sudoku rules apply.\n\nDraw one snake: a one-cell-wide path that runs through the centres of cells, moving orthogonally. It starts in Box 5 and ends in Box 9.\n\nThe snake may not branch, cross itself, or touch itself, not even diagonally.\n\nAlong the snake, two cells that are next to each other on the snake contain consecutive digits. Cells that are next to each other on the grid but not on the snake have no such rule.\n\nWithin each box, the box number (1 for top left, 2 for top centre, 3 for top right, and so on) has to be part of the snake.\n\nEach black dot sits on the edge between two orthogonally adjacent cells. The two digits on either side of a dot are in a 1:2 ratio, so one is twice the other.\n\nAll black dots are given.","solution":"685432197794186235123597648276318459348259761951764823567823914419675382832941576","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell wide snake, which starts in Box 5 and ends in Box 9, that moves orthogonally through the center of cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"7BghrPt24L","ctcId":2191,"ctcDifficulty":"MEDIUM","title":"Mathemagics","author":"Lithium-Ion","rules":"Normal Sudoku rules apply. Draw a one-cell wide loop that moves orthogonally through the center of cells and does not branch, intersect with itself or touch itself (neither orthogonally nor diagonally). The loop has to visit each box at least once. For each box, the maximum number of cells belonging to the loop is k, where k is the box number. Within each box, the box number has to be part of the loop. Boxes are numbered in normal reading order. Two orthogonally adjacent cells are only allowed to contain digits that sum to 7 or 10 if both cells are not part of the loop. The 24 cells that are enclosed by the loop have to contain two magic squares. A magic square is a 3x3 region containing the digits from 1 to 9 once each, where each row, column and diagonal must sum to the same value.","rulesClarified":"Normal Sudoku rules apply.\n\nDraw a one-cell wide loop through the centres of cells. The loop moves orthogonally, never branches, never crosses itself and never touches itself, not even diagonally.\n\nThe loop must visit each box at least once.\n\nThe boxes are the nine 3x3 regions of the grid, numbered 1 to 9 in reading order: left to right, top to bottom.\n\nFor each box, the number of its cells that belong to the loop is at most its box number k.\n\nWithin each box, the cell containing its box number must be part of the loop.\n\nTwo orthogonally adjacent cells may contain digits that sum to 7 or 10 only if neither cell is part of the loop. So if the two digits sum to 7 or 10, both cells lie off the loop.\n\nThe 24 cells enclosed by the loop must contain two magic squares.\n\nA magic square is a 3x3 block of the digits 1 to 9, each used once, where every row, column and diagonal sums to the same value.","solution":"839615427625734819471298356312459678756382941948167532293576184184923765567841293","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell wide loop that moves orthogonally through the center of cells and does not branch, intersect with itself or touch itself (neither orthogonally nor diagonally). The loop has to visit each box at least once. For each box, the maximum number of cells belonging to the loop is k, where k is the box number. Within each box, the box number has to be part of the loop. Two orthogonally adjacent cells are only allowed to contain digits that sum to 7 or 10 if both cells are not part of the loop. The 24 cells that are enclosed by the loop have to contain two magic squares.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7","c8"]}]},{"id":"lx67bjidk7","ctcId":2192,"ctcDifficulty":"MEDIUM","title":"Look and whisper","author":"Lithium-Ion and Holzanatom","rules":"Normal Sudoku rules apply. Adjacent digits along a green German whisper line must differ by at least 5. Both digits (which can be equal) on the endpoints of a green line form a look-and-say clue. If for example the digits on both endpoints of a line are 4 and 3, then the digit 3 has to appear exactly four times on this line AND the digit 4 has to appear exactly three times on the line. The line that starts in R2C6 ends at R2C8.","solution":"538249617697581423421736985859172346263458791714963258186394572345827169972615834","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Both digits (which can be equal) on the endpoints of a green line form a look-and-say clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"3ppzefe55t","ctcId":2193,"ctcDifficulty":"MEDIUM","title":"Nobody's perfect","author":"Lithium-Ion","rules":"Normal Sudoku rules apply. Orthogonally adjacent digits are not allowed to contain consecutive digits. Digits within a killer cage do not repeat and sum to a perfect number. A perfect number is a number that equals the sum of its proper divisors (i.e. each divisor excluding the number itself). For example, 20 is not a perfect number since the sum of the proper divisors is 1+2+4+5+10=22, which is not 20. Hint: There are only two perfect numbers that are less than 45.","solution":"796418253253796418418253796182537964964182537537964182379641825641825379825379641","constraints":["cage","non-consecutive"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ei2pkdyk0w","ctcId":2194,"ctcDifficulty":"MEDIUM","title":"Four Triangles","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. In each line of four cells the sum of the first two digits equals the sum of the last two digits.","solution":"539864172726139548184725369615278493472913856398456217947582631261347985853691724","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In each line of four cells the sum of the first two digits equals the sum of the last two digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"m7yoyjrok3","ctcId":2195,"ctcDifficulty":"MEDIUM","title":"Seicentomila","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nDivide each line into non-overlapping segments, each of which sums to 6.\n\nA clue outside the grid is the sum of the digits sandwiched between the 1 and the 9 in the corresponding row/column.\n\nCages show their sums.","solution":"853249617174865392269713485386594271917382564425176839641928753592637148738451926","constraints":["cage","custom","sandwich"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide each line into non-overlapping segments, each of which sums to 6.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"3d513yr35u","ctcId":2196,"ctcDifficulty":"HARD","title":"Basket","author":"Jay Dyer","rules":"Normal sudoku rules apply. Digits may not repeat on either marked diagonal.\n\nDigits on a line form a set of nonrepeating consecutive digits, which may be in any order.\n\nDigits connected by an X sum to 10, and digits connected by a V sum to 5.","solution":"864537219351829647729146835132685794485972163697314582546291378913758426278463951","constraints":["XV","diagonal","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"yuarri3g7w","ctcId":2200,"ctcDifficulty":"MEDIUM","title":"RAT RUN 11: Limited Addition","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT:\nFinkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nTELEPORTS: Entering a teleport will cause Finkz to be instantly transported to the matching coloured teleport. From there she can continue her journey. Matching teleports always have identical digits, but teleports that don't match always have different digits.\n\nREDCURRANTS: A redcurrant always sits between an even digit and an odd digit.\n\nTEST CONSTRAINT: In this experiment, any cell on the path equals the digit at the top of its column plus the digit at the left-hand end of its row.","solution":"916374528238596741457128963893461275675932184124785639781253496562849317349617852","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls. Matching teleports always have identical digits, but teleports that don't match always have different digits. REDCURRANTS: A redcurrant always sits between an even digit and an odd digit. TEST CONSTRAINT: In this experiment, any cell on the path equals the digit at the top of its column plus the digit at the left-hand end of its row.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c8","c9","c10"]}]},{"id":"0mrgocdo2k","ctcId":2201,"ctcDifficulty":"MEDIUM","title":"Ignition!","author":"Blashyrkh","rules":"Normal sudoku rules apply.\n\nDigits along a thermometer strictly increase from the bulb end.","solution":"983576421216489357745321986567918234328647195491235678832764519154892763679153842","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"4umjglf7z5","ctcId":2202,"ctcDifficulty":"MEDIUM","title":"Ascension","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nIdentical digits cannot be a knight's move apart.\n\nDigits along an arrow sum to the digit in the corresponding circle.","solution":"652718349789243651341659728516397284297481536834526197165934872928175463473862915","constraints":["antiknight","arrow"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"nnf5fqru6z","ctcId":2205,"ctcDifficulty":"VERY HARD","title":"Zebediah Killgrave","author":"starwarigami","rules":"Normal Killer Sudoku rules apply.\n\nDigits may not repeat in a cage.\n\nThe totals of cages an equal distance from the central cage along a lavender line must sum to the total of the central cage.\n\nThe digit in the cell marked with a square is even.","solution":"954167238736258491281493675495831762167524983328976514649312857512789346873645129","constraints":["cage","custom","even"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The totals of cages an equal distance from the central cage along a lavender line must sum to the total of the central cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"ot5h01fnjr","ctcId":2211,"ctcDifficulty":"HARD","title":"Snake Farm","author":"Cris Moore","rules":"Standard Sudoku rules apply. The grid is divided into 9 snakes. Each snake is a path of length 9, starting at its tail in the southwest and moving orthogonally north or east — never west or south — to its head in the northeast. Three heads (red diamonds) and two tails (green squares) are shown, pointing to the next cell in that snake.\n\nDigits in a snake cannot repeat. The snake that contains the blue dot is a thermosnake, with digits increasing from its tail to its head. Adjacent digits connected by a dot differ by 1 if the dot is white, and have a ratio of 1:2 if the dot is black.","solution":"563712894418956723972348651851469372249537186637281549385194267124675938796823415","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The grid is divided into 9 snakes. The snake that contains the blue dot is a thermosnake, with digits increasing from its tail to its head.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"bofuhbwz6i","ctcId":2212,"ctcDifficulty":"VERY HARD","title":"The Graveyard Of Knapp Daneben","author":"fjam","rules":"- Normal Sudoku rules apply.\n- In graves (cages), digits must sum to the day, month or year of the date of the day before or after the date on the grave. Digits cannot repeat within graves.\n- Escape the graveyard by carefully plotting an orthogonally connected path between the green and red cells. The path may not cross the highest or lowest digits in a grave.\n\nAll dates use the international standard Gregorian calendar in the DD/MM/YY format.","solution":"478623519592871643361594782927386451834715296615942378783259164249167835156438927","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- In graves (cages), digits must sum to the day, month or year of the date of the day before or after the date on the grave. Digits cannot repeat within graves. - Escape the graveyard by carefully plotting an orthogonally connected path between the green and red cells. The path may not cross the highest or lowest digits in a grave.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"wxhrpva2lr","ctcId":2213,"ctcDifficulty":"HARD","title":"RatRun 12:Visiting Order","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nGRAPES: Digits separated by a green grape have a difference of at least 5.\n\nTEST CONSTRAINT: In this experiment, dotted box borders divide the correct path into 'index lines'; In any box, the Nth cell visited by Finkz is called 'position N'. (So, for example, in box 7, r9c2 is position 1.) The digit in position N always indicates which position along that segment contains the digit N. Eg: In a box, Finkz might visit the digits 35142 in that order. The first digit being a 3 indicates that the third digit is a 1, the second digit being a 5 indicates that the fifth digit is a 2, and so on.","solution":"861592347952734816743861529385417962196253784274689153639125478527348691418976235","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The digit in position N always indicates which position along that segment contains the digit N. Eg: In a box, Finkz might visit the digits 35142 in that order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c8"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"4w0t03s87w","ctcId":2214,"ctcDifficulty":"MEDIUM","title":"Complimentary Interconnected Forces","author":"HalfBakedLunatic (aka David Workman)","rules":"• Normal Sudoku Rules Apply\n• Digits along a thermometer must increase from the bulb end\n• The digits in a cage must sum to the number printed in its corner, if given. Digits may not repeat within a cage. \n• Shade some cells such that the shaded cells and the unshaded cells each form a single orthogonally-connected region. No 2x2 area can be completely shaded or unshaded (Yin-Yang rules).\n• Even number digits in a cage are always shaded, odd digits are always unshaded\n• Odd number digits on a thermometer are always shaded, even digits are always unshaded","solution":"127498356856123479943576812485367921719852634362941587578614293631289745294735168","constraints":["cage","custom","thermometer","yin-yang"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Even number digits in a cage are always shaded, odd digits are always unshaded • Odd number digits on a thermometer are always shaded, even digits are always unshaded","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"jl4bufy55q","ctcId":2215,"ctcDifficulty":"MEDIUM","title":"89","author":"James Kopp","rules":"Normal sudoku rules apply.  Cells separated by a single knight's move (in chess) cannot contain the same digit. Diagonal cell pairs (sharing a corner) must have a difference of at least 2.","solution":"321987654654321987987654321432198765765432198198765432543219876876543219219876543","constraints":["antiknight","custom"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Diagonal cell pairs (sharing a corner) must have a difference of at least 2.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"3ucqlappvo","ctcId":2216,"ctcDifficulty":"HARD","title":"Between The Edges","author":"Jodawo","rules":"Normal Sudoku rules apply.\n\nBlack Kropki Dots : Indicate a 1:2 ratio between the digits. Not all Kropki Dots are given.\n\nDigits in the Circles must have a value between the digits on both ends of the row.\n\nDigits in the Green Shaded Cells must have a value between the digits on both ends of the column.\n\n(All Circles and Green Shaded Cells given)","solution":"148623597763945812592178364816492753935867421427531986379256148684319275251784639","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in the Circles must have a value between the digits on both ends of the row. Digits in the Green Shaded Cells must have a value between the digits on both ends of the column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"nivm1qdkzj","ctcId":2217,"ctcDifficulty":"HARD","title":"Alarm","author":"zetamath","rules":"Normal sudoku rules apply. Each thick grey line can be divided into one or more non-overlapping segments. Each segment contains digits that sum to 10. Eg 513173 is a valid fill for a length 6 line, because it can be broken into 5131 and 73, each of which sum to 10. Digits on a purple line form a set of non-repeating, consecutive digits. These digits can appear in any order. Digits along a thin grey line connecting two circles must have values between the digits in the circles. Eg if the two circles at a line’s ends contain 3 and 8 then digits on the line itself must be selected from [4567]. Digits separated by a black dot have a 1:2 ratio, meaning one digit is exactly double the other. Not all dots are necessarily given.","solution":"319857642564213987287649531691385724758421396423796815135962478872534169946178253","constraints":["between-line","custom","kropki","renban"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each thick grey line can be divided into one or more non-overlapping segments.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"w0298g25jm","ctcId":2218,"ctcDifficulty":"EASY","title":"Hot Potato","author":"sujoyku","rules":"- Normal sudoku rules apply, i.e. each row, column and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- Killer cages: Digits in a cage do not repeat and sum to the clue in the top left. Moreover, if cages are adjacent to each other (i.e. share an edge), they have to contain at least one common digit.","solution":"914526783583749261267138945358297614726451398149683572492875136831962457675314829","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Killer cages: Digits in a cage do not repeat and sum to the clue in the top left. Moreover, if cages are adjacent to each other (i.e. share an edge), they have to contain at least one common digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"zsk8n4tjvw","ctcId":2219,"ctcDifficulty":"HARD","title":"RAT RUN 13: Triskaidekaphilia","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nNULLIFIERS: In each row, column and 3x3 box there is one 'nullifier' cell to be located. The value of a nullifier cell is zero. Each nullifier cell contains a different digit.\n\nMOTION SENSORS: The value on a pink motion sensor indicates how many of the (up to 9) cells immediately surrounding the sensor are visited by Finkz. The sensor itself is counted, if visited.\n\nBLACKCURRANTS: Values connected by a blackcurrant have a 1:2 ratio.\n\nGRAPES: Values connected by a green grape have a difference of at least 5.\n\nFORBIDDEN DOORS: Values connected by a red X sum to 10. Finkz may not pass directly through a red X.\n\nTEST CONSTRAINT: In this experiment, if a row / column / box is visited by Finkz, then the values of ALL the visited cells in that row / column / box must sum to exactly 13 (even if the cells aren't all adjacent on the path.)","solution":"912768543478513629653249781247896315165327498839451276594682137386174952721935864","constraints":["XV","custom","german-whispers","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls. NULLIFIERS: In each row, column and 3x3 box there is one 'nullifier' cell to be located. MOTION SENSORS: The value on a pink motion sensor indicates how many of the (up to 9) cells immediately surrounding the sensor are visited by Finkz. TEST CONSTRAINT: In this experiment, if a row / column / box is visited by Finkz, then the values of ALL the visited cells in that row / column / box must sum to exactly 13 (even if the cells aren't all adjacent on the path.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5","c8","c14"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"GRAPES: Values connected by a green grape have a difference of at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c11"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"yrlckvek4z","ctcId":2220,"ctcDifficulty":"HARD","title":"See It, Say It, Sorted","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply.\n\nThe first digit on a diagonal seen by a camera indicates how many times that digit appears on that diagonal. Any leftover digits on the diagonal (the ones not equal to the first digit) are sorted from lowest to highest, i.e. they appear in non-decreasing order moving away from the camera.\n\nSpeech bubbles all say the same *odd* digit.","solution":"854321769129647853637589241385794126271865934946213578462158397798432615513976482","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The first digit on a diagonal seen by a camera indicates how many times that digit appears on that diagonal. Any leftover digits on the diagonal (the ones not equal to the first digit) are sorted from lowest to highest, i.e. they appear in non-decreasing order moving away from the camera. Speech bubbles all say the same *odd* digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]}]},{"id":"e99mf1heg8","ctcId":2222,"ctcDifficulty":"HARD","title":"The Unfrayed Modified German Whisper Loop","author":"AFrayedKnot","rules":"Normal Sudoku rules apply.\n\nEach pair of digits connected by a line segment must either differ by at least 5, or sum to at most 5.","solution":"283965741749318265165274839618453972532897614497621583954736128371582496826149357","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each pair of digits connected by a line segment must either differ by at least 5, or sum to at most 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"vcncpwgckm","ctcId":2227,"ctcDifficulty":"HARD","title":"RAT RUN 14: Thermoregulation","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBLACKCURRANTS: Digits connected by a blackcurrant have a 1:2 ratio.\n\nCAGES: All cages have the same total, to be deduced. An electricity symbol indicates the cage's shock value. Finkz may not enter any cage with a shock value of 5 or higher. Cages with a shock value lower than 5 are safe to enter.\n\nTEST CONSTRAINT: In this experiment, dotted 3x3 box borders divide the correct path into segments. The total of each segment must be higher than the total of the previous segment on Finkz' path.","solution":"219345867758216349364897125437652981926178534581439672895764213673921458142583796","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. An electricity symbol indicates the cage's shock value. TEST CONSTRAINT: In this experiment, dotted 3x3 box borders divide the correct path into segments.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7","c10"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"4hca9hq4bd","ctcId":2228,"ctcDifficulty":"MEDIUM","title":"80","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Along each separate grey line (lengths: 3, 5 or 7) the product of the digits is 80.\n\nEach cage contains a 2-digit prime number (read left-to-right). \nA+B = C+D = A+C = B+D = 80","solution":"132859467965174328487362195298531746543627981716498532821743659359216874674985213","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Along each separate grey line (lengths: 3, 5 or 7) the product of the digits is 80. Each cage contains a 2-digit prime number (read left-to-right). A+B = C+D = A+C = B+D = 80","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]}]},{"id":"2ad4183iyn","ctcId":2229,"ctcDifficulty":"HARD","title":"41 Circles","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. The value of a digit on a line between two circles must be between the two values of the digits in those circles. eg if the two circles joined by a line contain 3 and 6, the digits on the line could be 4 or 5.","solution":"982475136713962485654318972397124568168753249245689317831297654526841793479536821","constraints":["between-line"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"modified","modifiers":[],"params":null,"note":"The value of a digit on a line between two circles must be between the two values of the digits in those circles. eg if the two circles joined by a line contain 3 and 6, the digits on the line could be 4 or 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"s0l233wyqx","ctcId":2230,"ctcDifficulty":"MEDIUM","title":"Through the Looking Glass","author":"Qodec","rules":"- Sudoku: Each row, column, and region indicated by thick borders in the grid must contain the digits 1 to 9 once each.\n- Kropki and XV pairs: Digits separated by an X add up to 10. Digits separated by a V add up to 5. If digits are separated by a black dot, one is double the other. Digits separated by a white dot are consecutive. Not all possible dots or X/V clues are necessarily given.","rulesClarified":"Sudoku: each row, column, and each region marked by thick borders contains the digits 1 to 9 once each.\n\nAn X or a V is a label on the edge between two orthogonally adjacent cells.\n\nX: the two digits on either side of the X add up to 10.\n\nV: the two digits on either side of the V add up to 5.\n\nIf digits are separated by a black dot, one is double the other.\n\nIf digits are separated by a white dot, they are consecutive.\n\nNot all possible dots, X clues or V clues are necessarily given. A pair of cells with no X, V or dot between them tells you nothing.","solution":"368219457457863291921457638194378526735126849682945173243781965876594312519632784","constraints":["XV","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"w5gfd237vx","ctcId":2231,"ctcDifficulty":"MEDIUM","title":"Equivalence","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply.\nEvery cage has the same sum.","solution":"192845376648379152735621498983564721526917843471283965367458219854192637219736584","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Every cage has the same sum.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"c0tbslozh0","ctcId":2232,"ctcDifficulty":"MEDIUM","title":"Off Piste","author":"ZegreS","rules":"Normal Sudoku rules apply.\nHeadless-Arrows: The digit on one end of each line is the sum of the other digits on that line.\nX-Sums: Outside clues give the sum of the first X grid digits starting from the clue where X is the nearest.\nExample: if R5C1 is 4 then sum of R5C1-4 is 15.","solution":"681793245375248619249156837967314528412875396538629471854937162196482753723561984","constraints":["custom","x-sum"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Headless-Arrows: The digit on one end of each line is the sum of the other digits on that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"qn9k75pdfy","ctcId":2233,"ctcDifficulty":"HARD","title":"Double Scaled Harmony","author":"gdc","rules":"Normal Sudoku rules apply.\n𝗙𝗼𝗴: The grid is partially covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area.\n𝗬𝗶𝗻 𝗬𝗮𝗻𝗴: Shade some cell such that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected and each 2x2 area contains shaded and unshaded cells.\n𝗩𝗮𝗹𝘂𝗲𝘀: The value of an unshaded cell is its digit. The value of a shaded cell is double its digit.\n𝗔𝗿𝗿𝗼𝘄𝘀: Values along an arrow sum to the value of the attached circle. Arrows don't overlap.","solution":"234678519769541823185932764348715692597426381612389457823154976456297138971863245","fogLight":"R1C7,R1C8,R1C9,R2C7,R2C8,R2C9,R3C7,R3C8,R3C9","constraints":["arrow","custom","fog","yin-yang"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"𝗔𝗿𝗿𝗼𝘄𝘀: Values along an arrow sum to the value of the attached circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The value of a shaded cell is double its digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"1q74h2zlba","ctcId":2234,"ctcDifficulty":"MEDIUM","title":"Humble Pi","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent cells cannot contain consecutive digits.\nThe numbered arrows outside the grid indicate the sum of the digits along that diagonal path (which may repeat if allowed by other rules).\nCells separated by a black dot are in the ratio 1 to 2. Not all possible black dots are given.","solution":"759283614416957382283614759625849173948371526371526948837162495594738261162495837","constraints":["kropki","little-killer","non-consecutive"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"zjoztx1fbb","ctcId":2235,"ctcDifficulty":"HARD","title":"SVS400 - Sudoku Upper Right Heavy Killer","author":"Richard","rules":"Place the digits 1-9 exactly once in each row, column and 3x3 block. In any cell that contains a digit that is smaller than the digit in the diagonally adjacent upper right cell, the sum of those two digits is given, where a\nquestion mark can be replaced by any sum ranging from 3 to 17.","solution":"953672841746831529218495367589263714162748953437519682395126478671384295824957136","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In any cell that contains a digit that is smaller than the digit in the diagonally adjacent upper right cell, the sum of those two digits is given, where a","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"athyahqib1","ctcId":2237,"ctcDifficulty":"MEDIUM","title":"RAT RUN 15: Connectedness","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through the rounded end / corner of a wall.\n\nBLACKCURRANTS: Cells connected by a blackcurrant have a 1:2 ratio (one is double the other.) Not all possible blackcurrants have been given.\n\nTELEPORTS: Entering a teleport will cause Finkz to be instantly transported to the matching coloured teleport. From there she can continue her journey. Matching teleports always have identical digits, but teleports that don't match always have different digits.\n\nTEST CONSTRAINT: Finkz' path is formed of one or more segments. Any uses of teleports will divide Finkz' path up into physically separate segments, ie; if a teleport is used, the current path segment ends at the entry teleport, and a new separate path segment begins at the matching exit teleport. Any path segment must function as a renban; it must consist entirely of a set of non-repeating, consecutive digits, which can be arranged in any order along the path segment.","solution":"321456879857912643496837521719625384582394167643781295265179438178243956934568712","constraints":["custom","kropki","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. Matching teleports always have identical digits, but teleports that don't match always have different digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]}]},{"id":"1uv7hh848p","ctcId":2239,"ctcDifficulty":"HARD","title":"ABENNR","author":"FullDeck and Missing a Few Cards","rules":"**Standard Sudoku, Kropki Pairs, Ambiguous Renban/ Nabner, Even/Odd**\n\nEach line in this puzzle is either a Renban Line or a Nabner Line. The solver must determine which is which.\n\n- Standard sudoku rules apply: The digits 1 through 9 appear in every row, column, and box.\n- Renban Line: Digits along a Renban line must form a set of non-repeating consecutive digits in any order.\n- Nabner line: No two digits along a Nabner line can be consecutive, regardless of their position on the line. \n- Kropki pairs: Digits in cells separated by a black dot are in a 2:1 ratio. Digits in cells separated by a white dot are consecutive. Not all dots are necessarily given.\n- Even/Odd: Cells marked with a grey square contain even digits. Cells marked with a grey circle contain odd digits.","solution":"479582136261379548358164279987456312614723895523918764792635481145897623836241957","constraints":["custom","even","kropki","nabner-line","odd","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each line in this puzzle is either a Renban Line or a Nabner Line. The solver must determine which is which.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"b23h412fnm","ctcId":2241,"ctcDifficulty":"VERY HARD","title":"That's Even Better","author":"Mr.Menace","rules":"- Normal sudoku rules apply\n- Outside clues are Little Killer clues, and give the sum (or the parity (Odd or Even)) of the digits on the indicated diagonal.\n- Cells separated by a white dot contain consecutive digits. Cells separated by a black dot contain digits in a ratio 1:2.","solution":"584723916623419875719586243295371684361854729478962351847695132932147568156238497","constraints":["kropki","little-killer"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"zgmqhuvf3r","ctcId":2242,"ctcDifficulty":"HARD","title":"Sum-thing or Other","author":"Jay Dyer","rules":"Normal sudoku rules apply.\n\nShade the entire grid using two colours, so that each colour forms a single orthogonally connected area, and no 2x2 area is entirely one colour.\n\nAn arrow in a cell indicates that the digit in that cell equals the sum of the contents of all cells of the opposite colour in the direction of the arrow. If a cell contains multiple arrows, each arrow is summed separately.","solution":"184652937639874251725193468497238615513946782268517394942381576371465829856729143","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"An arrow in a cell indicates that the digit in that cell equals the sum of the contents of all cells of the opposite colour in the direction of the arrow.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"8mclyql7am","ctcId":2248,"ctcDifficulty":"EASY","title":"Forest Medallion","author":null,"rules":"Normal sudoku rules apply. Along a marked diagonal, digits do not repeat.","solution":"597324861418756392362189754156892437879431526243567918724915683981673245635248179","constraints":["diagonal"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"rn6k0lxtzd","ctcId":2249,"ctcDifficulty":"EASY","title":"Nayru's Pearl","author":null,"rules":"Normal sudoku rules apply. Digits do not repeat within a cage, which shows its sum. The coloring of cages is purely decorative.","solution":"184279563379165842562834971641928357238657194957341286723596418415783629896412735","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"QBHQmPJ7mJ","ctcId":2250,"ctcDifficulty":"EASY","title":"Crest of the Gorons","author":"Wei-Hwa Huang","rules":"Normal sudoku rules apply.","solution":"497328615516974823832615947745289361269431578381567294654793182123846759978152436","constraints":[],"constraintFacts":[]},{"id":"nNqmrtN2Lb","ctcId":2252,"ctcDifficulty":"EASY","title":"Farore's Pearl","author":"Wei-Hwa Huang","rules":"Normal sudoku rules apply. Orange bars in the grid sit between ALL adjacent pairs of consecutive digits.","solution":"286931574513742689974856312327498156641523798859167243135289467468375921792614835","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Orange bars in the grid sit between ALL adjacent pairs of consecutive digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"xgn9g0d94r","ctcId":2253,"ctcDifficulty":"MEDIUM","title":"Dynamic Chaos","author":"gdc","rules":"Divide the grid into nine orthogonally connected nine-cell regions, and place the digits 1-9 once in each row, column, and region.\n𝗗𝘆𝗻𝗮𝗺𝗶𝗰 𝗙𝗼𝗴: The grid is covered in fog. Placing a correct digit in a cell lifts fog in that cell and possibly other cells; revealing new clues.\n𝗦𝗾𝘂𝗮𝗿𝗲𝘀: Some cells contain a grey square inside them. The digit in such a cell is equal to the sum of the (up to 8) surrounding digits that are in different regions.\n𝗖𝗖 𝗞𝗿𝗼𝗽𝗸𝗶 𝗣𝗮𝗶𝗿𝘀: Digits separated by a white dot differ by 1 and belong to the same region.\n𝗖𝗖 𝗦𝘂𝗰𝗰𝗲𝘀𝘀𝗼𝗿 𝗔𝗿𝗿𝗼𝘄𝘀: A digit N on an arrow counts how many cells it sees of its region in the indicated direction, including itself. Region borders block vision. Additionally, the digit N+1 must appear immediately behind the first seen region border. Each arrow MUST therefore see a region border within the grid.","solution":"214753968482635791196587324571396842329148657743869215937214586865472139658921473","fogLight":"R1C2","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into nine orthogonally connected nine-cell regions, and place the digits 1-9 once in each row, column, and region. The digit in such a cell is equal to the sum of the (up to 8) surrounding digits that are in different regions. 𝗖𝗖 𝗦𝘂𝗰𝗰𝗲𝘀𝘀𝗼𝗿 𝗔𝗿𝗿𝗼𝘄𝘀: A digit N on an arrow counts how many cells it sees of its region in the indicated direction, including itself.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c5","c7"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"m35yptjo24","ctcId":2254,"ctcDifficulty":"MEDIUM","title":"Tilted","author":"Alaric Taqi A. (Crusader175)","rules":"• Normal sudoku rules apply.\n• Coordinate: The digits X, Y and Z in pill shapes (reading left to right) signify that rXcY = Z.\nFor example, if a pill read [825], then the cell in row 8 column 2 would have to be the digit 5.\n• Diagonal: Digits along the negative diagonal must not repeat.\n• Modular Lines: Any set of three sequential cells along a teal line must contain one digit from [1,4,7], one digit from [2,5,8] and one digit from [3,6,9].\n• X Pairs: Cells separated by an X sum to 10. Not all X's are given.","solution":"364815297852397641197264835728459316639128574541736928476982153915643782283571469","constraints":["XV","custom","diagonal","modular-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Coordinate: The digits X, Y and Z in pill shapes (reading left to right) signify that rXcY = Z.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"pmv1jze5n3","ctcId":2256,"ctcDifficulty":"HARD","title":"One Look Could Kill","author":"yttrio","rules":"Normal sudoku rules apply. Digits MAY repeat in cages if allowed by other rules.  The sum of digits in each cage must be a two-digit number that acts as a valid “look-and-say clue” for that cage.  Eg if the sum is 21, there must be exactly two 1s in the cage along with any combination of other digits (such that, overall, the digits in the cage sum to 21). Eg2 if the sum is 17, there must be exactly one 7 in the cage along with any combination of other digits (such that, overall, the digits in the cage sum to 17).","solution":"941326758538791624726458139462513987159287346387964215215879463874632591693145872","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The sum of digits in each cage must be a two-digit number that acts as a valid “look-and-say clue” for that cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"tlr3i291g8","ctcId":2258,"ctcDifficulty":"HARD","title":"Queens via LinkedIn","author":"Thomas Snyder","rules":"Place exactly one queen in every row, column and coloured region. Two queens  cannot touch each other. Not even diagonally. Use 1 for a Queen and 2 for an empty cell to make the 'solution check' function work.","solution":"222222221212222222222122222222222212222212222221222222222221222122222222222222122","constraints":["antiking","custom"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"modified","modifiers":[],"params":null,"note":"Two queens  cannot touch each other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Place exactly one queen in every row, column and coloured region.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"d510hfne1x","ctcId":2259,"ctcDifficulty":"VERY HARD","title":"A Degree in Thermology","author":"Knickolas","rules":"Normal sudoku rules apply. Nine cells (one in each row/column/3x3 box) are \"doublers\", and have a value of double their digit. Each digit appears in exactly one doubler. Values along a thermometer increase from the bulb end. Values in a cage sum to the given total. Digits may not repeat in a cage, but values may.","rulesClarified":"Normal sudoku rules apply to the written digits.\n\nNine cells are doublers, one in each row, column and 3x3 box. Each digit from 1 to 9 is written in exactly one doubler. A doubler's value is twice its digit. Every other cell's value is its digit.\n\nThermometers: values increase along each thermometer, starting from its bulb end.\n\nCages: the values in each cage sum to the total on its label. No digit may repeat in a cage, but two values may be equal (for example a doubled 3 and a 6).","solution":"573946281684321597129578634368257419415689723792413865937865142841792356256134978","constraints":["cage","custom","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Nine cells (one in each row/column/3x3 box) are \"doublers\", and have a value of double their digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Values along a thermometer increase from the bulb end.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"258y2m2nv3","ctcId":2261,"ctcDifficulty":"MEDIUM","title":"Y is the heating transport so X-tremely slow?","author":"olima","rules":"Normal Sudoku rules apply. Along a thermometer digits must not decrease from the bulp to the tip(s).","solution":"461238579592714638837965421185693247926147385374582916758429163643851792219376854","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"h46kngm99n","ctcId":2262,"ctcDifficulty":"HARD","title":"RAT RUN 17: Trapdoors","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nTRAPDOORS: Each rectangular trapdoor has a different total (the sum of its two digits.) Finkz should not step on a trapdoor without first locking it shut, making it safe to cross.\n\nBUTTONS: To make it safe to step on a trapdoor, Finkz must first press all the circular buttons that match the colour of the trapdoor. A digit on a coloured button indicates how many buttons of that colour contain that digit.\n\nTEST CONSTRAINT: In this experiment, the correct path will be entropic, ie; every group of 3 adjacent cells along the path must contain one low digit (1, 2 or 3), one medium digit (4, 5 or 6) and one high digit (7, 8 or 9).","solution":"364275198528619734971483562152736849896542317437198256749851623613927485285364971","constraints":["custom","entropic-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls. As well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. TRAPDOORS: Each rectangular trapdoor has a different total (the sum of its two digits.) BUTTONS: To make it safe to step on a trapdoor, Finkz must first press all the circular buttons that match the colour of the trapdoor. A digit on a coloured button indicates how many buttons of that colour contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7","c8"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"adkms6bibp","ctcId":2263,"ctcDifficulty":"MEDIUM","title":"Row Sum Lines","author":"Jobo","rules":"Normal sudoku rules apply.\n\nDigits along a line sum to the same value for each row the line passes through.","solution":"586371249234986715719245386341627598875194623962538174428753961657819432193462857","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits along a line sum to the same value for each row the line passes through.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"oaeuopmvrt","ctcId":2264,"ctcDifficulty":"HARD","title":"We're All Mad Here","author":"gdc","rules":"Normal Sudoku rules apply.\n𝗗𝘆𝗻𝗮𝗺𝗶𝗰 𝗙𝗼𝗴: The grid is covered in fog. Placing a correct digit in a cell lifts fog in that cell and possibly other cells; revealing new clues. \n[𝗠𝗮𝗱 𝗙𝗼𝗹𝗱-𝗜𝗻](https://sudokupad.app/a5fksb2o7y): The vertical dashed lines are folded onto each other so that columns 1, 2, 8 and 9 form a secondary grid. In this grid all clues are still valid.\n𝗞𝗶𝗹𝗹𝗲𝗿: Digits in a cage don't repeat and sum to the total in the top-left corner. Cages don't overlap.\n𝗞𝗿𝗼𝗽𝗸𝗶: Digits separated by a white dot are consecutive. Not all dots are given.\n𝗛𝗶𝘁𝗽𝗼𝗶𝗻𝘁𝘀: Clues outside the grid give the sum of all cells that contain a digit equal to the distance of that cell from that clue in the row or column. For example, a 4 in Row 2, Column 4 would count towards the 10 clue in row 2, and any other number would not. Horizontal distances in the folded 4x9 grid are limited to 1-4.","solution":"497231568126598734835467129352719846974682351618345297761923485543876912289154673","fogLight":"","constraints":["cage","custom","fog","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"[𝗠𝗮𝗱 𝗙𝗼𝗹𝗱-𝗜𝗻](https://sudokupad.app/a5fksb2o7y): The vertical dashed lines are folded onto each other so that columns 1, 2, 8 and 9 form a secondary grid. 𝗛𝗶𝘁𝗽𝗼𝗶𝗻𝘁𝘀: Clues outside the grid give the sum of all cells that contain a digit equal to the distance of that cell from that clue in the row or column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c10"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"h3oqqmu2wp","ctcId":2265,"ctcDifficulty":"VERY HARD","title":"Look at those lines","author":"Lithium-Ion","rules":"Normal Sudoku rules apply. Cells that are a knight's move away are not allowed to contain identical digits. Both digits (which can be equal) on the endpoints of a line form a look-and-say clue. For example, if the digits on the endpoints are 5 and 3, then there have to be exactly five 3s AND three 5s on this line. The different line colors are only used to avoid confusion regarding line crossings.","solution":"364729185825361947179845263547982631281536479936174852793618524458293716612457398","constraints":["antiknight","custom"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Both digits (which can be equal) on the endpoints of a line form a look-and-say clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"ksn2ld67um","ctcId":2266,"ctcDifficulty":"MEDIUM","title":"Friendly Borders","author":"Dorlir","rules":"Normal sudoku rules apply. A border square is a 2x2 square that crosses at least one 3x3 box border. For all border squares exactly 2 digits are the same. The middle 3x3 box in the grid is a magic square i.e. the sum of digits in each row, column and main 3-cell diagonal in that box is N (where N must be determined by the solver). There are exactly N ‘friendly’ cells in the grid. A cell is friendly if its digit is equal to at least one of its row number, column number or box number. (Rows are numbered top to bottom; columns are numbered left-to-right; boxes are numbered in normal reading order.) Digits separated by a black dot must be in ratio 1:2 (ie one digit is double the other). Not all dots are necessarily given.","solution":"163872945528439176794561832945618327216753498387294651872946513639125784451387269","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For all border squares exactly 2 digits are the same. The middle 3x3 box in the grid is a magic square i.e. the sum of digits in each row, column and main 3-cell diagonal in that box is N (where N must be determined by the solver). There are exactly N ‘friendly’ cells in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"0pshsj5ykr","ctcId":2267,"ctcDifficulty":"HARD","title":"Nordschleife","author":"Qodec","rules":"Sudoku: Each row, column, and region indicated by thick borders in the grid must contain the digits 1 to 9 once each.\n\nDraw a 1-cell-wide loop of orthogonally connected cells, which does not branch or touch itself, not even diagonally. Circled cells are not on the loop, and the digit in a circle indicates how many of the up to 8 surrounding cells are on the loop. For each pair of adjacent digits along the loop, the larger digit is an integer multiple of the smaller digit. The cell with the rectangle is on the loop.","rulesClarified":"Normal sudoku rules apply: each row, column and thick-bordered region holds the digits 1 to 9 once each.\n\nDraw one loop through the grid. It moves orthogonally from cell to cell, is one cell wide, never branches, and never touches itself, not even diagonally.\n\nCircled cells are not on the loop.\n\nA digit in a circle tells you how many of the up to eight cells surrounding that circle are on the loop.\n\nThe loop is closed. Going around it, each pair of neighbouring loop cells has digits where the larger is a whole-number multiple of the smaller. The last and first cells of the loop are neighbours too.\n\nThe cell with the rectangle is on the loop.","solution":"526973148384165972917824356145782693279436581638519724793648215852391467461257839","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Circled cells are not on the loop, and the digit in a circle indicates how many of the up to 8 surrounding cells are on the loop. For each pair of adjacent digits along the loop, the larger digit is an integer multiple of the smaller digit. The cell with the rectangle is on the loop.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5"]}]},{"id":"9pbr75sftp","ctcId":2268,"ctcDifficulty":"MEDIUM","title":"Christmas Star","author":"Riffclown","rules":"• Normal Sudoku rules apply. Place the digits 1-9 in each row, column and box without repetition.\n• Killer Cages: Digits in cages must sum to the number in the top left corner of the cage. Digits may not repeat within a cage.","solution":"148759623762843159359621847623478915874915236915362478486137592597284361231596784","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"J74NR4224q","ctcId":2271,"ctcDifficulty":"VERY HARD","title":"Renrenbanban","author":"Darth Paradox","rules":"Place the digits 1-9 once into each row, column, and 3x3 box.  Digits must not repeat along the marked diagonal.  The grey lines are palindromes and must contain the same sequence of digits in both directions along the line.\n\nThe purple lines are Double Renban lines.  Each such line contains two equal-sized sets of consecutive digits.  The sets might overlap partially or completely, and the digits can be in any order along the line.  For example, 123123, 172839, and 142332 are each valid ways to fill a six-cell Double Renban line.","solution":"124367859596284317378159426465731298289645173731892564857913642642578931913426785","constraints":["diagonal","palindrome","renban"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"The purple lines are Double Renban lines.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"zsmxjt7v5i","ctcId":2276,"ctcDifficulty":"MEDIUM","title":"Fair and Square","author":"James Kopp","rules":"Normal sudoku rules apply.\nThe grid is covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area.\nAdjacent digits along an orange line have a difference of at least four. Each orange line is in the shape of a square.\nCells separated by a black dot are in the ratio 1 to 2. Not all black dots are necessarily shown.","solution":"973184265518362749246597381389276154457913628621845973894621537132758496765439812","fogLight":"R4C4,R4C5,R4C6,R5C4,R5C5,R6C4","constraints":["dutch-whispers","fog","kropki"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"hypzc2xwbi","ctcId":2277,"ctcDifficulty":"HARD","title":"RAT RUN 18: Mirror Maze","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick maze walls.\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nTELEPORTS: Entering a teleport will cause Finkz to be instantly transported to the matching coloured teleport. From there she can continue her journey. Matching teleports always have identical digits, but teleports that don't match always have different digits.\n\nMIRROR CELLS: Each row, column and box contains exactly one mirror cell. Mirror cells may not contain teleports. The value of a mirror cell equals the digit in that cell subtracted from 10. Eg: a 2 in a mirror cell is 'mirrored' on the 1-9 scale, and has a value of 8. Every mirror cell contains a different digit. \n\nONE-WAY DOORS: Finkz may only pass directly through a purple arrow if moving in the direction the arrow is pointing. An arrow always points to the smaller of the two values it sits between.\n\nTEST CONSTRAINT: In this experiment, the values of any two physically adjacent cells along the path (ie; not separated by teleportation) must have a difference of at least 5.","solution":"654279183139856724782341956273985461965417238418623597546198372391762845827534619","constraints":["custom","inequality"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz the rat must reach the cupcake by finding a path through the maze. TELEPORTS: Entering a teleport will cause Finkz to be instantly transported to the matching coloured teleport. MIRROR CELLS: Each row, column and box contains exactly one mirror cell. TEST CONSTRAINT: In this experiment, the values of any two physically adjacent cells along the path (ie; not separated by teleportation) must have a difference of at least 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c8","c15"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]}]},{"id":"i3cvr72ff5","ctcId":2278,"ctcDifficulty":"MEDIUM","title":"Arrow Thermo","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Along a thermometer, digits must increase from the bulb end. Digits along an arrow must sum to the digit in that arrow's circle. Cells separated by a (single) king's move in chess cannot contain the same digit.","solution":"927583146356419872418726593279654381631298754845371269792165438563842917184937625","constraints":["antiking","arrow","thermometer"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"cg5a3nnzp1","ctcId":2279,"ctcDifficulty":"MEDIUM","title":"Think You Can Break In?","author":"Antiknight","rules":"Normal sudoku rules apply. Digits must not repeat in cells that are a single knight's move apart (in chess). The digits in a cage must sum to the small clue printed in the top left corner of the cage. Digits may not repeat within a cage. Adjacent digits along each green ‘German Whisper’ line must have a difference of at least 5. Lines and cages do not overlap. The grid is partially covered with fog.  Correctly placed digits will clear the fog around that cell. No guessing is required.","solution":"341769582267385914589412367158627439673894125924153678892536741735241896416978253","fogLight":"R2C1,R2C2,R4C1,R4C2,R6C1,R6C2,R4C8,R4C9,R6C8,R6C9,R2C8,R2C9","constraints":["antiknight","cage","fog","german-whispers"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"011pxhbylc","ctcId":2280,"ctcDifficulty":"HARD","title":"The Curse of King Minos","author":"Allagem","rules":"You are caught by the Curse of King Minos and must find a way to escape the lurking Minotaur! Only by following the ancient rules will you find your way to freedom:\nNormal Sudoku rules apply.\nYin-Yang: Color every cell in the grid one of two colors such that all cells of each color are orthogonally connected and no 2x2 region is a single color.\nSight Squares: A digit in a square indicates how many cells of the same color are seen orthogonally from that position, including itself, where cells of the other color block vision.\nAnti-King: Diagonally adjacent cells may not contain the same digit.","solution":"932754168146389572875216394318497256257638941469521783584173629793862415621945837","constraints":["antiking","custom","yin-yang"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Sight Squares: A digit in a square indicates how many cells of the same color are seen orthogonally from that position, including itself, where cells of the other color block vision.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"xuyeywkw3y","ctcId":2283,"ctcDifficulty":"MEDIUM","title":"Differences Count - part 3","author":"Sujoyku and Marty Sears","rules":"Normal sudoku rules apply.\nDigits separated by a black dot are in a 1:2 ratio.\nThe difference between two adjacent digits on a coloured line indicates exactly how many pairs of adjacent digits along that line have that exact difference.","solution":"635921874481573926297468513816354297924687135753219468542796381368142759179835642","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The difference between two adjacent digits on a coloured line indicates exactly how many pairs of adjacent digits along that line have that exact difference.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"atfgvx1pgc","ctcId":2285,"ctcDifficulty":"VERY HARD","title":"Balancing act","author":"AnalyticalNinja & palpot","rules":"Normal sudoku rules apply. Place the digits 1-9 once in each row, column, and 3X3 box. \n\nYin and Yang: Shade some cells such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected. No 2x2 area may be fully shaded or fully unshaded.\n\nAlong a line, any changes in shading divide that line into segments of fully shaded or fully unshaded cells. On each line, each such segment (shaded or unshaded) must have the same sum as all other segments.\n\nWithin the shaded areas, adjacent digits along the lines must differ by at least 5.\nWithin unshaded areas, any string of 3 or fewer digits along the lines must be from a different set of (147), (258) and (369).","solution":"489512673532967184716384952951623748823479561647158239294735816365891427178246395","constraints":["custom","german-whispers","modular-line","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On each line, each such segment (shaded or unshaded) must have the same sum as all other segments.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Within the shaded areas, adjacent digits along the lines must differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"modular-line","type":"modular-line","variant":"modified","modifiers":[],"params":null,"note":"Within unshaded areas, any string of 3 or fewer digits along the lines must be from a different set of (147), (258) and (369).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"z14kvlwqlh","ctcId":2286,"ctcDifficulty":"MEDIUM","title":"Erbsenzähler","author":"sujoyku and SamuPiano","rules":"- Normal sudoku rules apply, i.e. each row, column and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- Split Peas: The sum of the digits on a line strictly between two circles is equal to a concatenation of the two values in the circles, in some order. For instance, 3_346_1 could be a valid split pea line, as 3+4+6=13, which is 1 concatenated with 3. \n\n- Counting Circles: A circled digit indicates exactly how many circles contain that digit. Note: This also includes all circles which are bounding the split pea lines.\nIf, for example, a 3 appears in a circle, then there must be exactly 3 circles that contain a 3.","solution":"321657984549832167876194325162745839957381642438926571215463798793218456684579213","constraints":["counting-circle","custom"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Split Peas: The sum of the digits on a line strictly between two circles is equal to a concatenation of the two values in the circles, in some order. For instance, 3_346_1 could be a valid split pea line, as 3+4+6=13, which is 1 concatenated with 3.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"djh35mkgjg","ctcId":2288,"ctcDifficulty":"MEDIUM","title":"Bent Into Shape","author":"99%Sneaky","rules":"Normal sudoku rules apply. Adjacent digits along orange lines must have a difference of at least 4. A digit in a white circle must appear once in the four surrounding cells. Any two cells which are in the same relative position within their respective 3x3 boxes must contain different digits. For example, if 7 was placed in the top-left corner of box 1, then no other boxes could have a 7 in their top-left corner.","solution":"497513628856924173231786594384271956715639482629458317162845739548397261973162845","constraints":["disjoint-groups","dutch-whispers","quadruple"],"constraintFacts":[{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"GQ4jnH2R6T","ctcId":2289,"ctcDifficulty":"VERY HARD","title":"Global Ocean","author":"SamuPiano","rules":"This is a 9x9 map of the ocean - there are ocean cells and island cells. Normal sudoku rules apply. Digits in cages must sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage with nine or fewer cells. Cells separated by an X must contain digits summing to 10. Not all Xs are given. HOWEVER, 18 cells - two in each box, row and column -are 'island' cells - these do not count toward the cage totals. Only 'ocean' cells count towards cage totals. There can be as many island cells as needed in any cage.","solution":"478539126956218374321467589789146235234795618165382497812954763643871952597623841","constraints":["XV","cage","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in cages must sum to the small clue in the top left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"HOWEVER, 18 cells - two in each box, row and column -are 'island' cells - these do not count toward the cage totals.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"RMqLfJ9qMf","ctcId":2290,"ctcDifficulty":"MEDIUM","title":"Unique Sums","author":"SamuPiano","rules":"Normal sudoku rules apply. The sum of the digits in each cage has a unique total. The grey square contains an even digit.","solution":"986713452324856197157294368248367915593182746671945283719528634862439571435671829","constraints":["custom","even"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits in each cage has a unique total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"29pegnk9xe","ctcId":2291,"ctcDifficulty":"MEDIUM","title":"Knights and Bishops in the Fog","author":"SamuPiano","rules":"Normal sudoku rules apply - place the digits 1 to 9 in every box, row and column with no repeats.\nAntiknight sudoku rules apply - cells a knight's (in chess) move apart cannot contain the same digit.\nThe grid is partially covered in fog. Placing a correct digit will clear some fog in the grid.\nSome cells have a number in the top left corner. This number gives the sum of all digits along one of the diagonals containing the cell. Which diagonal must be deduced by the solver. \nArrow sudoku rules apply - digits along an arrow must sum to the digit in the bulb. All arrows are 2 cells long.","solution":"786231549219645873345978621934786215621459387578123964453812796192367458867594132","fogLight":"R5C6,R5C9","constraints":["antiknight","arrow","custom","fog"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Some cells have a number in the top left corner.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"qwd7jxoeym","ctcId":2292,"ctcDifficulty":"HARD","title":"Inner Peas","author":"SamuPiano","rules":"Normal sudoku rules apply.\nYin/yang: shade some cells so that all shaded cells are orthogonally connected, and all unshaded cells are orthogonally connected. No 2x2 region can be completely shaded or unshaded. \nHot/cold: one of the shaded regions is \"hot\" - every cell in this region has 1 added to its value. The other shaded region is \"cold\" - every cell in this region has 1 subtracted from its value.\nSplit pill arrows (split peas): the sum of the values of cells on lines connecting two circles is equal to a concatenation of the two values in the circles, in some order. For example, 3_346_1 is valid, as 3+4+6=13.\nEvery line between two circles is summed separately.","solution":"795318642124756398863249571617532984548197236239684715476823159952471863381965427","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Hot/cold: one of the shaded regions is \"hot\" - every cell in this region has 1 added to its value. Split pill arrows (split peas): the sum of the values of cells on lines connecting two circles is equal to a concatenation of the two values in the circles, in some order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c6"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"f6xcgzdav3","ctcId":2293,"ctcDifficulty":"VERY HARD","title":"Foggy Pea-losophy","author":"SamuPiano","rules":"𝗦𝘂𝗱𝗼𝗸𝘂: Normal sudoku rules apply.\n𝗙𝗼𝗴: The grid is partially covered in fog. Placing correct digits will clear some of the fog in the grid.\n𝗬𝗶𝗻 𝗬𝗮𝗻𝗴: Shade some cells so that all shaded cells are orthogonally connected, and all unshaded cells are orthogonally connected. No 2x2 region can be completely shaded or unshaded. R5C5 is neither shaded nor unshaded in the final grid.\n𝗦𝗽𝗹𝗶𝘁 𝗣𝗲𝗮𝘀: The sum of the digits on a line strictly between two circles must be equal to a concatenation of the digits in that line's circles. For instance, 3-346-1 could be a valid split pea line, as 3+4+6=13, which is a concatenation of 3 and 1. (ie One circle contains the ‘tens’ digit of that line’s sum; and one circle contains the ‘units’ digit of that line’s sum.)\n𝗣𝗲𝗮 𝗖𝗶𝗿𝗰𝗹𝗲𝘀: Each circle in the puzzle indicates the number of cells along each line directly connected to the circle, including the bounding circles, which are of the same shading as the circle.\n𝗟𝗶𝗻𝗲 𝗠𝗼𝘃𝗲𝗺𝗲𝗻𝘁: All lines travel orthogonally. Lines may not branch or cross, except at circles.\n𝗫𝗩: Digits separated by an X sum to 10. Digits separated by a V sum to 5. Not all X or V are given.","solution":"531792648796841325482356719917635284354287961628419537173964852849523176265178493","fogLight":"R1C1,R1C2,R1C3,R2C1,R2C2,R2C3,R3C1,R3C2,R5C5","constraints":["XV","custom","fog","yin-yang"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12","c13"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"𝗦𝗽𝗹𝗶𝘁 𝗣𝗲𝗮𝘀: The sum of the digits on a line strictly between two circles must be equal to a concatenation of the digits in that line's circles. 𝗣𝗲𝗮 𝗖𝗶𝗿𝗰𝗹𝗲𝘀: Each circle in the puzzle indicates the number of cells along each line directly connected to the circle, including the bounding circles, which are of the same shading as the circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c9"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"mzabnx43dl","ctcId":2294,"ctcDifficulty":"MEDIUM","title":"Arrow Thermo 2","author":"Aad van de Wetering","rules":"Normal sudoku rules apply (ie place the digits 1-9, once each, in every row, column and 3x3 box). Along a thermometer, digits must increase from the bulb end. Digits along an arrow must sum to the digit in that arrow's circle.","solution":"358726941471359286692841357723965418846173529519284763235698174184537692967412835","constraints":["arrow","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"vo44xbbb7i","ctcId":2295,"ctcDifficulty":"MEDIUM","title":"Xmas","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along a green line have a difference of at least five.\nAll digits along a blue line must sum to the same total in each 3x3 box the line visits","solution":"317958624695243718824716935531627849946831257782495361278164593463589172159372486","constraints":["german-whispers","region-sum-line"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"p21cjfonte","ctcId":2297,"ctcDifficulty":"HARD","title":"Hidden Sandwiches","author":"Secret Santa","rules":"• Normal sudoku rules apply.\n• The grid is partially covered in fog. Entering correct digits will clear the fog from surrounding cells.\n• The number in the top left corner of a red cage (if given) indicates the sum of the digits sandwiched between 1 and 9 in that row.\n• The number in the top left corner of a blue cage (if given) indicates the sum of the digits sandwiched between 1 and 9 in that column.\n• The digit in a cage indicates how many digits (including the crust of 1 and 9) the corresponding sandwich sum contains.","solution":"718265493495713826623948751836179245942536187157824639584697312269381574371452968","fogLight":"R1C1,R2C1,R3C1","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• The number in the top left corner of a red cage (if given) indicates the sum of the digits sandwiched between 1 and 9 in that row. • The number in the top left corner of a blue cage (if given) indicates the sum of the digits sandwiched between 1 and 9 in that column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"mpi5qhto7n","ctcId":2298,"ctcDifficulty":"VERY HARD","title":"RatRun 20:Gifted","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT:\nFinkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick walls. (The walls have been decorated with red tinsel.)\n\nAs well as moving orthogonally, Finkz may move diagonally if there's a 2x2 space in which to do so.\n\nDYNAMIC FOG: Entering correct digits may clear fog somewhere in the maze.\n\nCHRISTMAS LIGHTS: An orange Christmas light indicates that any digits visited by Finkz in its row or column are odd. A blue Christmas light indicates that any digits visited in its row or column are even.\n\nTELEPORTS: Every teleport is part of a matching pair. Entering a teleport will cause Finkz to be instantly transported to the matching coloured teleport. From there she can continue her journey. Matching teleports always have identical digits, but teleports that don't match always have different digits.\n\nBLACKCURRANTS: Blackcurrants sit between two digits with a 1:2 ratio.\n\nBAUBLES: The number on a gold bauble gives the total of any cells it touches.\n\nTEST CONSTRAINT: In this experiment, any two cells that are adjacent along the path contain consecutive digits (except when separated by teleportation, where the digits are identical.)","solution":"569312784742895163183647259417589326698123547235764891856971432974238615321456978","fogLight":"R1C1,R1C2,R1C3,R2C1,R2C2,R2C3,R3C1,R3C2,R3C3","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Finkz the rat must reach the cupcake by finding a path through the maze. The path must not visit any cell more than once, cross itself, or pass through any thick walls. CHRISTMAS LIGHTS: An orange Christmas light indicates that any digits visited by Finkz in its row or column are odd. A blue Christmas light indicates that any digits visited in its row or column are even. TELEPORTS: Every teleport is part of a matching pair. Matching teleports always have identical digits, but teleports that don't match always have different digits. BAUBLES: The number on a gold bauble gives the total of any cells it touches. TEST CONSTRAINT: In this experiment, any two cells that are adjacent along the path contain consecutive digits (except when separated by teleportation, where the digits are identical.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c8","c9","c10","c13","c15","c16"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]}]},{"id":"zph1u3t3zq","ctcId":2299,"ctcDifficulty":"VERY HARD","title":"Nos482","author":"starwarigami","rules":"Normal Sudoku rules apply.\n\nWithin a cage, digits may not repeat, and the sum of their values is equal to the expression in the top left corner.\n\nThere are nine vampire cells and nine prey cells in the grid, one of each in every row, column and box.\nEvery digit from 1-9 appears exactly once in a vampire cell, and exactly once in a prey cell.\nDigits in vampire cells steal the value of the digit in the prey cell in the same box and add it to their own.\nThe value of the digits in a prey cell is 0.","solution":"546823179978614325213957846752486931439571682681239754124368597897145263365792418","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There are nine vampire cells and nine prey cells in the grid, one of each in every row, column and box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"330kjo10ui","ctcId":2307,"ctcDifficulty":"HARD","title":"Foggy Fillomino","author":"Die Hard","rules":"Normal fillomino rules apply (ie divide the grid along grid lines into non-overlapping regions of orthogonally-connected cells such that no two regions of the same size touch each other orthogonally; and fill each cell in each region with that region's size ie the number of cells in its region). Use only the digits 1 to 9 and the digit N cannot appear in row N or column N. Digits on the marked diagonals cannot repeat and must sum to the total (if given). The grid is covered by fog. Correctly placing digits may clear fog somewhere in the grid.","solution":"877775555888877154888227444331833322438844441444895555888899665799999961777777666","fogLight":"","constraints":["custom","fog","little-killer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Normal fillomino rules apply (ie divide the grid along grid lines into non-overlapping regions of orthogonally-connected cells such that no two regions of the same size touch each other orthogonally; and fill each cell in each region with that region's size ie the number of cells in its region). Use only the digits 1 to 9 and the digit N cannot appear in row N or column N. Digits on the marked diagonals cannot repeat and must sum to the total (if given).","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hr2psfhzcz","ctcId":2308,"ctcDifficulty":"VERY HARD","title":"Welcome, 2025!","author":"Gliperal","rules":"Normal sudoku rules apply. Digits may not repeat in cages. If a cage contains a clue in the top left corner, that cage must be comprised of 1-, 2-, 3-, and/or 4-digit numbers that sum to that value. Numbers are made from either horizontally adjacent digits read left-to-right; or vertically adjacent digits read top-to-bottom (ie numbers cannot bend!). Every digit within a cage must be part of exactly one number, and numbers may not cross cage borders.","solution":"648392517135867924792154863574618392219743658863925471981476235457239186326581749","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits may not repeat in cages.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If a cage contains a clue in the top left corner, that cage must be comprised of 1-, 2-, 3-, and/or 4-digit numbers that sum to that value.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"3kcwwu5uq1","ctcId":2309,"ctcDifficulty":"MEDIUM","title":"Sum Odd Sandwiches (SOS)","author":"Jodawo","rules":"Normal sudoku rules apply\nNumbers outside the grid are both Sandwich Clues and X-Sum Clues.\n   1: Sandwich Clues : Show the the sum of digits between the 1 and the 9 in that row or column. \n   2: X-Sums Clues : Show the total sum of the first X digits, where X is the first digit, from that direction.\nShaded Circles are odd numbers.","solution":"361829574972465813485371692794638125528147369136952748817293456659784231243516987","fogLight":"R2C3,R1C4,R1C5,R1C6,R2C7,R3C7,R4C6,R5C5,R6C5,R7C5,R9C5","constraints":["odd","sandwich","x-sum","fog"],"constraintFacts":[{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"v3zxi1cddk","ctcId":2310,"ctcDifficulty":"HARD","title":"Arrow Knots","author":"Myxo","rules":"Divide the grid into nine regions each containing 9 orthogonally-connected cells, such that each cell is part of exactly one region. Some region borders have already been given. Fill the grid with the digits 1-9 such that no digit repeats in any row, column or region.\n\nFrom each circle, draw some arrows that travel in a straight line either horizontally only or vertically only. The number in the bottom right corner of a circle cell indicates the number of arrows that must be drawn from that circle. Digits along an arrow must sum to the digit in the attached circle.\n\nAdditionally, all cells along arrows must be part of the same region as the circle they originate from. If an arrow doesn't reach the edge of the grid, the cell directly after the tip must be in a different region than the arrow.","rulesClarified":"Divide the grid into nine regions, each containing nine orthogonally connected cells, so that every cell is in exactly one region. Some region borders are already drawn.\n\nFill the grid with the digits 1 to 9 so that no digit repeats in any row, column or region.\n\nEach circle cell holds a digit. The small number in the bottom right corner of a circle tells you how many arrows must be drawn from that circle.\n\nArrows go straight, either horizontally or vertically, never diagonally. Each arrow starts at its circle. The circle's own cell is not one of the arrow's cells.\n\nThe digits along an arrow add up to the digit in its circle.\n\nAll cells along an arrow are in the same region as the circle it comes from.\n\nIf an arrow does not reach the edge of the grid, the cell directly beyond its tip must be in a different region from the arrow.","solution":"341826579189752463634279158763981245278543691512437986456398712927615834895164327","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits along an arrow must sum to the digit in the attached circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into nine regions each containing 9 orthogonally-connected cells, such that each cell is part of exactly one region. From each circle, draw some arrows that travel in a straight line either horizontally only or vertically only.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c4"]}]},{"id":"1w3s6u8q7d","ctcId":2311,"ctcDifficulty":"HARD","title":"Ho Ho Ho","author":"James Kopp","rules":"Normal sudoku rules apply.\nDigits along a blue line must sum to the same total in each 3x3 box the line visits.\nAdjacent digits along a red line have a difference of at least six.\nIf digits are separated by a red cherry, one is double the other.","solution":"943168725687925431251473896195847263872536149436219578729681354514392687368754912","constraints":["german-whispers","kropki","region-sum-line"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"94c0vtokc3","ctcId":2312,"ctcDifficulty":"HARD","title":"Sort of miraculous","author":"apetersen","rules":"Normal Sudoku rules apply.\nCells separated by a single knight's move (in chess) cannot contain the same digit.\nThe 3x3 boxes in the grid are numbered in normal reading order. In odd numbered boxes, odd digits appear in ascending order (with respect to position within that box).\nIn even numbered boxes, even digits appear in ascending order (with respect to position within that box). Cells within 3x3 boxes are also numbered in normal reading order.\nIn cells separated by a black dot, one digit is double the other.","rulesClarified":"Normal Sudoku rules apply.\n\nCells separated by a single knight's move (as in chess) cannot contain the same digit.\n\nThe nine 3x3 boxes are numbered 1 to 9 in reading order: the top row left to right (boxes 1, 2, 3), then the middle row (4, 5, 6), then the bottom row (7, 8, 9).\n\nInside each box, the nine cells are numbered 1 to 9 in reading order, left to right and top to bottom.\n\nIn the odd-numbered boxes (1, 3, 5, 7, 9), the odd digits in the box, read in cell-number order, increase.\n\nIn the even-numbered boxes (2, 4, 6, 8), the even digits in the box, read in cell-number order, increase.\n\nA black dot sits on the edge between two cells. One of the two digits on either side of the dot is double the other.","solution":"246579813813246579579813246357681924924357681681924357468792135135468792792135468","constraints":["antiknight","custom","kropki"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The 3x3 boxes in the grid are numbered in normal reading order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"thwkj8oc4q","ctcId":2315,"ctcDifficulty":"MEDIUM","title":"Deja Vu","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. In the positive diagonals (ie the blue marked diagonal and the diagonals parallel to it), the difference between two neighboring digits is only 4 or 5. Along the blue marked diagonal all digits are different.","solution":"874192356396578124521346798768923541245781963913465287689217435457639812132854679","constraints":["custom","diagonal"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In the positive diagonals (ie the blue marked diagonal and the diagonals parallel to it), the difference between two neighboring digits is only 4 or 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"34vev6zoay","ctcId":2318,"ctcDifficulty":"HARD","title":"Zipper Zipper","author":"Antiknight","rules":"Normal sudoku rules apply. Digits an equal distance from the center of a lavender 'Zipper Line' sum to the digits in the middle of that line. Digits on a white dot are consecutive. Not all dots are given. Nine cells in the grid (one per row, column, and box) are Doublers, which count as double their value on Zipper lines. Each digit appears in exactly one Doubler. Doublers aren't necessarily on Zipper lines.","solution":"495217638671834925283695174716529483829463751534781296948376512357142869162958347","constraints":["kropki","zipper-line"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"zipper-line","type":"zipper-line","variant":"modified","modifiers":[],"params":null,"note":"Digits an equal distance from the center of a lavender 'Zipper Line' sum to the digits in the middle of that line.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"ra51oj8xo0","ctcId":2319,"ctcDifficulty":"MEDIUM","title":"2B pencil","author":"Aron Lidé (Aspartagcus)","rules":"Sudoku: Fill each row, column and region with the digits 1-9.\nGerman whispers: Neighboring numbers along the line must differ by at least 5.\nTwo of the cells covered by the circle contain the same digit.","solution":"435796128982513764671842395259637481814259673367481259196378542743925816528164937","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Two of the cells covered by the circle contain the same digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"vgbfcjxvav","ctcId":2320,"ctcDifficulty":"HARD","title":"Renban Caves","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nShade some cells such that all shaded cells are connected orthogonally by other shaded cells to the edge of the grid, and the remaining unshaded cells form one orthogonally connected area. Note that 2x2 areas that are entirely shaded or entirely unshaded *are* allowed.\n\nDigits in circles cannot be shaded, and represent the total number of unshaded cells seen horizontally and vertically from that cell, including itself. Shaded cells block the vision.\n\nDigits in cells separated by a white dot must have consecutive values. Additionally, one of those cells must be shaded and the other must be unshaded.\n\nEvery set of orthogonally connected unshaded cells within a 3x3 Sudoku region acts as a Renban line: that is, those cells must contain a nonrepeating set of consecutive digits in any order. Note that a 3x3 region may have more than one such set of cells. Also note that such a set may consist of just one cell.","solution":"657398124941276835832154967789431256564829371213765489425613798176982543398547612","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade some cells such that all shaded cells are connected orthogonally by other shaded cells to the edge of the grid, and the remaining unshaded cells form one orthogonally connected area. Digits in circles cannot be shaded, and represent the total number of unshaded cells seen horizontally and vertically from that cell, including itself. Every set of orthogonally connected unshaded cells within a 3x3 Sudoku region acts as a Renban line: that is, those cells must contain a nonrepeating set of consecutive digits in any order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"tuf714ivht","ctcId":2321,"ctcDifficulty":"HARD","title":"The Pea-thagorean Theorem","author":"sujoyku & ChinStrap","rules":"- Normal sudoku rules apply, i.e. each row, column and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- Dynamic Fog: The grid is covered in fog. Placing a correct digit in a cell lifts fog from that cell and possibly other cells; revealing new clues.\n\n- Split Pea Index Lines: All lines and attached circles are split pea lines, and between the circles the lines function as index lines.\n\n- Split Pea Lines: Digits on a line between two circles sum to a two-digit number written using the digits in the circles. For example, 3_346_1 could be a valid split pea line, as 3+4+6=13, which is 1 concatenated with 3.\n\n- Index Lines: Each index line has an invisible diamond at one end, next to a circle (to be determined by the solver). The digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears. For example, 3214 is a valid index line, the 1st digit, 3, indicates that the 3rd digit is a 1, and so on.\n\nLines do not cross or share cells with themselves or other lines.  Each connected set of lines and circles has a distinct color and line style.  Lines have been made thicker to be able to see a line moving diagonally.","solution":"827653914465791328319482576291847635534216789678935142952374861143568297786129453","fogLight":"R1C1,R4C1,R4C2,R4C3,R4C4,R3C4,R2C4,R1C4","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Split Pea Lines: Digits on a line between two circles sum to a two-digit number written using the digits in the circles. For example, 3_346_1 could be a valid split pea line, as 3+4+6=13, which is 1 concatenated with 3. - Index Lines: Each index line has an invisible diamond at one end, next to a circle (to be determined by the solver). The digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears. For example, 3214 is a valid index line, the 1st digit, 3, indicates that the 3rd digit is a 1, and so on.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ru676yn5px","ctcId":2322,"ctcDifficulty":"MEDIUM","title":"Squiggle","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nBox borders divide each blue line into segments with the same sum.","solution":"642831975173259648589476132814367529365912487927584316438625791251793864796148253","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7ry8w31ry3","ctcId":2324,"ctcDifficulty":"HARD","title":"Box 8 is Sus!","author":"Panthera","rules":"Normal Sudoku rules apply.\nNormal Japanese Sums rules apply. Clues outside the grid indicate the sums of runs of contiguous cells that must be shaded. The shaded runs must be separated by at least 1 non-shaded cell.\n\nThe imposter has messed up this Japanese Sums Sudoku!\n\nThe imposter changed SOME column/row clues to represent the runs of UNshaded cells instead of the shaded ones! And he even erased one of the clues (row 5)! All I remember is that there are less shaded cells than unshaded. Can you still solve this puzzle??\n\nNote: a row or column clue will only give you a clue about one type of cell: shaded or unshaded. There are no mixed clues within a column or row.","solution":"685724139719358624342196587124679853596283471873415962438967215961532748257841396","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Normal Japanese Sums rules apply.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6zpysyrai2","ctcId":2325,"ctcDifficulty":"VERY HARD","title":"Ambiguous Arrows Sudoku","author":"Jay Dyer","rules":"Normal sudoku rules apply. Each line must contain a digit equal to half the sum of its digits. Digits may repeat on a line if allowed by other rules.","solution":"815923674369417258274586913583172469692854137741369825957241386426738591138695742","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each line must contain a digit equal to half the sum of its digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jiz9k1fcdl","ctcId":2326,"ctcDifficulty":"MEDIUM","title":"Cool S(udoku)","author":"ChinStrap","rules":"Normal sudoku rules apply.\n\nDutch Whispers Lines: Consecutive digits along an orange Dutch Whispers lines must differ by at least 4.\n\nRenban Lines: Pink Renban lines contain a set of consecutive digits in any order.\n\nSlow Thermometer: Starting at the bulb end, digits on a dark grey slow thermometer must not decrease.\n\nWhite Kropki Dot: Digits separated by a white dot are consecutive. Not all such dots are given.","solution":"816742359543169728792358641175826493639417582428593167981634275254971836367285914","constraints":["dutch-whispers","kropki","renban","thermometer"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"mwpu102gkm","ctcId":2327,"ctcDifficulty":"MEDIUM","title":"Make It Count","author":"ChinStrap","rules":"Normal sudoku rules apply.  \n\nCounting Circles: A digit in a circle indicates how many circles contain that digit. \n\nIndex Lines: On an index line, the digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears. Eg: 3214 would be a valid line; the 1st digit, 3, indicates that the 3rd cell contains a 1, the 2nd cell a 2, and so on.","solution":"192456378483971526765238914856719432237584169941623857629145783578392641314867295","constraints":["counting-circle","custom"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Index Lines: On an index line, the digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"unrk3m4tg3","ctcId":2328,"ctcDifficulty":"MEDIUM","title":"Assigned Seating","author":"ChinStrap","rules":"Normal sudoku rules apply.  \n\nYin Yang: Color every cell in the grid light or dark. Cells of the same color are orthogonally connected. Every 2x2 contains both colors. \n\nIndex Lines: On an index line, the digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears. Eg: 3214 would be a valid line with 3 as the diamond; the 1st digit, 3, indicates that the 3rd cell contains a 1, the 2nd cell a 2, and so on.\n\nIndex Line Coloring: All cells that reference their own position on a line (the digit N is in position N) should be dark. Cells that are not self referencing should be light. For example for the line 3214 with 3 as the diamond, the 2 and 4 would be dark and the 1 and 3 would be light. \n\nYin Yang White Kropki Dots: Digits separated by a white dot are consecutive and have the same color. Not all such dots are necessarily given.","solution":"627851349413629875895347612964532781382176594751984263578493126246715938139268457","constraints":["custom","kropki","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Index Lines: On an index line, the digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears. Index Line Coloring: All cells that reference their own position on a line (the digit N is in position N) should be dark.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7n6wneuch2","ctcId":2329,"ctcDifficulty":"HARD","title":"Field Research","author":"ChinStrap","rules":"Normal sudoku rules apply.\n\nDynamic Fog: The grid is covered in fog. Placing a correct digit in a cell lifts fog in that cell and possibly other cells; revealing new clues.\n\nIndex Lines: On an index line, the digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears. For example: 3214 would be a valid line with the 3 on the diamond; the 1st digit, 3, indicates that the 3rd digit is a 1, and so on.\n\nInequality signs point to the smaller of the two digits. Digits separated by a white dot are consecutive. Digits separated by an X sum to 10. Not all such symbols are necessarily given.","solution":"543218679972465813618739425185624937769153248324987561291876354856341792437592186","fogLight":"R2C8,R3C8,R4C8,R5C8,R6C8,R6C9,R7C7,R7C8,R8C7,R8C8,R9C7","constraints":["XV","custom","fog","inequality","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Index Lines: On an index line, the digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"xtu2lb9ufm","ctcId":2331,"ctcDifficulty":"HARD","title":"Two Truths And A Truth","author":"ChinStrap","rules":"Normal Sudoku rules apply.\n\nFor each set of 3 lines that are the same color (and line styling), 2 of those are index lines and 1 is a thermometer. No line can be ambiguously both.\n\n- Thermometers: Digits along a thermometer must strictly increase starting from the bulb.\n\n- Index Lines:  The digit in the Nth cell along the line (starting from the bulb) indicates the position along the line where the digit N appears. For example, 3214 is a valid index line, the 1st digit, 3, indicates that the 3rd digit is a 1, and so on.","solution":"243657918157948236896213547674531892518492673932876154365124789421789365789365421","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Index Lines:  The digit in the Nth cell along the line (starting from the bulb) indicates the position along the line where the digit N appears. For example, 3214 is a valid index line, the 1st digit, 3, indicates that the 3rd digit is a 1, and so on.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"- Thermometers: Digits along a thermometer must strictly increase starting from the bulb.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"sqdra9pozn","ctcId":2332,"ctcDifficulty":"HARD","title":"Weighted Cells","author":"Oddlyeven","rules":"Rules: Normal Sudoku rules apply. Put the digits 1 to 9 once each into every row, column and 3x3 box.\nFog: The grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells.\nWeighted Cells: One cell in each row, column and box is lighter than normal. Lighter cells have a value equal to half of their digit. Each digit from 1 to 9 appears once in the set of lighter cells. One cell in each row, column and box is heavier than normal. Heavier cells have a value equal to one and a half times their digit. Each digit from 1 to 9 appears once in the set of heavier cells. No cell is both lighter and heavier.\nRegion Sum Lines: The sum of the values on a line within a box must be the same for each box that line passes through. If a line passes through a box more than once, each time it passes through counts separately. Lines do not branch, cross or share cells.","solution":"819475623452316789736928154124639578378542916695187342541863297283791465967254831","fogLight":"R1C1,R1C2,R1C3,R2C1,R2C2,R2C3,R3C1,R3C2,R3C3","constraints":["custom","fog","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Weighted Cells: One cell in each row, column and box is lighter than normal. One cell in each row, column and box is heavier than normal.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c8"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Region Sum Lines: The sum of the values on a line within a box must be the same for each box that line passes through.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]}]},{"id":"4geira1lnl","ctcId":2333,"ctcDifficulty":"HARD","title":"Thermo Knots","author":"Myxo","rules":"Divide the grid into nine regions, each containing 9 orthogonally connected cells such that each cell is part of exactly one region. Fill the grid with digits 1-9 such that no digit repeats in any row, column or region. Thermo knots: From each big circle, draw straight horizontal or vertical thermometers in all possible directions, such that each thermo occupies at least two cells (including the circle). Digits along a thermo must increase, starting from the circle. Additionally, all cells along thermos must be part of the same region as their circle. If a thermo doesn't reach the edge of the grid, it MUST keep extending until it reaches the the edge of its region, and the cell directly after the tip must be in a different region and must contain a SMALLER digit than the tip. Cells separated by a small white circle must be in DIFFERENT regions and contain consecutive digits.","solution":"728316459816594723397425816563281974471968235934657182152743698689132547245879361","constraints":["custom","kropki","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into nine regions, each containing 9 orthogonally connected cells such that each cell is part of exactly one region. Additionally, all cells along thermos must be part of the same region as their circle. If a thermo doesn't reach the edge of the grid, it MUST keep extending until it reaches the the edge of its region, and the cell directly after the tip must be in a different region and must contain a SMALLER digit than the tip. Cells separated by a small white circle must be in DIFFERENT regions and contain consecutive digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c5","c6","c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"06vt5y9nwu","ctcId":2335,"ctcDifficulty":"HARD","title":"Mousetrap","author":"Tallcat","rules":"Normal sudoku rules apply. \n\nGOAL: Mus the mouse must reach the cupcake and Felix the cat must reach the escape hole finding paths through the maze. Individually, their paths must not visit any cell more than once, cross itself, or pass through any thick maze walls. As well as moving orthogonally, both Mus and Felix can move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. Importantly, the paths of Felix and Mus can cross each other. This can only happen on even digits and if it does happen, both paths MUST continue on to another cell in a straight line. \n\nONE-WAY DOORS: Mus and Felix may only pass through black arrows if moving in the direction the arrow is pointing. An arrow always points to the smaller of the two values it sits between. \n\nBLACKCURRANTS: Cells connected by a blackcurrant have a 1:2 ratio (one is double the other.) Not all possible blackcurrants have been given. \n\nGRAPES: Digits separated by a green grape have a difference of at least 5. Not all possible grapes have been given. \n\nPATH CONSTRAINTS: For Mus, the path within each box must be a thermometer with the bulb being the first square entered and the tip being the last square in the box. Digits along a thermometer increase from bulb to tip. Repeat visits to the same box are considered separate thermos. For Felix, adjacent cells along the path must be of different parity (odd/even).","solution":"278316549569247381431958276987463125654129738123875694896731452345692817712584963","constraints":["custom","german-whispers","inequality","kropki","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"GOAL: Mus the mouse must reach the cupcake and Felix the cat must reach the escape hole finding paths through the maze. Individually, their paths must not visit any cell more than once, cross itself, or pass through any thick maze walls. As well as moving orthogonally, both Mus and Felix can move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. Importantly, the paths of Felix and Mus can cross each other. This can only happen on even digits and if it does happen, both paths MUST continue on to another cell in a straight line. ONE-WAY DOORS: Mus and Felix may only pass through black arrows if moving in the direction the arrow is pointing. For Felix, adjacent cells along the path must be of different parity (odd/even).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c7","c16"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]}]},{"id":"1xfvrsbx6o","ctcId":2337,"ctcDifficulty":"MEDIUM","title":"The Heat Between Us","author":"Marty Sears","rules":"Normal sudoku rules apply. Entering correct digits may clear fog somewhere in the grid. No guessing is necessary.\n\nIn this puzzle, coloured lines are 'edge thermos'... these run along cell edges.\n\nAny cell edge covered by a thermo contains a thermo spot. The value of a thermo spot equals the sum of the digits in the two cells it sits between. Values of spots along a thermo strictly increase moving away from the bulb (the large spot at one end.) Each thermo is a different colour, and they don't overlap or intersect each other.","solution":"463195782721438956598762143876249315154387629932516874217653498349821567685974231","fogLight":"R5C5,R6C1,R6C2,R6C5,R6C8,R6C9,R7C1,R7C2,R7C5,R7C8,R7C9,R8C5,R9C5","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In this puzzle, coloured lines are 'edge thermos'... these run along cell edges.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ja8iov3ag3","ctcId":2338,"ctcDifficulty":"MEDIUM","title":"Tenacious Whispers","author":"sujoyku","rules":"- Normal sudoku rules apply, i.e. each row, column and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- German Whispers: Adjacent digits along a green line must differ by at least 5.\n\n- Ten lines: Each grey line can be split into contiguous, non-overlapping segments that sum to exactly 10. If allowed by other rules, digits inside a segment may repeat. For example, a valid ten line could read 37424 where the segments 37 and 424 both sum to 10.","rulesClarified":"Normal sudoku rules apply: each row, column and 3x3 region contains the digits 1 to 9 once each.\n\nGerman Whispers: along a green line, any two neighbouring digits differ by at least 5.\n\nTen lines: each grey line is split into segments, read from one end of the line to the other. Every digit on a grey line belongs to exactly one segment, and the digits in each segment add up to exactly 10. Digits inside a segment may repeat, if the other rules allow it.\n\nFor example, a valid ten line could read 37424, split as 37 and 424, because 3 + 7 = 10 and 4 + 2 + 4 = 10.","solution":"394187256816523749275469183652831974481976325937245861729614538163758492548392617","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Ten lines: Each grey line can be split into contiguous, non-overlapping segments that sum to exactly 10. If allowed by other rules, digits inside a segment may repeat. For example, a valid ten line could read 37424 where the segments 37 and 424 both sum to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"drnjmx02i1","ctcId":2339,"ctcDifficulty":"MEDIUM","title":"Satellites","author":"Eric Rathbun","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow’s circle. Digits in a cage cannot repeat and must sum to the small clue in the top left corner of the cage (if given). Digits separated by a white dot are consecutive. In cells separated by a black dot one digit must be double the other. Not all dots are given.","solution":"915483267762591348834267915583142679146975832279836154628714593451329786397658421","constraints":["arrow","cage","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4","c5"]}]},{"id":"tiea0253j6","ctcId":2341,"ctcDifficulty":"HARD","title":"Anticamel Coloring Book","author":"gdc","rules":"𝗖𝗵𝗮𝗼𝘀 𝗖𝗼𝗻𝘀𝘁𝗿𝘂𝗰𝘁𝗶𝗼𝗻: Divide the grid into 9 regions of orthogonally connected cells. Place the digits 1-9 once each in every row, column and region.\n𝗔𝗻𝘁𝗶-𝗖𝗮𝗺𝗲𝗹: Digits separated by a [camel move](https://sudokupad.app/vcprgzvqm1) (in fairy chess) may not contain the same digit. A camel moves 3 steps forward and 1 step to the side.\n𝗜𝗻𝘁𝗲𝗿𝗻𝗮𝗹 𝗫-𝗦𝘂𝗺𝘀: A digit in a circle counts the number of cells it sees of its own region in its row and column combined, including itself. Region borders and elephants block vision. If given, a 2-digit number in a rectangle gives the sum of all 'seen' digits.","solution":"259781364372418659791246583164357928946835712528693147435962871687129435813574296","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"𝗖𝗵𝗮𝗼𝘀 𝗖𝗼𝗻𝘀𝘁𝗿𝘂𝗰𝘁𝗶𝗼𝗻: Divide the grid into 9 regions of orthogonally connected cells. 𝗔𝗻𝘁𝗶-𝗖𝗮𝗺𝗲𝗹: Digits separated by a [camel move](https://sudokupad.app/vcprgzvqm1) (in fairy chess) may not contain the same digit. 𝗜𝗻𝘁𝗲𝗿𝗻𝗮𝗹 𝗫-𝗦𝘂𝗺𝘀: A digit in a circle counts the number of cells it sees of its own region in its row and column combined, including itself. Region borders and elephants block vision. If given, a 2-digit number in a rectangle gives the sum of all 'seen' digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c3","c5","c6","c7"]}]},{"id":"pyv0ykw8h5","ctcId":2342,"ctcDifficulty":"MEDIUM","title":"The Magical Ingredients","author":"Cane_Puzzles","rules":"Normal sudoku rules apply. Each purple line contains a set of non-repeating consecutive digits, which may appear in any order on the line. The digits in a cage sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage.","solution":"428193675159672348673845129897214563215386497346957281562739814931428756784561932","constraints":["cage","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"orrpwulfgl","ctcId":2343,"ctcDifficulty":"MEDIUM","title":"Cornered Thermos","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits along a thermometer must increase from the bulb end.","solution":"268975431351468927497312568534826719976143285812597346783251694629784153145639872","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"29hyhl8ay5","ctcId":2344,"ctcDifficulty":"HARD","title":"The Third Law Of Thermodynamics","author":"gdc","rules":"Normal sudoku rules apply.\n𝗧𝗵𝗲𝗿𝗺𝗼: Digits along a grey thermo increase from the bulb end. Thermos contain exactly 4 digits, only move horizontally and vertically (never diagonally) and don't branch or overlap. Thermos are partially invisible.\n𝗗𝘆𝗻𝗮𝗺𝗶𝗰𝘀: The grid is covered in dynamic fog. Placing a correct digit in a cell lifts fog from that cell and possibly other cells; revealing new clues.\n𝗘𝗻𝘁𝗿𝗼𝗽𝘆: Every 2x2 area in the grid contains at least one digit from (123), (456), and (789).","rulesClarified":"Normal sudoku rules apply.\n\nThermos: each grey thermo is a line of exactly 4 cells. It runs horizontally or vertically, never diagonally, and does not branch or overlap another thermo.\n\nThe digits along a thermo increase away from its bulb, the end with the circle.\n\nThermos are partially invisible: part of a thermo may be hidden.\n\nDynamic fog: the grid is covered in fog. Placing a correct digit lifts the fog from that cell and possibly from other cells, which can reveal new clues.\n\nEntropy: every 2x2 block of four cells in the grid contains at least one digit from 1, 2 and 3, at least one digit from 4, 5 and 6, and at least one digit from 7, 8 and 9.","solution":"691852734524137689378946125253419867486725391719368542845691273137284956962573418","fogLight":"R3C2,R4C1,R4C2","constraints":["custom","fog","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"𝗘𝗻𝘁𝗿𝗼𝗽𝘆: Every 2x2 area in the grid contains at least one digit from (123), (456), and (789).","evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"o0ypyh2f0y","ctcId":2345,"ctcDifficulty":"MEDIUM","title":"Frolic","author":"Nordy","rules":"Normal Sudoku, Region Sum Lines, and German Whispers rules apply:\n• Normal Sudoku: Place the digits 1 to 9 in every row, column, and 3x3 box.\n• Region Sum Lines: Box borders divide each blue line into segments with equal sums. Different lines may have different sums.\n• German Whispers: Adjacent digits on each green line must differ by at least 5.","solution":"147382659968571423532946817621839745473265198895417236319728564284653971756194382","constraints":["german-whispers","region-sum-line"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"fg8p36r2g0","ctcId":2346,"ctcDifficulty":"VERY HARD","title":"Some Kind of Chaos","author":"Marty Sears","rules":"SOMEDOKU: Fill the grid with the digits 1-9. Each row N and column N contain exactly N distinct digits, with the rest of the row / column being filled with repeats.\n\nCHAOS CONSTRUCTION: Divide the grid into 9 regions, each containing 9 orthogonally connected cells. The finished pattern of regions will have 180 degree rotational symmetry.\n\nCIRCLES: The digit in a circle indicates how many distinct digits appear in its region. Eg: A 6 in a circle indicates that the region includes 6 distinct digits (and 3 repeats.) No two circles contain the same digit.\n\nREGION SUM LINES: Region borders divide blue lines into segments, each of which have the same sum. Each blue line must cross at least one region border.","solution":"111111111121212222115544454111253533111535546115532865111432968126548179126495387","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each row N and column N contain exactly N distinct digits, with the rest of the row / column being filled with repeats. CHAOS CONSTRUCTION: Divide the grid into 9 regions, each containing 9 orthogonally connected cells. CIRCLES: The digit in a circle indicates how many distinct digits appear in its region.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"ws3dy3a8gi","ctcId":2348,"ctcDifficulty":"MEDIUM","title":"ZL GW DA","author":null,"rules":"Normal Sudoku rules apply. Adjacent digits along a green line must differ in value by at least 5. The lines and hexagons are double arrows. Digits on each line sum to the same number as the sum of the digits in the hexagons at the ends. Values at equal distance to the center of a lavender line sum to the central value.","solution":"954132678283576491176984352597421836468793125321865947739218564842659713615347289","constraints":["custom","german-whispers","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits on each line sum to the same number as the sum of the digits in the hexagons at the ends.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"25xvdpdyba","ctcId":2350,"ctcDifficulty":"MEDIUM","title":"Picky neighbors","author":"Lithium-Ion","rules":"Normal Sudoku rules apply. Box borders divide blue lines into segments with the same sum. Different blue lines can have different sums. If two digits (called x and y) are (orthogonally or diagonally) adjacent along a blue line, then x as well as y has to be an integer multiple of the difference between x and y. For example, 6 and 4 are allowed to be adjacent on a blue line since both 6 and 4 are a multiple of 2 (the difference between 4 and 6).","solution":"348965217295713846761842539429178365517236984683459721872694153956321478134587692","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If two digits (called x and y) are (orthogonally or diagonally) adjacent along a blue line, then x as well as y has to be an integer multiple of the difference between x and y.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"cuf9l203ev","ctcId":2352,"ctcDifficulty":"MEDIUM","title":"Peapods","author":"sujoyku and ChinStrap","rules":"Normal sudoku rules apply.\n\nPeapods: Digits on a line sum up to a two digit number made out of the digit in the line's circle repeated twice. For example, 245 on a line would have a 1 in its circle.","solution":"791642853452831976638597214329768541567214389814359627975123468283476195146985732","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Peapods: Digits on a line sum up to a two digit number made out of the digit in the line's circle repeated twice.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9ryz1zmsa7","ctcId":2353,"ctcDifficulty":"VERY HARD","title":"Quantum Entanglement","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nEntangled Cages: Every cage in the grid is paired with exactly one other cage of the same color. Digits may not repeat within a pair of cages, and when combined, sum to a concatenation of the two numbers in the top left corners of the cages. For example, if a 1 cage was paired with a 3 cage, the digits in both cages would sum to either 13 or 31. 0 is allowed to be the leading digit for sums in this puzzle.\n\nKropki: Digits separated by a white dot must be consecutive. Not all possible dots are necessarily shown.","solution":"534687921928145763716293584289534176365719842147826395452378619671952438893461257","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Entangled Cages: Every cage in the grid is paired with exactly one other cage of the same color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"3b5i89p48o","ctcId":2354,"ctcDifficulty":"MEDIUM","title":"Rhubarb and Custard","author":"Qodec","rules":"- Sudoku: Each row, column, and region indicated by thick borders in the grid must contain the digits 1 to 9 once each.\n- Little killers: Digits along diagonals indicated by arrows outside the grid must sum to the given number at that arrow.\n- Odd: The cell with the opaque grey circle contains an odd digit.","solution":"825941763176385924439627158793852641581463279264179385952714836617538492348296517","constraints":["little-killer","odd"],"constraintFacts":[{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"s22t2sbanr","ctcId":2355,"ctcDifficulty":"MEDIUM","title":"Add On","author":"James Kopp","rules":"Normal sudoku rules apply. \nEach 3x3 box contains a circled digit which is equal to the addend of that box. The addend applies to all cells of the box it lies within. The value of each cell is equal to the digit placed in the cell added to the addend of its box. The nine circled cells contain a different digit.\nCells separated by a black dot have values in which one is double the other. Not all black dots are necessarily given. \nBox borders divide the blue lines into segments whose values have the same sum. Different lines may have different sums.","solution":"965231748184567329273984516752198463841673952396425187619342875528719634437856291","constraints":["custom","kropki","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each 3x3 box contains a circled digit which is equal to the addend of that box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Cells separated by a black dot have values in which one is double the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Box borders divide the blue lines into segments whose values have the same sum.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]}]},{"id":"6f3k4btidk","ctcId":2356,"ctcDifficulty":"VERY HARD","title":"Taiga","author":"IcyFruit","rules":"Normal sudoku rules apply. Identify two 'indexer' cells in each row, column, and box, with one indexing in the row and the other indexing in the column. The digit in an indexer cell indicates the position of the other indexer cell in its row or column. Positions are counted left to right in rows and top to bottom in columns. The value of an indexer cell is the digit in the cell it indexes. For all other cells, their value is their own digit. All lines are region-subset lines: ie 3x3 box boundaries divide each line into segments. For any pair of segments on the same line, the values on one of those segments must all appear on the other segment. Examples: i) If () represents an indexer cell, then 12(6)34(7)598 would be a valid row of digits, because there are exactly two indexer cells, and one of the cells indexes the other: the (7) is in position 6, and the other indexer cell contains a 6. The value of the (6) cell would be 7, because that is the digit in the cell it indexes. Given that this is a row, we would also know that r7c6 must be an indexer cell, because the (7) cell indexes it. ii) A region-subset line could contain the values 189-8-98-918, where a dash represents a box boundary. This is valid because (8) is a subset of (89) and (189), (89) is a subset of (189), and (189) is a subset of itself.","solution":"847925613695413728321678549736892154954761832218354967589236471463187295172549386","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Identify two 'indexer' cells in each row, column, and box, with one indexing in the row and the other indexing in the column. All lines are region-subset lines: ie 3x3 box boundaries divide each line into segments.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7"]}]},{"id":"ur11o44tv3","ctcId":2357,"ctcDifficulty":"MEDIUM","title":"Weird Arrows","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply.\n\nBULBOUS ARROWS - The sum of the digits in white bulb equals the sum of the digits on each attached arrow.","solution":"742319856691285743538746129283567491167498532459123678815934267924671385376852914","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"BULBOUS ARROWS - The sum of the digits in white bulb equals the sum of the digits on each attached arrow.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"qj5fmj2art","ctcId":2359,"ctcDifficulty":"HARD","title":"Drop Bear","author":"starwarigami","rules":"Normal Sudoku Rules apply. along with the following additional constraints\n\nAnti-Knight: Cells a chess knights move away from each other must not contain the same digit.\n\nRegion Sum Lines: Region borders split blue lines into segments where the digits on each segment have the same sum. This sum may be different for different lines","solution":"742659138538147926961823547625791384187364295493285761259418673314976852876532419","constraints":["antiknight","region-sum-line"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"kwio77hpis","ctcId":2360,"ctcDifficulty":"HARD","title":"Ping Pong","author":"Antiknight","rules":"Normal sudoku rules apply. Digits do not repeat along gold Nabner lines. Additionally, no pair of digits anywhere on a Nabner line can be consecutive. The digits along each arrow must sum to the digit in the circled cell. A black dot between cells indicates cell values with a 2:1 ratio. A white dot between cells indicates cells with consecutive values. Not all dots are shown.","solution":"712539684369748512584126973826497351471365298935812467258973146193684725647251839","constraints":["arrow","kropki","nabner-line"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"xfiaf0aoqm","ctcId":2361,"ctcDifficulty":"MEDIUM","title":"Euler’s Constant","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along the green line have a difference of at least five.\nNo two orthogonally connected cells can sum to 5.\nCells separated by a black dot have digits in which one is double the other. Not all black dots are necessarily given.","solution":"642789153938152674517364829826543917451927368793816542369471285175298436284635791","constraints":["custom","german-whispers","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No two orthogonally connected cells can sum to 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"xubeuskt61","ctcId":2362,"ctcDifficulty":"MEDIUM","title":"Sudoku Bowl LIX","author":"Scott Strosahl","rules":"Normal Sudoku rules apply. Place the digits 1-9 exactly once in every row, column, and box.\n\nGerman Whispers Lines: All lines in the grid are German Whispers lines (regardless of color). Adjacent digits along the line must have a difference of at least 5.\n\nKropki Footballs: Digits separated by a white football are consecutive. Digits separated by a black football have a 1:2 ratio, meaning one is exactly double the other. Not all footballs are necessarily given.","solution":"975418623613259478428763951362845197547192836891637245259381764784526319136974582","constraints":["german-whispers","kropki"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"8u7avt009b","ctcId":2373,"ctcDifficulty":"HARD","title":"Exponentially Bounded Thermos","author":"Amin Khalek","rules":"Normal sudoku rules apply. Normal thermo rules DO NOT apply. Each thermo consists of at least two numbers (each possibly multi-digit, with the unit digit towards the tip) that increase - at least doubling and at most tripling each time. Cells with an arrow pointing to an adjacent thermo cell must indicate how many digits the adjacent number on the thermo has. In cages, digits must sum to the clue in the top left corner of the cage.","solution":"328165479751394286694728351249536718837219564516487923465971832173842695982653147","constraints":["cage","custom","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells with an arrow pointing to an adjacent thermo cell must indicate how many digits the adjacent number on the thermo has.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Normal thermo rules DO NOT apply.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"ben75yl8kq","ctcId":2374,"ctcDifficulty":"HARD","title":"Factor Me In The Corner","author":"Amin Khalek","rules":"Normal sudoku rules apply. In cages, digits cannot repeat and their sum must equal the product of “corner cell” digits of that cage. A corner cage cell borders a horizontal and vertical dotted line.","solution":"352967184748215693916384572239158746567429318184673259823541967671892435495736821","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In cages, digits cannot repeat and their sum must equal the product of “corner cell” digits of that cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hb97vsx1xm","ctcId":2375,"ctcDifficulty":"VERY HARD","title":"Parity Pairs","author":"Amin Khalek","rules":"Normal sudoku rules apply. Cells with a blue circle contain the number of neighboring odd digits, orthogonally and diagonally, excluding the cell itself. Along thermometers, digits must increase from the round bulb to each end. Cells separated by a white dot must contain consecutive digits.","solution":"784235619321496578956871432169352847475689321238714956843927165617548293592163784","constraints":["custom","kropki","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells with a blue circle contain the number of neighboring odd digits, orthogonally and diagonally, excluding the cell itself.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"Gf8p33BmMb","ctcId":2376,"ctcDifficulty":"HARD","title":"Spectral Distortions","author":"Amin Khalek","rules":"Normal sudoku rules apply. There are nine doubler cells in the grid, one in every row, column and box. Each digit from 1-9 appears in a doubler cell exactly once. A doubler cell's value counts as double its digit. Along a green line, values of neighboring cells must differ by at least 5. For cells separated by an ‘x', the two cells' values must sum to 10. For cells separated by a white dot, the two cells' values must be consecutive. For cells separated by a black dot, one cell's value must be double the other. For cells separated by a grey dot, one cell's value must be triple the other.","solution":"563829174941675238728143965387254691492716853156938427619387542274561389835492716","constraints":["XV","custom","german-whispers","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There are nine doubler cells in the grid, one in every row, column and box. For cells separated by a grey dot, one cell's value must be triple the other.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c9"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Along a green line, values of neighboring cells must differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8"]}]},{"id":"100ywt1d63","ctcId":2377,"ctcDifficulty":"HARD","title":"Non-repeating Palindromes","author":"Amin Khalek","rules":"Normal sudoku rules apply.\n\nThere are nine doubler and nine halver cells in the grid. Place one doubler and one halver in every row, column and box such that doublers and halvers cannot share a cell, and each digit from 1-9 appears once in a doubler cell and once in a halver cell. A doubler cell's value counts as double its digit while a halver cell's value counts as half its digit.\n\nValues on a grey palindrome line read the same forwards and backwards.\n\nBox borders divide each blue line into segments whose values have the same sum.\n\nEach inequality symbol points to the smaller value of the two cells on either side of it.","rulesClarified":"Normal sudoku rules apply.\n\nThere are nine doubler cells and nine halver cells in the grid.\n\nPlace one doubler and one halver in every row, column and box. A doubler and a halver cannot share a cell, and each digit from 1 to 9 appears once in a doubler cell and once in a halver cell.\n\nEvery cell has a value, and the rules below use that value. A doubler cell's value is double its digit. A halver cell's value is half its digit.\n\nValues on a grey palindrome line read the same forwards and backwards.\n\nEach blue line is cut by the box borders into segments. The values in the segments of a blue line all have the same sum.\n\nEach inequality symbol points to the smaller value of the two cells on either side of it.","solution":"654823917783169452291475386329748561468591273517632849976354128835217694142986735","constraints":["custom","inequality","palindrome","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There are nine doubler and nine halver cells in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"palindrome","type":"palindrome","variant":"modified","modifiers":[],"params":null,"note":"Values on a grey palindrome line read the same forwards and backwards.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Box borders divide each blue line into segments whose values have the same sum.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]}]},{"id":"3xkgia0gur","ctcId":2384,"ctcDifficulty":"HARD","title":"Entropea","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nSPLIT PEA LINES: Along a peach line, the digits between (not including) the green circles sum to a two digit number; these two digits appear in the green circles in either order.\n\nENTROPIC LINES: In this puzzle, the lines are also entropic (including the green circles). Any three adjacent digits along a line must contain one small digit (1,2, or 3), one medium digit (4,5 or 6) and one high digit (7,8 or 9).","solution":"519674328876213594342859716168347952423985167795162843634598271981726435257431689","constraints":["custom","entropic-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"SPLIT PEA LINES: Along a peach line, the digits between (not including) the green circles sum to a two digit number; these two digits appear in the green circles in either order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"rlkbec6hy3","ctcId":2385,"ctcDifficulty":"MEDIUM","title":"Trickster","author":"James Sinclair","rules":"Normal sudoku rules apply. Each digit in column 1 indicates the position of the 1 in its row (that is, if R5C1 is a 6, R5C6 is a 1). The same is true of columns 5 and 9, regarding the digits 5 and 9, respectively. Adjacent digits along a green line must differ in value by at least 5. Gold lines contain a non-repeating set of digits, and no two digits on the same line can be consecutive (regardless of their position on the line). Digits in cells with a shaded square must be even.","solution":"172965384458123679963874521634281957895736412217549836726398145341652798589417263","constraints":["custom","even","german-whispers","nabner-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each digit in column 1 indicates the position of the 1 in its row (that is, if R5C1 is a 6, R5C6 is a 1). The same is true of columns 5 and 9, regarding the digits 5 and 9, respectively.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"DpFgDGMphp","ctcId":2386,"ctcDifficulty":"HARD","title":"Lone Hut","author":"Black_Doom","rules":"Normal sudoku rules apply. Each purple line contains a set of consecutive non-repeating digits. Each gold (nabner) line contains a set of non-repeating digits and no two digits anywhere on such a line can be consecutive. Digits separated by a V must sum to 5.","solution":"938475621145926837762831459574189362329567184816342795457698213693214578281753946","constraints":["XV","nabner-line","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"sacpbwcs19","ctcId":2387,"ctcDifficulty":"MEDIUM","title":"Critical Hit","author":"Black_Doom","rules":"Normal sudoku rules apply.\nHit Points: clues outside the grid give the sum of all cells that contain a digit equal to the distance of that cell from that clue in the row or column. For example, a 3 in Row 3, Column 2 would count towards the 15 clue in column 2, and any other number would not.\nGerman Whispers: adjacent digits on the green lines must differ by at least 5.","solution":"239814567748526319651937248572348196813659724964172853386295471127463985495781632","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Hit Points: clues outside the grid give the sum of all cells that contain a digit equal to the distance of that cell from that clue in the row or column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"olig7yj3gj","ctcId":2388,"ctcDifficulty":"VERY HARD","title":"Double Arrow Melt","author":"Black_Doom","rules":"Normal sudoku rules apply.\nDoublers: there are 18 doubler cells in the grid - 2 in each row, column and 3x3 box, and they must contain exactly 2 sets of digits 1-9. Those cells are considered to have double their value for the purposes of the arrow clues.\nArrow: values along an arrow sum to the value in the attached circle. Digits can repeat on arrows if allowed by other rules.\nSandwich Sums: clues outside the grid give the sum of digits between the two doublers in that row or column.","solution":"483972156769451823152863794291386475834527619576194382927648531348215967615739248","constraints":["arrow","custom","sandwich"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Arrow: values along an arrow sum to the value in the attached circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Doublers: there are 18 doubler cells in the grid - 2 in each row, column and 3x3 box, and they must contain exactly 2 sets of digits 1-9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"hb6eo13lg1","ctcId":2389,"ctcDifficulty":"HARD","title":"Take More U-Turns","author":"Black_Doom","rules":"Normal sudoku rules apply.\nEntropic Lines: each consecutive group of 3 cells on a peach line must contain one digit from each of the following sets: [1,2,3], [4,5,6], and [7,8,9].\nTen Lines: each thick grey line consists of one or more contiguous groups of cells, each of which sums to 10. These groups of cells cannot overlap. Digits may repeat within sums. \nAverage Arrows: digit in a circle must be equal to the average (arithmetic mean) of the digits along its arrow.\nKropki: Digits separated by a black dot must have a ratio of 1:2. Not all dots are given.","solution":"648592713193748526725316498237681954869254137514973862486125379371469285952837641","constraints":["custom","entropic-line","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Ten Lines: each thick grey line consists of one or more contiguous groups of cells, each of which sums to 10. Average Arrows: digit in a circle must be equal to the average (arithmetic mean) of the digits along its arrow.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c6"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"2yiw0yc01y","ctcId":2390,"ctcDifficulty":"MEDIUM","title":"Tenfold","author":"Black_Doom","rules":"Normal sudoku rules apply. Draw a one-cell-wide loop of orthogonally connected cells. The loop can't touch itself, not even diagonally. Additionally, the loop consists of non-overlapping segments, each of which sums to 10. Digits may repeat on the loop and even within an individual segment, if allowed by the other rules. The digit in a caged cell shows how many (of the up to 8) surrounding cells are on the loop. The caged cells cannot be on the loop. The number in the top-left corner of a caged cell shows the sum of digits in the loop cells around it.","solution":"643721589819534276257896143325418967476259831981367425592683714738145692164972358","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop of orthogonally connected cells. The loop can't touch itself, not even diagonally. Additionally, the loop consists of non-overlapping segments, each of which sums to 10. The digit in a caged cell shows how many (of the up to 8) surrounding cells are on the loop. The caged cells cannot be on the loop. The number in the top-left corner of a caged cell shows the sum of digits in the loop cells around it.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c6","c7","c8"]}]},{"id":"ka3olc7kq1","ctcId":2391,"ctcDifficulty":"HARD","title":"Rellik Loop","author":"blackjackfitz","rules":"Normal sudoku rules apply.\n\nKiller: Digits in the given killer cages must sum to the total in the top left hand corner.\n\nKropki: Digits separated by a black dot are in a 1 to 2 ratio. Digits separated by a white dot are consecutive.\n\nRellik Loop: Draw a single closed loop that moves orthogonally through the centers of cells, and does not branch, overlap, or touch itself (not even diagonally). All of the purple diamond 'relliks' are on the loop. The loop creates a set of rellik cages where every discreet set of orthogonally connected digits within a single box is considered a rellik cage. In a rellik cage, any combination of one or more digits CANNOT sum to the rellik cage value. A rellik cage value is equal to the number of cells in the rellik cage. If the loop passes through a box multiple times, each individual segment is its own rellik cage. e.g. A 6 cell rellik cage may not contain (1,2,3), (1,5), (2,4) or a 6.","rulesClarified":"Normal sudoku rules apply.\n\nKiller: the digits in each labelled killer cage add up to the number in its top left corner.\n\nKropki: a black dot between two cells means their digits are in a 1 to 2 ratio. A white dot between two cells means their digits are consecutive.\n\nRellik Loop: draw a single closed loop through the centres of cells. The loop moves orthogonally from cell to cell. It never branches, never overlaps itself, and never touches itself, not even diagonally. The loop is not drawn on the grid; you draw it. Every purple diamond ('rellik') lies on the loop.\n\nRellik cages: the loop divides into rellik cages. Each run of loop cells that lies inside one box is one rellik cage. If the loop enters the same box more than once, each separate run is its own rellik cage.\n\nRellik value: a rellik cage's value is the number of cells in it. No combination of one or more of its digits may add up to that value.\n\nExample: a 6-cell rellik cage may not contain 1, 2 and 3 together, nor 1 and 5, nor 2 and 4, nor a single 6.","solution":"785962314369714258412385697948631725276548931153297486831426579594873162627159843","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Rellik Loop: Draw a single closed loop that moves orthogonally through the centers of cells, and does not branch, overlap, or touch itself (not even diagonally). All of the purple diamond 'relliks' are on the loop. The loop creates a set of rellik cages where every discreet set of orthogonally connected digits within a single box is considered a rellik cage. In a rellik cage, any combination of one or more digits CANNOT sum to the rellik cage value. A rellik cage value is equal to the number of cells in the rellik cage. If the loop passes through a box multiple times, each individual segment is its own rellik cage. e.g. A 6 cell rellik cage may not contain (1,2,3), (1,5), (2,4) or a 6.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c7","c8","c9","c10"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"jdcz0c4rtb","ctcId":2392,"ctcDifficulty":"HARD","title":"Duplicates","author":"blackjackfitz","rules":"Place digits from 1-9 in every cell. For every row 'n' and column 'n' there are exactly 'n' unique digits present. The remaining cells are filled with duplicates. e.g. Row 3 could be filled (1,2,7,1,2,7,7,7,7).\nDigits in a cage do not repeat and sum to the number in the top left hand corner of the cage, if given.\nDigits separated by a white dot are consecutive.\nDigits separated by a blue diamond are duplicates (i.e. the same). Not all dots or diamonds are given.","rulesClarified":"Place a digit from 1 to 9 in every cell.\n\nRows are numbered 1 to 9 from the top, and columns 1 to 9 from the left. Row 1 and column 1 contain exactly 1 different digit. Row 2 and column 2 contain exactly 2 different digits. Continue this way: row 9 and column 9 contain exactly 9 different digits.\n\nThe remaining cells are filled with duplicates. For example, row 3 could read 1, 2, 7, 1, 2, 7, 7, 7, 7: three different digits.\n\nKiller cages are the outlined groups of cells. The digits in a cage do not repeat. A number in a cage's top-left corner is that cage's total, and the digits in that cage add up to it. A cage with no number has no total, so no sum applies to it.\n\nEach white dot sits on the edge between two neighbouring cells. The two digits either side of a white dot are consecutive: one is exactly one more than the other.\n\nEach blue diamond sits on the edge between two neighbouring cells. The two digits either side of a blue diamond are the same.\n\nNot every white dot or blue diamond is drawn. An edge with no dot or diamond gives no information: its two digits may or may not be consecutive or equal.","solution":"777777777778888878732323223772526556778719489732338435737819742778325691732518964","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For every row 'n' and column 'n' there are exactly 'n' unique digits present. Digits separated by a blue diamond are duplicates (i.e. the same).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"917ci3wr7m","ctcId":2393,"ctcDifficulty":"HARD","title":"Noughts and Crosses Somedoku","author":"blackjackfitz","rules":"Fill each cell with a digit from 1-9. For every row 'n' and column 'n' there are exactly 'n' unique digits. The remaining cells are filled with repeats. A digit in a circle indicates exactly how many circles contain that digit. Cells separated by an X sum to 10.","solution":"555555555556666666555582882555554643554284644556281919594863737594234178596873421","constraints":["XV","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle indicates exactly how many circles contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"T3ttPM3pH8","ctcId":2394,"ctcDifficulty":"MEDIUM","title":"Overlap","author":"blackjackfitz","rules":"Normal sudoku rules apply. Along a marked diagonal, digits cannot repeat. Cells along a purple line contain a non-repeating, consecutive set of digits. (These digits can appear in any order).","solution":"862493157973215468154687932647932581318756249295841376781324695539168724426579813","constraints":["diagonal","renban"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Cells along a purple line contain a non-repeating, consecutive set of digits.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"egn520dswg","ctcId":2395,"ctcDifficulty":"MEDIUM","title":"Out of Order","author":"blackjackfitz","rules":"Normal sudoku rules apply. Digits separated by a black dot are in a 1 to 2 ratio. Digits along a pink line form a consecutive set that MUST appear out of order. i.e. 4321 is not valid while 4312 is.","solution":"786315924195824736243769815864231579352978461971546382429183657637452198518697243","constraints":["kropki","renban"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"lkmxt8n8dz","ctcId":2396,"ctcDifficulty":"MEDIUM","title":"Killer Pool","author":null,"rules":"Normal sudoku rules apply. Within a cage, digits do not repeat and sum to the total given. A grey square contains an even number. A grey circle contains an odd number. The nine pool balls in the bottom half of the grid contain all nine digits.","solution":"436578912792631845158429763561783429273914586984265137325847691649152378817396254","constraints":["cage","custom","even","odd"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The nine pool balls in the bottom half of the grid contain all nine digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"97xewlvvf5","ctcId":2397,"ctcDifficulty":"HARD","title":"Putting Green","author":null,"rules":"Normal sudoku rules apply. A purple line contains a set of consecutive digits in any order. Adjacent digits on a green line differ by at least 5. Box borders divide a blue line into segments of the same sum. A white dot joins consecutive digits. The grey circle contains an odd digit. Digits shown in a circle appear in at least one of the surrounding cells.","solution":"793861542265943871814572963638154729157296384429387615571438296382619457946725138","constraints":["german-whispers","kropki","odd","quadruple","region-sum-line","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Box borders divide a blue line into segments of the same sum.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"n13kcw13ck","ctcId":2398,"ctcDifficulty":"MEDIUM","title":"Putting Green 2","author":null,"rules":"Normal sudoku rules apply. A purple line contains a set of consecutive digits in any order. Adjacent digits on a green line differ by at least 5. Adjacent digits on an orange line differ by at least 4. A white dot joins consecutive digits. Digits shown in a circle appear in at least one of the surrounding cells.","solution":"831695472694327851572814396167538249945271638283946715728459163319762584456183927","constraints":["dutch-whispers","german-whispers","kropki","quadruple","renban"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"gtGL8fQ66t","ctcId":2399,"ctcDifficulty":"MEDIUM","title":"Tee Time","author":"Brinel","rules":"Normal sudoku rules apply. Digits do not repeat in a cage, and sum to the number given.  Neighbouring digits along a green line have a difference of at least five. Box borders divide a blue line into segments with the same sum. A white dot joins consecutive digits.","solution":"351948267692713485748256193519384726483672951276591834935427618164839572827165349","constraints":["cage","german-whispers","kropki","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"u9azfq7eta","ctcId":2407,"ctcDifficulty":"MEDIUM","title":"7 Thermosnakes","author":"Nordy","rules":"Normal Sudoku rules apply. \n\nEach gray thermosquare is the start of a non-branching thermosnake that moves orthogonally through the grid. A thermosnake cannot touch itself orthogonally or diagonally, but it may touch any other thermosnake any number of times. Two different thermosnakes cannot enter the same cell. \n\nEach thermosnake is exactly 7 cells long, and the digits along a thermosnake increase from start to end.","solution":"283459761457162839169873245378914526594326187612587394725648913836791452941235678","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"ra3rf0qcnz","ctcId":2408,"ctcDifficulty":"MEDIUM","title":"Whispering Yin Yang","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nYin Yang: Shade some cells such that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2x2 area is fully shaded or fully unshaded.\n\nThe shaded cells act as a German Whispers line: if two orthogonally connected cells are both shaded, then the digits in those cells must have a difference of at least 5.\n\nA digit in a cell with an arrow counts the total number of shaded cells seen in the direction of the arrow (not counting the cell itself).","solution":"549381762623457198718692534396278451854163927172945386987524613461839275235716849","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The shaded cells act as a German Whispers line: if two orthogonally connected cells are both shaded, then the digits in those cells must have a difference of at least 5. A digit in a cell with an arrow counts the total number of shaded cells seen in the direction of the arrow (not counting the cell itself).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ykcj1iv01r","ctcId":2409,"ctcDifficulty":"HARD","title":"Perfectly Balanced","author":"IcyFruit","rules":"Normal sudoku rules apply. \nBox borders divide blue lines into sections with the same sum.\nAn arrow points to the smaller of its adjacent digits.","solution":"815932476694187235732465891963874512287651943541329687476518329158293764329746158","constraints":["inequality","region-sum-line"],"constraintFacts":[{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"zbpjp31ogi","ctcId":2410,"ctcDifficulty":"HARD","title":"Love Triangle","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along an orange line have a difference of at least four.\nAdjacent digits along a green line have a difference of at least five.\nAdjacent digits along a blue line have a difference of at least six.\nThe digits on the arrows sum to the digit in their corresponding circle.","solution":"234658791587931462916274358728593614163427985495816273672385149849162537351749826","constraints":["arrow","dutch-whispers","german-whispers"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"h2NFBB87fJ","ctcId":2423,"ctcDifficulty":"EASY","title":"For Clementine H","author":"Frans Wentholt","rules":"Normal sudoku rules apply. Along thermometers, digits must increase from the bulb end. Each purple region contains all of the digits 1-9.","solution":"145723689689145723273896514456287391927531846318469257764952138832614975591378462","constraints":["region","thermometer"],"constraintFacts":[{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"FL38N7nN23","ctcId":2424,"ctcDifficulty":"MEDIUM","title":"Black Sheep","author":"Leonhard Kohl-Lörting","rules":"Place the digits 1-5 twice in each row, column and box, except for one digit, which is the 'Black Sheep'. It is only placed once in every row, column and box.\n\nDigits in a cage sum to the clue given in the top left corner. Digits may repeat once in a cage.\n\nAdjacent digits on a grey 'Austrian Whisper' line must have a difference of at least 3.\n\nOn a blue 'Region Sum' line, digits have an equal sum within each box (region) it passes through. Different lines may have different region sums.","solution":"315252414412534125542411235524321541254214513131545224225153441451142352143425152","constraints":["cage","custom","dutch-whispers","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a cage sum to the clue given in the top left corner.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Place the digits 1-5 twice in each row, column and box, except for one digit, which is the 'Black Sheep'.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"modified","modifiers":[],"params":null,"note":"Adjacent digits on a grey 'Austrian Whisper' line must have a difference of at least 3.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"lqvpt4f0lv","ctcId":2425,"ctcDifficulty":"MEDIUM","title":"Rotational Disks","author":"Leonhard Kohl-Lörting","rules":"Normal Sudoku rules apply.\n\nA circle indicates the center of a disk, which is a 5x5 area.\nFor each cell inside the disk, if the disk is rotated by 180 degrees around its center, the contents of the new and old cell have to sum up to 10.\n\nKiller cages show their sums.","solution":"148267935263954718975318246517482693482693571639571482351746829726839154894125367","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For each cell inside the disk, if the disk is rotated by 180 degrees around its center, the contents of the new and old cell have to sum up to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"zvd9zuzz6p","ctcId":2426,"ctcDifficulty":"MEDIUM","title":"Saturn's Outermost Ring","author":"Leonhard Kohl-Lörting","rules":"Normal Sudoku rules apply. \n\nFor each highlighted cell, if the grid is rotated by 180 degrees around the center of the Sudoku, the contents of the new and old cell have to sum up to 10.\nE.g.: R2C1 and R8C9 have to sum up to 10.\n\nDigits in killer cages may not repeat and must sum to the number given in its corner (if given).","solution":"581263497649175382723984651198427536237596148465831279974652813852319764316748925","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For each highlighted cell, if the grid is rotated by 180 degrees around the center of the Sudoku, the contents of the new and old cell have to sum up to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"62jG8GMhp7","ctcId":2427,"ctcDifficulty":"MEDIUM","title":"Defrag","author":"mormagli","rules":"Normal sudoku rules apply. Each purple line contains a set of non-repeating consecutive digits.  (These digits can appear in any order). Cells separated by a black dot contain digits where one digit is double the value of the other.","solution":"214589673986137524753426981465893712198742356327651498872365149641978235539214867","constraints":["kropki","renban"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"P3DDj2thmF","ctcId":2428,"ctcDifficulty":"EASY","title":"165","author":"Leonhard Kohl-Lörting","rules":"Normal sudoku rules apply. Clues outside the grid are X-Sum clues and indicate the sum of the first X cells, where X is the value of the first cell in that column. The total sum of all X-Sum clues is 165. Digits in cages sum to their clue.","solution":"936147258825936147714825936693714825582693714471582693369471582258369471147258369","constraints":["cage","custom","x-sum"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The total sum of all X-Sum clues is 165.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"640zvjabj2","ctcId":2429,"ctcDifficulty":"HARD","title":"Pack of Aces","author":"Mormagli","rules":"Normal sudoku and renban rules apply;\n\nAces high: the digit 1 can count as either a 1 or a 10. For example, the digits 189 & 123 would make up a valid renban, but 129 would not;\n\nThe digits 1 and 9 may never be orthogonally adjacent.","solution":"963547182851329764724618953239851476475963218618274539182796345397485621546132897","constraints":["non-consecutive","renban"],"constraintFacts":[{"slug":"non-consecutive","type":"non-consecutive","variant":"modified","modifiers":[],"params":null,"note":"The digits 1 and 9 may never be orthogonally adjacent.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Normal sudoku and renban rules apply;","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c1"]}]},{"id":"bmh85ce33k","ctcId":2430,"ctcDifficulty":"MEDIUM","title":"Cornered Colors","author":"Leonhard Kohl-Lörting","rules":"Normal sudoku rules apply.\nShade some cells such that all shaded cells form an orthogonally connected area, all unshaded cells form an orthogonally connected area and no 2x2 area is entirely shaded or unshaded.\nDigits in cages may not repeat and sum to the given clue. In cages, shaded digits count as positive numbers, and unshaded digits count as negative numbers.","rulesClarified":"Normal sudoku rules apply.\n\nShade some cells so that all shaded cells form one orthogonally connected area, all unshaded cells form one orthogonally connected area, and no 2x2 block is entirely shaded or entirely unshaded.\n\nDigits in a cage cannot repeat.\n\nEach cage's clue is a signed total. A shaded digit counts as positive and an unshaded digit counts as negative, and the signed digits in the cage add up to the clue. A clue of 7 means the shaded digits minus the unshaded digits total 7. A negative clue, such as -7, means the unshaded digits exceed the shaded digits by 7.","solution":"867512349542639817139478625785346192394281576216957438428195763971863254653724981","constraints":["cage","custom","yin-yang"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in cages may not repeat and sum to the given clue.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In cages, shaded digits count as positive numbers, and unshaded digits count as negative numbers.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"8grq4908um","ctcId":2431,"ctcDifficulty":"MEDIUM","title":"Boundaries","author":"Playmaker6174","rules":"Normal Sudoku rules apply.\n\nWithin a cage, digits must sum to the small number written at the top left of that cage.\n\nDigits along an arrow sum to the digit in the circle cell attached to that arrow.\n\nBox borders divide the blue line into small segments with the same sum of digits along each segment.\n\nAlong a green line, two adjacent digits have the difference of at least 5.","solution":"357824169469715832821369745713492586286157394594683217635971428942538671178246953","constraints":["arrow","cage","german-whispers","region-sum-line"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"x9qn7ktsg1","ctcId":2432,"ctcDifficulty":"HARD","title":"Tic-Tac-Torque","author":"Skeptical Mario","rules":"Normal Sudoku rules apply. Place the digits 1 through 9 in each empty cell. Digits must not repeat within the same row, column, or box.\n\nAdjacent digits along each german whisper line must have a difference of at least 5. In this puzzle, each line sums to five times its length.\n\nAdjacent cells connected with an X must sum to 10. \n\nThe inequality symbol indicates which of the adjacent cells is greater.","solution":"813647952256193487794285361148569273625734819937821546471952638582316794369478125","constraints":["XV","custom","german-whispers","inequality"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In this puzzle, each line sums to five times its length.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"fmlum9pis1","ctcId":2433,"ctcDifficulty":"MEDIUM","title":"Killer's Circle","author":"Skeptical Mario","rules":"Normal sudoku rules apply; place the digits 1-9 in each cell without repeating in a row, column, or box.\nKiller cages - Digits in a cage cannot repeat and sum to the clue in the upper left corner.","solution":"952463178714258639638719254275396481391845762846127395183572946467981523529634817","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ceqp9e6ufs","ctcId":2434,"ctcDifficulty":"MEDIUM","title":"Off Killter","author":"Skeptical Mario","rules":"Normal sudoku rules - Place the digits from 1-9 in each cell without repeating in a row, column, or box.\n\nKiller cages - digits in a cage cannot repeat and must sum to the clue in the upper left corner of the cage.","solution":"479638215328915467651247983145876329297153846863492571586321794714589632932764158","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"misno24ves","ctcId":2437,"ctcDifficulty":"HARD","title":"Less Than Three","author":"AnalyticalNinja","rules":"Normal sudoku rules apply.\nCells separated by a white heart have a difference of <3.\nCells separated by a black heart have a ratio of <3. (The larger number divided by the smaller number yields a number of less than 3)","solution":"368479521254318769971256834596124378837965142412783695783592416649831257125647983","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells separated by a white heart have a difference of <3. Cells separated by a black heart have a ratio of <3.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"7Gr3rNnD2N","ctcId":2439,"ctcDifficulty":"MEDIUM","title":"862 Hz","author":"Kennet's Dad","rules":"Normal sudoku rules apply. Digits along a gray arrow must sum to the digit in that arrow's circle. Orange lines are palindromes in which the digits along the line must read the same both forward and backward. Digits in a cage sum to the number given. Digits joined by a white dot are consecutive.","solution":"326195478851764239947832615478356192215489367693271854532918746189647523764523981","constraints":["arrow","cage","kropki","palindrome"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"26e1w4r81e","ctcId":2440,"ctcDifficulty":"HARD","title":"The Devil is in the Details","author":"Gliperal","rules":"Normal sudoku rules apply. Cages indicate the sum of certain numbers within them in the top-left corner. Digits may not repeat within a cage. Arrows indicate the sum of certain numbers along their diagonal. Digits may repeat along a diagonal. The numbers involved in clues can be single-digit or straight multi-digit numbers (but each digit can only contribute to one such number). Vertical numbers are read top-to-bottom, and horizontal and diagonal numbers are read left-to-right.","solution":"431892675985671342267435891893516427572948163614327589756283914329164758148759236","constraints":["cage","little-killer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Cages indicate the sum of certain numbers within them in the top-left corner.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"qjB3NN6jH3","ctcId":2451,"ctcDifficulty":"MEDIUM","title":"2x Cages for the price of 1","author":"NurglesGift","rules":"Normal sudoku rules apply. Along the thermometer, digits must increase from the bulb.  Digits joined by a black dot have a 1:2 ratio. Digits joined by X must equal 10. Cage totals equal the highest digit in the cage x2, or in other words the rest of the digits must equal the highest digit of the cage.","solution":"865913427723648519419752638954327861136589274287461395672894153341275986598136742","constraints":["XV","custom","kropki","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cage totals equal the highest digit in the cage x2, or in other words the rest of the digits must equal the highest digit of the cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"w1oz8pek6a","ctcId":2453,"ctcDifficulty":"MEDIUM","title":"Stolen Numerals King XV","author":"NurglesGift","rules":"Normal sudoku rules apply.\nCells connected by an X must sum to 10.\nCells connected by an V must sum to 5.\nThe green dots are either X or V\nAll X's and V's are given.\nCells connected by a black dot must be in a 1:2 ratio.\nCells connected by a white dot must be consecutive.\nAny two cells separated by a king's move (in chess) cannot contain the same digit.","rulesClarified":"Normal sudoku rules apply.\n\nAny two cells a king's move apart (as in chess) cannot contain the same digit.\n\nEach green dot joins two cells. Each green dot is either an X or a V.\n\nCells joined by an X must sum to 10.\n\nCells joined by a V must sum to 5.\n\nAll X's and V's are given.\n\nCells connected by a black dot must be in a 1:2 ratio.\n\nCells connected by a white dot must be consecutive: one digit is exactly one more than the other.","solution":"943716285625498371871325694258649137197283456364157829712934568536871942489562713","constraints":["XV","antiking","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"Cells connected by an X must sum to 10. All X's and V's are given.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2","c5"]},{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6","c7"]}]},{"id":"aalg2syl3j","ctcId":2454,"ctcDifficulty":"MEDIUM","title":"Sudoku found tattooed on Lenin's body","author":"Øyvind Thorsby","rules":"Normal sudoku rules apply.\n\nDigits along a thermometer increase from the bulb end.\n\nA digit in a white circle indicates how many times that digit appears in white circles.\n\nIf the same digit appears in the same position in two boxes, that digit also appears in the same position in one more box.","solution":"864297513975138642321456987513964278642785139798321456289513764137642895456879321","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a white circle indicates how many times that digit appears in white circles. If the same digit appears in the same position in two boxes, that digit also appears in the same position in one more box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"n39davprm6","ctcId":2455,"ctcDifficulty":"MEDIUM","title":"Inverted Killer","author":"NurglesGift","rules":"Normal sudoku rules apply.\nCages sum to the total given in the cage corner.\nThe highest digit in each cage is inverted. (i.e. 9 counts as -9, 8 as -8 etc)\nDigits can not repeat within a cage.","solution":"243516879678249531951837246395172468786495312124683795539721684867954123412368957","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The highest digit in each cage is inverted. (i.e. 9 counts as -9, 8 as -8 etc)","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"mss23tnw9u","ctcId":2456,"ctcDifficulty":"VERY HARD","title":"Tetrafolium","author":"Myxo","rules":"Sudoku: Place the digits 1-9 exactly once in each row, column and box.\n\nKiller: Digits in cages must sum to the indicated total. In some cases, only the parity of that total is given.\n\nThermo: Digits along grey thermometers must form a strictly increasing sequence, starting from the bulb.\n\nGerman Whispers: Adjacent digits on a green line must differ by at least five.","solution":"738526491465319728921478653513267984284195376697843215356982147849731562172654839","constraints":["cage","german-whispers","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"bpM7GtF94D","ctcId":2480,"ctcDifficulty":"VERY HARD","title":"Confined Sandwich Chaos","author":"PrimeWeasel","rules":"Place the digits 1-9 in each row, column and region. Regions are orthogonally connected and have to be determined. These regions cannot cover any 2x2 section of the grid. A clue outside the grid shows the sum of the digits sandwiched between the 1 and the 9 for that row or column. All of a sandwich's cells (including both crusts) are in the same region. A digit in a circle shows the amount of cells touching it, orthogonally and diagonally, not including itself, which are part of the same region. All circles are given.","solution":"529413876462875391196387542631298754817534629375642918748951263984726135253169487","constraints":["custom","sandwich"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Regions are orthogonally connected and have to be determined. All of a sandwich's cells (including both crusts) are in the same region. A digit in a circle shows the amount of cells touching it, orthogonally and diagonally, not including itself, which are part of the same region.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c6"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"34PNbHhptN","ctcId":2482,"ctcDifficulty":"VERY HARD","title":"Litt Whisper Nightmares!","author":"Sayori","rules":"Normal sudoku rules apply. Adjacent digits on a grey line must NOT differ by 5 or more. Digits separated by a white dot must be consecutive, and digits separated by a black dot must have a ratio of 1:2. Digits in a cage may not repeat and must sum to the number indicated.","solution":"542869371139274685678315492285493167361782549794651823417938256923546718856127934","constraints":["cage","german-whispers","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Adjacent digits on a grey line must NOT differ by 5 or more.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"fpNR4n8FN8","ctcId":2483,"ctcDifficulty":"VERY HARD","title":"789","author":"Sayori","rules":"Normal sudoku rules apply. Digits cannot repeat in a cage, and cages show their sums. A number in a circle indicates the digit that must appear in at least one of the four surrounding cells. Digits cannot repeat along a marked diagonal.","solution":"254638197671942853983751462549163728817295346326874519492587631765319284138426975","constraints":["cage","diagonal","quadruple"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"FQQf6HQfm7","ctcId":2484,"ctcDifficulty":"MEDIUM","title":"Heisenberg","author":"randall","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nArrows: Digits along an arrow sum to the number in its bulb\n\nBuild-your-own X-Sums: Digits along an arrow are an X-sum *clue* - the following X digits (in the direction of the arrow) sum to the clue, where X is the first cell in that direction. 2-cell arrows are double-digit clues: The nearest digit to the arrow circle is the tens digit, followed by the units digit.\n\nThe inequality symbol (>) points to the smaller of the two digits surrounding the symbol.","solution":"932841756514673928768952314673485291481329567295716483147298635826534179359167842","constraints":["arrow","inequality","x-sum"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"x-sum","type":"x-sum","variant":"modified","modifiers":[],"params":null,"note":"Build-your-own X-Sums: Digits along an arrow are an X-sum *clue* - the following X digits (in the direction of the arrow) sum to the clue, where X is the first cell in that direction.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"NRqj3LMrLr","ctcId":2485,"ctcDifficulty":"HARD","title":"Tie Those Thermos!","author":"Sayori","rules":"Normal sudoku rules apply. Digits along a thermo must increase from the bulb end. A purple line contains a set of consecutive digits in some order.","solution":"345762819198435762672891543234576981867914235519328476486253197953147628721689354","constraints":["renban","thermometer"],"constraintFacts":[{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"HmmDgD66rH","ctcId":2486,"ctcDifficulty":"HARD","title":"Smoggy Knight","author":"PotatoHead21","rules":"Normal sudoku rules apply. The grid is covered with fog. Placing a correct digit will clear the fog from the surrounding cells. Cells separated by a knight's move (in chess) cannot contain the same digit. Cells separated by an X contain digits summing to 10. In cages digits must sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage. A cell with a grey circle must contain an odd digit. A cell with a grey square must contain an even digit.  Cells separated by a white dot contain consecutive digits. Cells separated by a black dot contain digits in an 1:2 ratio (ie one digit will be double the other). The ring of 16 cells on the outside of the central 3x3 box (ie touching it either orthogonally or diagonally) – sometimes called the “Phistomefel Ring” – contains digits summing to 109.","solution":"926154387781326459543789621634578912279613845158942763412897536867235194395461278","fogLight":"R9C10","constraints":["XV","antiknight","cage","custom","even","fog","kropki","odd"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The ring of 16 cells on the outside of the central 3x3 box (ie touching it either orthogonally or diagonally) – sometimes called the “Phistomefel Ring” – contains digits summing to 109.","evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10","c11"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"7gNQ4nBtpn","ctcId":2488,"ctcDifficulty":"HARD","title":"Quad van de Wetering","author":"PotatoHead21","rules":"Normal sudoku rules apply. Digits in circles must appear in one of the four cells surrounding that circle.","solution":"594236718136578492872194635451863279689721543723459861915642387367985124248317956","constraints":["quadruple"],"constraintFacts":[{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"54j9prbaax","ctcId":2491,"ctcDifficulty":"MEDIUM","title":"Sum of the Shade","author":"randall","rules":"Normal Sudoku rules apply. Place the digits 1-9 exactly once in every row, column, and 3x3 box.\nYin Yang. Shade some cells such that all shaded cells in the grid form a single orthogonally connected region and all unshaded cells also form a single orthogonally connected region. No 2x2 region may be fully shaded or unshaded.\nCircles: Numbers in circles are the sum of the digits within shaded cells that touch the circle. Only shaded cells count toward the total.","solution":"639542187572813946841967253164238579387195624925674318498351762253786491716429835","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Yin Yang. No 2x2 region may be fully shaded or unshaded. Circles: Numbers in circles are the sum of the digits within shaded cells that touch the circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5","c6"]}]},{"id":"dfjxdryzuo","ctcId":2493,"ctcDifficulty":"HARD","title":"Anti-Sums","author":"Sayori","rules":"Normal Sudoku Rules Apply.\n\nDigits in a cage must NOT sum to a total that satisfies the inequality in the top left corner of the cage. For example,  the cage in box 1 must not sum to a total that is greater than 7. Digits MAY repeat in cages if allowed by other rules. \n\nDigits on an arrow must NOT sum to the number in the attached circle.","solution":"148537962536928741972164385324816597689753124715492638257649813461385279893271456","constraints":["arrow","cage"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits on an arrow must NOT sum to the number in the attached circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a cage must NOT sum to a total that satisfies the inequality in the top left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"1xjpfvl0y4","ctcId":2495,"ctcDifficulty":"MEDIUM","title":"Gurthy Clones","author":"gdc","rules":"Normal sudoku rules apply.\n𝗛𝗮𝗹𝘃𝗲𝗿𝘀: Place 9 halvers (one per row/column/box) into the grid. Each digit must appear in a halver cell. The value of a halver is half its digit. \n𝗥𝗲𝗴𝗶𝗼𝗻 𝗦𝘂𝗺 𝗟𝗶𝗻𝗲𝘀: Box borders divide lines into segments with equal sums.\n𝗥𝗼𝘁𝗮𝘁𝗶𝗻𝗴 𝗖𝗹𝗼𝗻𝗲𝘀: Cages with identical labels must contain identical digits in the same relative positions to the label.","solution":"283976145197854236456312987832561794549783612761429358928147563614235879375698421","constraints":["clone","custom","region-sum-line"],"constraintFacts":[{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"𝗛𝗮𝗹𝘃𝗲𝗿𝘀: Place 9 halvers (one per row/column/box) into the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"z7oxi1ve8x","ctcId":2499,"ctcDifficulty":"MEDIUM","title":"Thermohaline Circulation","author":"Shintaro Fushida-Hardy","rules":"Standard Sudoku rules apply.\n\nLoop: shade some cells to form a 1-cell-wide orthogonally connected loop. The loop may not touch itself orthogonally, but can touch itself diagonally.\n\nNon-loop cells form several orthogonally connected groups. Such a group of size N contains exactly the digits from 1 to N.\n\nThermo-sightline arrows: Each cell with an arrow (called an 'arrow cell') lies on the loop. The digit in an arrow cell is the number of visible loop cells in the indicated direction, where non-loop cells obstruct vision. (The arrow cell is not included in this count). Additionally, digits increase along loop cells seen by an arrow, starting with the digit in the arrow cell.","rulesClarified":"Standard Sudoku rules apply.\n\nLoop: shade some cells to form one loop that is 1 cell wide and connected orthogonally. The loop may not touch itself orthogonally, but it may touch itself diagonally.\n\nThe cells not on the loop form several groups, each connected orthogonally. A group of N cells contains exactly the digits 1 to N, each once.\n\nEach arrow cell lies on the loop. The digit in an arrow cell is the number of loop cells the arrow sees in the direction it points. The arrow cell itself is not counted. Sight starts at the arrow cell and stops at the first non-loop cell, so non-loop cells block the view.\n\nAlong the loop cells that an arrow sees, the digits increase, starting from the digit in the arrow cell and moving away from it.","solution":"312746598568932174794518623187263459659874231423195786976351842831427965245689317","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Loop: shade some cells to form a 1-cell-wide orthogonally connected loop. Such a group of size N contains exactly the digits from 1 to N. The digit in an arrow cell is the number of visible loop cells in the indicated direction, where non-loop cells obstruct vision. Additionally, digits increase along loop cells seen by an arrow, starting with the digit in the arrow cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c7","c9"]}]},{"id":"P7j2jrgNNJ","ctcId":2505,"ctcDifficulty":"MEDIUM","title":"[\\]","author":"Sotek","rules":"Normal sudoku rules apply. Digits on the marked diagonal do not repeat. Adjacent digits along a green line have a difference of at least 5.","solution":"529176843784235916163849725658423197317598264942761538271384659836952471495617382","constraints":["diagonal","german-whispers"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9wm6ctm2hv","ctcId":2512,"ctcDifficulty":"EASY","title":"My Favorite Song","author":"theasylm","rules":"Normal sudoku rules apply. Normal thermometer rules apply. Normal Japanese sums rules apply. Colors used in this grid are Purple, Blue, broWn, Green, golD, Red, Orange, grAy, and blacK. For best results, remove all unshaded markings you have done once complete, then read the song title hidden vertically in the grid.\n\nThermometer rules: digits must strictly increase from the bulb end.\n\nJapanese Sums rules: the squares outside the grid indicate the order of the runs of contiguous cells that must be shaded the color of the clue. The number in the square indicates the sum of the cells in the run. There must be at least one unshaded cell between runs of the same color, but that is not required for runs of different colors. All shaded runs are given.","solution":"542691783816573249937824615261749358475318926398256471789132564654987132123465897","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Normal Japanese sums rules apply.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"unwvl51pjs","ctcId":2513,"ctcDifficulty":"HARD","title":"No Petting!","author":"theasylm","rules":"Normal sudoku rules apply. Colors used in this puzzle are green (g), brown (b), and black (k). A clue outside the grid with an arrow (little killer) shows the sum of the cells on the indicated diagonal. Digits separated by a black (kropki) dot have a 1:2 ratio. Clues in colored squares outside the grid (none of which lie) indicate the sum of all cells in that row or column that are shaded the color of the clue. Shading does not need to be contiguous. If a cell is shaded, and if a cell has a clue in the lower right corner, the clue gives the digit in the cell. If a clue is unshaded, then the number in the lower right corner is a lie, so the digit in the cell is not the clue. Some clues are lying, while others tell the truth. All truthful clues are fully-shaded; lying clues must not be fully-shaded. Note that there are an equal number of truth-tellers and liars for both the little killers and the Kropki dots.","solution":"461758932398162475752349681617593824983426157524871369145687293276934518839215746","constraints":["custom","kropki","little-killer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Clues in colored squares outside the grid (none of which lie) indicate the sum of all cells in that row or column that are shaded the color of the clue. If a cell is shaded, and if a cell has a clue in the lower right corner, the clue gives the digit in the cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c7"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Digits separated by a black (kropki) dot have a 1:2 ratio.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"3GNbdGpbLH","ctcId":2529,"ctcDifficulty":"MEDIUM","title":"Arrow Cartwheel","author":"Wypman","rules":"Normal sudoku rules apply. Digits on an arrow sum to the number in the attached circle, and all digits on circles (including arrow circles!) must be odd, and all digits on squares must be even.","solution":"487163259563279418129548637375916824891452376246837591918625743632794185754381962","constraints":["arrow","even","odd"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hb3fq3jqP2","ctcId":2530,"ctcDifficulty":"MEDIUM","title":"XV ballpit","author":"Wypman","rules":"Normal sudoku rules apply. In cages, digits do not repeat and sum to the number shown. \nThere are 5 types of balls in the grid:  \nA -> 1 set of digits around it must sum to 10  \nB -> 2 sets of digits around it must sum to 10  \nC -> 1 set of digits around it must sum to 5 \nD -> 2 sets of digits around it must sum to 5  \nE -> 1 set of digits must sum to 5, 1 set of 2 digits must sum to 10  \nA ‘set of digits’ always contains 2 orthogonally connected digits. No digit is part of 2 sets on the same circle, but it may be part of sets on different circles. There are no negative constraints, so other pairs may add to 5 or 10 around circles or elsewhere.","solution":"965724183712398546348651972129587364834962751576413829657239418491876235283145697","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There are 5 types of balls in the grid:","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"q4ysz7id1i","ctcId":2531,"ctcDifficulty":"EASY","title":"carved out","author":"Wypman","rules":"normal sudoku rules apply, the pumpkin (orange line) is an entropic line that alternates low (1,2,3) middle (4,5,6) and high (7,8,9) digits, the stem (green line) is a german whisper, where digits have a difference of at least 5, the face consists of thermometers, on which the digits increase from the bulb end, digits separated by an X sum to 10 and digits separated by an V sum to 5, not every X or V is given","solution":"683572941942618735751493628475321896369845217218967354196734582534286179827159463","constraints":["XV","entropic-line","german-whispers","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"njt50oqooj","ctcId":2533,"ctcDifficulty":"EASY","title":"Playful Fog","author":"Wypman","rules":"Normal sudoku rules apply. Fog appears in the grid. Placing correct digits clears fog from surrounding cells. Digits on an arrow sum to the number in the attached circle. On a red line, each set of three digits includes one low (1,2,3), one middle (4,5,6) and one high (7,8,9). The entropic lines move horizontally and vertically, and do not overlap with each other.","rulesClarified":"Normal sudoku rules apply.\n\nFog appears in the grid.\n\nPlacing correct digits clears fog from surrounding cells.\n\nDigits on an arrow sum to the number in the circle at the start of that arrow.\n\nThe red lines are entropic lines. On a red line, each set of three digits includes one low (1, 2, 3), one middle (4, 5, 6) and one high (7, 8, 9).\n\nEntropic lines move horizontally and vertically, and do not overlap with each other.","solution":"964325781813697254725841936596713842278456193341289675439168527652974318187532469","fogLight":"R1C4,R1C5,R1C6,R2C5,R4C9,R5C8,R5C9,R6C9,R8C5,R9C4,R9C5,R9C6,R4C1,R5C1,R5C2,R6C1,R9C9,R1C1,R1C9,R9C1","constraints":["arrow","entropic-line","fog"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"FF7LtbJ3Hn","ctcId":2537,"ctcDifficulty":"HARD","title":"The Ultimate Prime Cages","author":"Xenonetix","rules":"Normal Sudoku rules apply. The digits in each cage sum to a prime number but no two cages sum to the same prime. Digits in a cage MAY repeat. For convenience, the prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.","solution":"726345189418962375593178462251689734874513296369724851147856923632497518985231647","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digits in each cage sum to a prime number but no two cages sum to the same prime.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"z7eug3yrqd","ctcId":2538,"ctcDifficulty":"HARD","title":"Cradle","author":"Xenonetix","rules":"- Normal Sudoku rules apply.\n\n- Zipper Lines: Digits an equal distance from the centre of the purple line must sum to the digit in the centre of that purple line.\n\n- Consecutive Sums: A clue outside the grid indicates the total of any digits in its row or column that neighbour at least one consecutive digit within that row or column. For example, if a column, reading downwards, contains the digits 128396547, the clue at the top of the column would be 18; the sum of 1, 2, 4, 5, and 6, which are the only digits which neighbour a consecutive digit within that sequence.\n\n- Cells across the black Kropki dot contain one digit double the other (1:2 ratio).","solution":"947182365568743129213659784894375612132964578756821493475218936689537241321496857","constraints":["custom","kropki","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Consecutive Sums: A clue outside the grid indicates the total of any digits in its row or column that neighbour at least one consecutive digit within that row or column. For example, if a column, reading downwards, contains the digits 128396547, the clue at the top of the column would be 18; the sum of 1, 2, 4, 5, and 6, which are the only digits which neighbour a consecutive digit within that sequence.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7b12b8k1tf","ctcId":2539,"ctcDifficulty":"MEDIUM","title":"I'll halve what's she's halving","author":"ChinStrap","rules":"Normal sudoku rules apply. Place 9 ‘halvers’ (one in each row, column and 3x3box) into the grid. Each digit must appear in a halver cell. The value of a halver is half its digit. The 3x3 box borders divide each blue line into segments and the sum of the values on each segment must be the same. (Different lines may have different segment sums). The shaded dominoes are clones: ie they contain the same digits in the same positions. Eg if r2c3 is a 1 then r5c7 is a 1 and r9c4 is a 1.","solution":"395481267287653491146279583859327614423168759761945328572894136914536872638712945","constraints":["clone","custom","region-sum-line"],"constraintFacts":[{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Place 9 ‘halvers’ (one in each row, column and 3x3box) into the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"The 3x3 box borders divide each blue line into segments and the sum of the values on each segment must be the same.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"7f9px0exki","ctcId":2545,"ctcDifficulty":"HARD","title":"Shield Birds","author":"99%Sneaky","rules":"Normal sudoku rules apply.\nA digit in a cell with arrows facing outward must be greater than all of its orthogonal neighbors.\nDigits along arrows sum to the digit in the attached circle.\nDigits in cells separated by a white dot are consecutive.\nDigits in cells separated by a black dot are in a 1:2 ratio.","solution":"962351487475826139813479625297564813631287594548913276724195368159638742386742951","constraints":["arrow","kropki","maximum"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"maximum","type":"maximum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"rd2kn6vy6d","ctcId":2547,"ctcDifficulty":"MEDIUM","title":"Regional Heatwave","author":"ThePedallingPianist","rules":"Normal sudoku rules apply. Some of the grid is covered in fog; entering a correct digit will clear all fog in that digits immediate neighbourhood. Guessing is not required. The 3x3 box borders divide lines into segments, whose sums must strictly increase from one end to the other. No line has more than one segment in any single 3x3 box; different lines are different colours; lines may not branch or share cells with other lines; and lines may cross diagonally but only at cell vertices.","solution":"875342169319675824462819357287934516631527498954186732123468975546793281798251643","fogLight":"R1C6,R3C6,R6C3,R6C1","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The 3x3 box borders divide lines into segments, whose sums must strictly increase from one end to the other.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"wf01kkrga1","ctcId":2548,"ctcDifficulty":"MEDIUM","title":"Thermonuclear Reaction","author":"Eric Rathbun","rules":"Normal sudoku rules apply. Digits cannot repeat within a cage. Digits along a thermometer increase from the bulb end. Cells separated by a black dot contain digits with a 1:2 ratio ie one digit will be double the other. Not all dots are given.","solution":"537284196186973524924651387715328649849165273362497851453819762671542938298736415","constraints":["cage","kropki","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"ad7u8gmzsg","ctcId":2549,"ctcDifficulty":"MEDIUM","title":"Deviant Arrow","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Cells separated by a single knight's move (in chess) cannot contain the same digit. Digits along an arrow sum to the digit in that arrow's circle.","solution":"431825796725961438869734152614378529352496871978152643287513964546289317193647285","constraints":["antiknight","arrow"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"pw9xd2w523","ctcId":2550,"ctcDifficulty":"HARD","title":"Fifth Wheel","author":"IcyFruit","rules":"Normal sudoku rules apply.\nAlong a line, each set of 3 adjacent digits sums to a multiple of 5.","solution":"983574162241986375765132984594218637136759428872643519617895243458321796329467851","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Along a line, each set of 3 adjacent digits sums to a multiple of 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"n8uzh6og6f","ctcId":2552,"ctcDifficulty":"MEDIUM","title":"Fillomino Knights","author":"Die Hard","rules":"Normal fillomino rules apply ie Divide the grid into regions of orthogonally-connected cells. Fill each cell with a number equal to its region’s size (ie the number of cells in its region).  No two regions of the same size can share an edge (although they may touch diagonally). Use only region sizes of 1 to 9 and the digit N cannot appear in row N or column N. Two digits separated by a black dot must be in a 1:2 ratio (ie one digit should be double the other). Cells separated by a single knight's move (in chess) cannot contain the same digit.","solution":"332242233315144513255545551215133522441243144445241544255545553235243523331233123","constraints":["antiknight","custom","kropki"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Normal fillomino rules apply ie Divide the grid into regions of orthogonally-connected cells. Use only region sizes of 1 to 9 and the digit N cannot appear in row N or column N. Two digits separated by a black dot must be in a 1:2 ratio (ie one digit should be double the other).","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"umo2rblj9k","ctcId":2553,"ctcDifficulty":"EASY","title":"Heavy Fog","author":"James Kopp","rules":"The grid is covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area.\nDigits along a purple line are a set of consecutive digits in any order with no repeats.\nDigits on an arrow sum to the digit in the circle of that arrow.\nAdditionally, adjacent digits on the purple lines and the arrows (including the circles) are different and not consecutive.","solution":"398725641571649238624318795869573124437291586215864379153487962786952413942136857","fogLight":"R4C6,R5C6,R6C6","constraints":["arrow","custom","fog","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Additionally, adjacent digits on the purple lines and the arrows (including the circles) are different and not consecutive.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"11dz689p6l","ctcId":2554,"ctcDifficulty":"MEDIUM","title":"Parity Tic Tac Toe","author":"Marty Sears","rules":"Normal sudoku rules apply. Entering correct digits may clear fog somewhere in the grid - no guessing is necessary.\n\nDigits separated by a white dot are consecutive. \nDigits separated by a black dot are in a 1:2 ratio.\n\nOVERALL GAME:\nTodd and Steven are playing a game of Tic-Tac-Toe in a sudoku grid, where they attempt to 'claim' each 3x3 box. It's a very close game, with one player claiming four boxes and the other claiming five. However, the winner isn't necessarily the player to claim most boxes. To win the overall game, a player must claim at least one straight line of three 3x3 boxes (horizontally, vertically or diagonally), without their opponent managing to get a line of three boxes themselves.\n\nCLAIMING A BOX:\nTo determine who claims each 3x3 box, Todd and Steven play a mini game in each box. Todd places odd digits and Steven places even digits. A player claims a 3x3 box by getting at least one straight line of three digits of their parity (horizontally, vertically or diagonally) in that box, and without their opponent managing to get a line of three digits themselves. \n\nEvery 3x3 box has a definitive winner, and there is also a definitive winner of the overall multi-box game. But who is it?!","solution":"138679425947852316652143987281597634763421598594386271376214859829765143415938762","fogLight":"R4C4,R5C4,R6C4,R6C5,R6C6,R5C6,R4C6,R4C5,R5C5","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"To determine who claims each 3x3 box, Todd and Steven play a mini game in each box. Todd and Steven are playing a game of Tic-Tac-Toe in a sudoku grid, where they attempt to 'claim' each 3x3 box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c11"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"y5u0ncu31x","ctcId":2556,"ctcDifficulty":"HARD","title":"The Mysterious Loop","author":"Die Hard","rules":"Normal sudoku rules apply. Draw a closed loop that moves orthogonally or diagonally between the centers of no more than 23 cells. The loop passes through all boxes except box 5 (the shaded box). The digit 1 appears on the loop once, the digit in the circle appears on the loop twice, and every other digit N that appears anywhere on the loop appears on the loop N times. Adjacent digits on the loop are different and box borders divide the loop into regions of equal sums.","solution":"268573491345219786179684253496135827582746319731892645853461972617928534924357168","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a closed loop that moves orthogonally or diagonally between the centers of no more than 23 cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"wlt063c4m7","ctcId":2557,"ctcDifficulty":"MEDIUM","title":"illuminati","author":"Sumanta (ANU)","rules":"Normal Sudoku rules apply.\n\nilluminati cell: Green cells are illuminati cells. A digit on a illuminati cell cannot repeat along the 4 orthogonal and 4 diagonal directions from the given cell.\n\nMagic square: Green cells also form a magic square (extended).\n\nKropki dots: White dots connect consecutive digits. Black dots connect dots with 1:2 ratio. Not all possible dots are given.\n\nRenban: Purple lines contain consecutive digits in any order. for example, 465 is fine on a three-cell line.\n\nKiller cage: Digits in a cage sum to the total given in the corner of the respective cages.","solution":"847635129362917485951428763513246978478159632296783514139874256625391847784562391","constraints":["cage","custom","kropki","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit on a illuminati cell cannot repeat along the 4 orthogonal and 4 diagonal directions from the given cell. Magic square: Green cells also form a magic square (extended).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"zm4m78m9xh","ctcId":2559,"ctcDifficulty":"MEDIUM","title":"Foggy Segmented Yin Yang Snake","author":"apetersen","rules":"Normal Sudoku rules apply.\nThe grid is partially covered in fog. Correctly placed digits will remove fog from surrounding cells.\nDraw a one-cell wide snake of orthogonally connected cells that does not branch or touch itself.\nThe non-snake cells must form a single, orthogonally connected area.\nNo 2x2 region can be entirely snake or entirely non-snake.\nDigits separated by a white dot are consecutive.\nCells separated by dots will contain one snake cell and one non-snake cell.\nBox borders divide the snake into segments, each of which have the same sum.","rulesClarified":"Normal Sudoku rules apply.\n\nThe grid is partly covered in fog. A correctly placed digit removes the fog from the cells around it.\n\nSnake: draw one snake through the grid. It is one cell wide, its cells are orthogonally connected, it does not branch, and it does not touch itself.\n\nThe cells that are not part of the snake form a single area, and they are all orthogonally connected to each other.\n\nNo 2x2 block may be entirely snake, and no 2x2 block may be entirely non-snake.\n\nBox borders cut the snake into segments. A segment is a run of snake cells with no box border between them. Every segment has the same digit sum.\n\nDigits separated by a white dot are consecutive.\n\nTwo cells separated by a dot contain exactly one snake cell and one non-snake cell.","solution":"785293641632471598194685723519834267347962185826517439451328976263759814978146352","fogLight":"R1C1,R4C4,R7C2,R9C2,R7C7","constraints":["custom","fog","kropki","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell wide snake of orthogonally connected cells that does not branch or touch itself. Cells separated by dots will contain one snake cell and one non-snake cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c8"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"n6xrjvt168","ctcId":2560,"ctcDifficulty":"HARD","title":"Nucular Power","author":"Blashyrkh","rules":"Normal sudoku rules apply.\n\nDigits along an arrow sum to the number in the attached circle.","solution":"524817369163492875978365124837946512416523798295178436382651947659734281741289653","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"s7e0q68rum","ctcId":2561,"ctcDifficulty":"HARD","title":"Sandwich Additives","author":"DiMono","rules":"Standard sudoku: Place the digits 1-9 once each into every row, column, and box.\n\nThere are clues outside the grid. Each side either contains all Sandwich clues, or all X-Sum clues. Which side contains which type of clue is to be determined by the solver.\n\nSandwich: Clues outside the grid give the total of the digits placed between 1 and 9 in the row or column.\n\nX-Sum: Clues outside the grid give the sum of the first X cells that are seen in the row or column from the clue, where X is the first seen cell (i.e. a clue of 8 could be satisfied by 26 or 314 or 341).","solution":"315749268296583174847216935978431526163825749452967381734158692529674813681392457","constraints":["sandwich","x-sum"],"constraintFacts":[{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"hk23d16b6f","ctcId":2562,"ctcDifficulty":"HARD","title":"Equal Split Lines","author":"gdc & sujoyku","rules":"Normal sudoku rules apply.\nDots divide lines into segments with equal sums. Digits may not repeat within a segment. E.g: 8-35-125.","solution":"684275913739481526521693748196824357278539164453716892817942635345168279962357481","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Dots divide lines into segments with equal sums. Digits may not repeat within a segment.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"kccvhsp1ff","ctcId":2563,"ctcDifficulty":"MEDIUM","title":"Kid Leader","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nAdjacent digits along a green line must differ by at least 5.\n\nEach pink line (or branching line) contains a set of consecutive, non-repeating digits, which can appear in any order.\n\nDigits on a gray line must sum to 10.\n\nLines may share endpoints, but otherwise don't overlap.","solution":"827645193345197862916832754594376281768921345132584679289753416471269538653418927","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits on a gray line must sum to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"mfvog22gzk","ctcId":2564,"ctcDifficulty":"HARD","title":"Exhausting","author":"BremSter & Sotek","rules":"- Normal Sudoku rules apply.\n- Digits can not repeat along the main diagonals.\n- Some of the grid is covered with fog. Placing correct digits into cells clears the fog from all adjacent cells.\n- Digits in cages must sum to the number in the top left corner of the cage. Digits may not repeat within cages.","solution":"318795642276834591954261738843956127592417386761328459635189274187542963429673815","fogLight":"R1C1,R1C2,R2C1,R1C8,R1C9,R2C9,R8C1,R9C1,R9C2,R8C9,R9C8,R9C9","constraints":["cage","diagonal","fog"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"h1zrlsc75s","ctcId":2565,"ctcDifficulty":"MEDIUM","title":"Please Ignore","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nOne digit from 1-9 (to be determined) is 'inactive' and always gets ignored by any line it appears on.\n\nREGION SUM: Box borders divide blue lines into segments which each have the same sum (not counting any inactive digits.) The region sum may be different for different blue lines.\n\nRENBAN: All active digits on a pink line must form a non-repeating consecutive set.\n\nNABNER: Any two active digits anywhere on a yellow line may not be consecutive or the same.","solution":"217439568489562731563817942145376289832954617796128453978641325651293874324785196","constraints":["custom","nabner-line","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"One digit from 1-9 (to be determined) is 'inactive' and always gets ignored by any line it appears on.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"dndxixp4qb","ctcId":2566,"ctcDifficulty":"HARD","title":"Decapitated","author":"Black_Doom","rules":"Chaos Construction: Divide the grid into regions, each consisting of nine orthogonally connected cells. Each row, column and region contains the digits 1-9 once each.\nArrow: digits along an arrow must sum to the number in the attached circle. Additionally, each arrow must be contained within one region, and the circle cannot belong to the same region as its arrow. The number in the circle shows how many region cells it sees in its row and column (including the cell with the circle itself) until it reaches the borders of the region.","rulesClarified":"Chaos construction: divide the grid into regions, each made of nine orthogonally connected cells. The regions are not drawn; you find them. Each row, each column and each region contains the digits 1 to 9 once each.\n\nArrows: each drawn arrow runs from its circle along its path. The digits on the arrow's shaft, the cells after the circle, add up to the number in the circle. The circle's own cell is not part of that sum.\n\nEach arrow lies entirely within one region. The circle of an arrow is in a different region from that arrow.\n\nEach circle's number counts region cells: starting from the circle, count the cells of the circle's own region along its row and along its column, counting the circle's own cell and stopping at the border of the region.","solution":"169425837237859641973614528641387259415762983528936174852173496784291365396548712","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Additionally, each arrow must be contained within one region, and the circle cannot belong to the same region as its arrow. The number in the circle shows how many region cells it sees in its row and column (including the cell with the circle itself) until it reaches the borders of the region.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]}]},{"id":"s8eq4xfzrq","ctcId":2567,"ctcDifficulty":"VERY HARD","title":"Old Maid","author":null,"rules":"Normal Sudoku rules apply.\nPlace doubler-cells into the grid so that there is exactly one doubler-cell in each row, column and box. Each doubler-cell must contain a different digit and the value of a doubler-cell is twice the value of the contained digit.\nOn both marked diagonals there are no repeated VALUES. \nVALUES along a purple line form a non-repeating consecutive set, in any order.\nBox borders divide each blue line into segments with the same sum (VALUES).","solution":"231564879794283516865719234579632148416875392382941657128397465953426781647158923","constraints":["custom","diagonal","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Place doubler-cells into the grid so that there is exactly one doubler-cell in each row, column and box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"modified","modifiers":[],"params":null,"note":"On both marked diagonals there are no repeated VALUES.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Box borders divide each blue line into segments with the same sum (VALUES).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"VALUES along a purple line form a non-repeating consecutive set, in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"dwz5f8ntmd","ctcId":2568,"ctcDifficulty":"MEDIUM","title":"Phantom Locker","author":"Sumanta (Anu)","rules":"Normal sudoku rules apply. Digits do not repeat in the marked cage. Neighbouring digits along a green line differ by at least 5 or more. Along a thermometer, digits increase from the bulb end. The grey (non-thermometer) lines are palindromes ie digits read the same forwards and backwards.","solution":"691428357783965421254371869537682914149537286826194735375846192912753648468219573","constraints":["german-whispers","palindrome","region","thermometer"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"e0ry5e3pzy","ctcId":2569,"ctcDifficulty":"MEDIUM","title":"Cube Roots of Pi","author":"Blobz","rules":"Normal sudoku rules apply.\n\nBox borders divide blue lines into segments with the same sum.\n\nAlong pink lines, digits form a non-repeating consecutive sequence in any order.\n\nEach cage's sum is a perfect cube.","solution":"389142756451786932726539184937451628865273491142968573673894215298615347514327869","constraints":["cage","region-sum-line","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"xmluoxvukw","ctcId":2571,"ctcDifficulty":"MEDIUM","title":"Gears","author":"ThePedallingPianist","rules":"Normal sudoku rules apply. Digits in a cage do not repeat and sum to the given total.","solution":"489235716167498532253176498648523971712849653935761284324917865871652349596384127","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"x75we00sgg","ctcId":2572,"ctcDifficulty":"MEDIUM","title":"Hitlines","author":"Marty Sears & Ratfinkz","rules":"Normal sudoku rules apply.\n\nEntering correct digits may clear fog somewhere in the grid. No guessing is necessary.\n\nDigits along a beige 'hitline' do not repeat. The number on a blue circle (or two-digit pill reading downwards or from left to right) points to the first cell ('position 1') along a hitline, and indicates the total of any digits that equal their position number along that hitline.\n\nEg: on a 4-cell hitline, if the sequence of digits reads 1694 starting from the cell being pointed at, then the blue total would be 5 (the sum of 1 and 4) because 1 is in the 1st position and 4 is in the 4th position, and these are the only digits which match their position numbers.","solution":"129734586834596721567218493358671942712943865946852137481325679275469318693187254","fogLight":"R1C1,R1C2,R1C3,R1C4,R1C5,R1C6,R1C7","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits along a beige 'hitline' do not repeat. The number on a blue circle (or two-digit pill reading downwards or from left to right) points to the first cell ('position 1') along a hitline, and indicates the total of any digits that equal their position number along that hitline.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"d3ogeeiymu","ctcId":2573,"ctcDifficulty":"MEDIUM","title":"Filaments","author":"Skunkworks","rules":"Normal sudoku rules apply.\nRegion Sum line: Digits on a line sum to the same total for each box the line enters. Different lines may have different totals.\nEntropic lines: Any set of three sequential cells along an entropic line must contain a low digit (1,2,3), a middle digit (4,5,6), and a high digit (7,8,9). Digits may repeat on a line, if allowed by other rules.\nAll lines in this puzzle conform to both rulesets.\nA Skunkworks collaboration by Riffclown & Heliopolix","solution":"546978312138462957792513864675284139481639275923751648357826491269147583814395726","constraints":["entropic-line","region-sum-line"],"constraintFacts":[{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"iugptjcutc","ctcId":2574,"ctcDifficulty":"MEDIUM","title":"Fishtomefel","author":"Skeptical Mario","rules":"Normal sudoku rules apply. Along the teal line, any set of three adjacent digits must contain one digit from (147), one digit from (258) and one digit from (369). Digits in a cage sum to the small clue in the top left corner. In two cells separated by a black dot one digit must be double the other. Digits separated by a white dot differ by 1.","solution":"258637149149528673376149582635812497824975361917463258583296714462781935791354826","constraints":["cage","kropki","modular-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"1xf09aa30a","ctcId":2575,"ctcDifficulty":"HARD","title":"Lizard babies grow so fast...","author":"olima","rules":"Normal Sudoku rules apply. Adjacent digits on a green line differ by at least 5. Digits on a purple line are distinct and consecutive, but may be in any order. Box borders divide blue lines into segments with equal sums. Black dots indicate digits in a 1:2 ratio. Not all dots are necessarily shown.","solution":"263179458875234916194586372946813527351427689782965134539742861628391745417658293","constraints":["german-whispers","kropki","region-sum-line","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"bfw89rdo1o","ctcId":2576,"ctcDifficulty":"MEDIUM","title":"Medulla","author":"Math Pesto","rules":"Normal sudoku rules apply. The 3x3 box borders divide a blue line into segments; each segment along a line must have the same sum. (Different lines may have different segment sums.)","solution":"693178524752394861418256793981642375376815942524739618135467289269581437847923156","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"2a8ncwsjcb","ctcId":2577,"ctcDifficulty":"HARD","title":"The Phantom Locker","author":"Sumanta (Anu)","rules":"Normal sudoku rules apply. Cells separated by a single chess knight's move cannot contain the same digit. The grey line is a Palindrome ie its digits read the same in both forward and backward directions. Digits in a cage must not repeat and must sum to the small clue in the top left corner of the cage.","solution":"159247368683159742247368951975624813831975426462831579798512634314796285526483197","constraints":["antiknight","cage","palindrome"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"o0n73yxg22","ctcId":2578,"ctcDifficulty":"MEDIUM","title":"Parity Fish","author":"Marty Sears","rules":"Normal sudoku rules apply; fill the grid with the digits 1-9 so that digits don't repeat in any row, column, and marked 3x3 box.\nTwo cells adjacent along a red line must contain one even digit and one odd digit.\nTwo cells connected by a white dot contain consecutive digits.\nTwo cells connected by a black dot contain digits where one is double the other.","solution":"854369172976251834123478956419582367568937421237146598785694213691823745342715689","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Two cells adjacent along a red line must contain one even digit and one odd digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"3jqijal91m","ctcId":2579,"ctcDifficulty":"MEDIUM","title":"Kyoto","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nDigits in a cage sum to the small number in the top left corner of the cage.","solution":"249356187713298465865741932487639251326415879591872346158964723974523618632187594","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"rmac5anfcn","ctcId":2581,"ctcDifficulty":"MEDIUM","title":"How Shall We Split This?","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\n• Each line is divided into segments at 'split points', to be discovered on certain cell edges crossed by the line.\n• Each segment along a line has the same sum, but this sum can be different for different lines.\n• Digits MAY repeat along a segment, if allowed by sudoku.\n• The digit in a green circle indicates the number of split points on that line.","solution":"138657429645298731792341568521934876879126354463875192954712683216583947387469215","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Each segment along a line has the same sum, but this sum can be different for different lines. • The digit in a green circle indicates the number of split points on that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5"]}]},{"id":"fbhfM7M84N","ctcId":2586,"ctcDifficulty":"HARD","title":"45-45-90","author":"arctan","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow’s circle. Digits in yellow circles indicate how many yellow circles contain that digit. Additionally, digits in yellow circles must be grouped into pairs.  Each pair form opposite corners of a square, one other corner of which must be the sum of the pair. (Eg if r4c7 and r7c4 were a pair, the sum could go in r4c4 or r7c7.) Different pairs cannot use the same square for their sum. (Eg if r3c4 and r4c3 were also a pair, then r4c4 could be used for the sum of this pair OR the sum of the previous pair, but NOT both.) It is possible that the sum for one pair of circles may itself be in a cell which is already circled. Which circles are paired and where their sums go must be determined by the solver.","solution":"625938714739541682184672593876419325241385967953726148568293471317864259492157836","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in yellow circles indicate how many yellow circles contain that digit. Each pair form opposite corners of a square, one other corner of which must be the sum of the pair.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5"]}]},{"id":"36fnN33h7L","ctcId":2587,"ctcDifficulty":"MEDIUM","title":"Leap Day","author":"arctan","rules":"Normal sudoku rules apply. Digits in cages sum to the indicated total, as do digits along diagonals. In both cases, digits may repeat if allowed by other rules. To celebrate leap day (29 February), totals for cages and diagonals 'leap' over twos and nines (i.e. these digits count as zero towards the sum of any cages/diagonals they appear in/on).","solution":"674589123529371486831246759453697812987412365216835947168753294342968571795124638","constraints":["cage","diagonal","little-killer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":["repeats-allowed","extra-rule"],"params":{"zeroDigits":[2,9]},"note":"Digits may repeat inside a cage here, and 2s and 9s count as zero towards the total.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"geometry-reused","modifiers":["sum-is-derived","repeats-allowed"],"params":null,"note":"The marked diagonals give sums here; they are not the usual diagonals that hold 1 to 9 once.","evidence":"rules","lessonPolicy":"closed","sectionIds":[]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"18p5s54kcz","ctcId":2588,"ctcDifficulty":"MEDIUM","title":"You Know How I Roll","author":"Arctan","rules":"Normal sudoku rules apply. Digits separated by a V sum to five. Digits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. The grid is covered in fog; placing correct digits will clear the fog.","solution":"327198456149567832586234791263719584914685327875342619432956178691873245758421963","fogLight":"R1C1,R1C2,R2C1,R2C2","constraints":["XV","fog","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"nhz9bqp4ol","ctcId":2590,"ctcDifficulty":"MEDIUM","title":"c.dot","author":"arctan","rules":"normal sudoku rules apply. digits separated by a white dot are consecutive. digits separated by a black dot are in a 1:2 ratio (i.e. one digit is twice the other). digits may not repeat on either of the marked diagonals.","solution":"371869542462517983958432176734186259815293764296745831123678495647951328589324617","constraints":["diagonal","kropki"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"annx3u5j3p","ctcId":2591,"ctcDifficulty":"MEDIUM","title":"Rapuzzle","author":"Scojo","rules":"Normal sudoku rules apply. Cells separated by a single chess knight's move cannot contain the same digit. Cells that are part of the grey tower must be greater than all orthogonally adjacent non-tower cells. Note: any cell that the tower even partially covers is considered a tower cell. Every group of 3 cells along Rapunzel's hair must contain one low digit (1, 2, 3), one medium digit (4, 5, 6), and one high digit (7, 8, 9). Note, for the avoidance of doubt, that Rapunzel's hair begins in row 4 column 2.","solution":"471928536836571924925436187194382675387695241652147398549813762218769453763254819","constraints":["antiknight","custom","entropic-line"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells that are part of the grey tower must be greater than all orthogonally adjacent non-tower cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"86fQt7nfBQ","ctcId":2592,"ctcDifficulty":"MEDIUM","title":"Odd Nebula","author":"Nurator","rules":"Normal sudoku rules apply. In the grid is a “galaxy” ie an orthogonally-connected group of cells centred on the middle cell of the grid and rotationally symmetric by 180° around that cell.  Eg if r3c3 was in the galaxy then r7c7 must also be in the galaxy. The galaxy contains ALL of the cells containing odd digits but none of the cells containing even digits. Digits do not repeat in a cage and sum to the total given in the top left corner of the cage. Cells separated by an X contain digits summing to 10. The grid is covered in fog. Placing correct digits will clear the fog from the surrounding cells. No guessing is necessary.","solution":"625849173439271685871536429756924831283715964914683257568497312342158796197362548","fogLight":"R4C5","constraints":["XV","cage","custom","fog"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The solver shades an orthogonally connected group of cells, 180-degree rotationally symmetric about r5c5 and containing it, which holds exactly the cells with odd digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"emienzh9f1","ctcId":2593,"ctcDifficulty":"HARD","title":"Cosmic Balance","author":"Nurator","rules":"Normal Sudoku rules apply.\nThe grid is covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area.\nDigits separated by a black dot are in a 1:2 ratio. Digits separated by a white dot are consecutive. Not all dots are given.\nDigits in big white circles (quads) must appear in the surrounding 4 cells.\nDigits in a grey circle must be odd.\n\nSpiral Galaxy: Divide the grid into galaxies, which are orthogonally connected groups of cells that have 180 degree rotational symmetry about their centers, and do not overlap with other galaxies. All cells must be part of a galaxy. The digits in each galaxy do not repeat and sum up to 27.\n\nAll circular clues (dots, quads, grey circles) are centers of galaxies. All centers of galaxies contain a circular clue.","solution":"369724185871953624245618739512469378687532941493871256156347892728195463934286517","fogLight":"R6C7,R7C7,R6C9,R8C4,R1C6,R1C7,R2C6,R2C7","constraints":["custom","fog","kropki","odd","quadruple"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Spiral Galaxy: Divide the grid into galaxies, which are orthogonally connected groups of cells that have 180 degree rotational symmetry about their centers, and do not overlap with other galaxies. The digits in each galaxy do not repeat and sum up to 27.","evidence":"rules","lessonPolicy":"open","sectionIds":["c9","c11"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"4bssym76fv","ctcId":2594,"ctcDifficulty":"MEDIUM","title":"Unexpected Places","author":"Nurator","rules":"Normal Sudoku rules apply.\nDigits in cages cannot repeat and their digits sum to the total given in the leftmost cell of its top row.\nThe grid is covered by fog. Putting in correct digits will lift the fog and reveal more clues. \nNo guessing is required.","solution":"256193487789246351431857926572961834963485712814732695128679543645328179397514268","fogLight":"R8C8,R9C8,R7C1,R1C7","constraints":["cage","fog"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"99c09jh573","ctcId":2595,"ctcDifficulty":"MEDIUM","title":"Hit, Reveal, Solve","author":"Nurator","rules":"Normal Sudoku Rules apply.\n\nDynamic Fog: The grid is covered in fog. Placing a correct digit in a cell lifts fog in that cell and possibly other cells.\n\nHitpoint Arrows: A digit in a cell with an arrow is equal to the sum of all digits where the digit equals the distance from that arrow clue. \nIf multiple arrows are in one cell, the sum total of all such digits in those directions is used.\n\nE.g. if the digit in Row1, Column7 is a 2, it would contribute to the sum in Row3, Column7 while every other digit in that cell would not.","solution":"751392468283614795964578312326857149478961523195243687542139876837426951619785234","fogLight":"R3C7","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Hitpoint Arrows: A digit in a cell with an arrow is equal to the sum of all digits where the digit equals the distance from that arrow clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"j22idv1qhe","ctcId":2596,"ctcDifficulty":"VERY HARD","title":"Sudokulike (Dynamic Fog Edition)","author":"Nurator","rules":"Welcome to the dungeon! Can you find your way through the different rooms of the dungeon and reach all checkpoints with an evolving class?\n\nNormal Sudoku Rules apply.\nDigits in cages (rooms) do not repeat and sum to the total if given.\n\nAdventure Path: \nDraw a path starting at the first check point (the green square with a 1) to every visible checkpoint in ascending order. The path only travels orthogonally \nand must visit each cage (room). \nThe path can never travel outside of rooms nor checkpoints and can only enter and exit any cage (room) exactly once.\n\nDynamic Fog: Each time you determine the exact path and the digit in the highest visible checkpoint cell, put it in to reveal a new checkpoint and new cages. \n\nDynamic Classes: Each time you reveal new cells, delete the path and all entered digits that are not on checkpoints. Then change your class, which determines the line type all cells on the path have to obey.\n\nList of classes (you start with Palindrome):\n1->2 : Palindrome: Digits on a palindrome path read the same forwards and backwards.\n1->2->3: German Whisper: Two cells connected by a German Whisper path must have a difference of at least 5.\n1->2->3->4: Region Sum: Box borders divided the path into segments of equal sums.\n1->2->3->4->5: Dutch Whisper: Two cells connected by a Dutch Whisper path must have a difference of at least 4.\n\nYou have completed the dungeon when all 5 checkpoints are revealed and the complete grid is filled.","solution":"782651349419837265653492817368945172194726538527318694935184726271569483846273951","fogLight":"R2C5,R2C4,R2C3,R2C2,R3C2,R3C3,R3C4,R3C5,R4C5,R5C5,R5C4,R6C5,R6C6,R6C7,R6C8,R5C8,R2C9","constraints":["cage","custom","dutch-whispers","fog","german-whispers","palindrome","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a path starting at the first check point (the green square with a 1) to every visible checkpoint in ascending order. and must visit each cage (room). The path can never travel outside of rooms nor checkpoints and can only enter and exit any cage (room) exactly once. Then change your class, which determines the line type all cells on the path have to obey.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c8","c9","c12"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c17"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c15"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c16"]}]},{"id":"3i3xlin7gl","ctcId":2597,"ctcDifficulty":"MEDIUM","title":"Graded on a Curve","author":"ChinStrap and sujoyku","rules":"- Normal sudoku rules apply, i.e. each row, column and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- Index Lines: Each turquoise line is an Index Line, i.e. the digit in the Nth cell along such a line (starting from the diamond) indicates the position along the line where the digit N appears. For example, if a diamond cell contains a 3, the third cell along that line must have a 1.\n\n- Nabner Lines: The yellow lines are Nabner Lines, i.e. on such a line there may not be consecutive or repeated digits. For example, if a 5 lies on a Nabner line, this line may not contain another 5 and neither a 4 nor a 6.","rulesClarified":"Normal sudoku rules apply: each row, column and 3x3 region contains the digits 1 to 9 once each.\n\nIndex lines. Each turquoise line is an index line, and its diamond is where that line starts. The digit in the Nth cell along the line, counted from the diamond, gives the position along the line where the digit N appears. For example, if the diamond contains a 3, the third cell along that line must contain a 1.\n\nNabner lines. Each yellow line is a Nabner line. It may not contain the same digit twice, and it may not contain two digits that differ by one. For example, if a 5 lies on a Nabner line, that line may not contain another 5, nor a 4, nor a 6.","solution":"192567843638149752475382169849215376756438921213796485524973618987651234361824597","constraints":["custom","nabner-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Index Lines: Each turquoise line is an Index Line, i.e. the digit in the Nth cell along such a line (starting from the diamond) indicates the position along the line where the digit N appears. For example, if a diamond cell contains a 3, the third cell along that line must have a 1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"94v9ipg7hq","ctcId":2598,"ctcDifficulty":"HARD","title":"Jam Packed Thick Crust Club Sandwich","author":"Shintaro Fushida-Hardy","rules":"Standard sudoku rules apply.\n\nOutside clues are the absolute difference between the sum of digits between 7 and 8, and the sum of digits between 8 and 9, in their corresponding row or column. '?' represents a digit (0~9) to be determined by the solver.\n\nAll sandwiches have at least one filling, i.e. there are no runs of three adjacent cells in any row or column containing only the digits 7, 8, and 9.","solution":"347685192215479368968321754674293815831754629529168437183942576752816943496537281","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Outside clues are the absolute difference between the sum of digits between 7 and 8, and the sum of digits between 8 and 9, in their corresponding row or column. '?' represents a digit (0~9) to be determined by the solver. All sandwiches have at least one filling, i.e. there are no runs of three adjacent cells in any row or column containing only the digits 7, 8, and 9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"pnli3vy6ph","ctcId":2601,"ctcDifficulty":"HARD","title":"Gatekeeper","author":"IcyFruit","rules":"Normal sudoku rules apply.\nAlong a line, each set of 3 adjacent digits sums to  multiple of 5.\n Digits around a black dot must have a ratio of 2:1.","solution":"294358176531674289867219543623597814475831692189462735358746921716923458942185367","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Along a line, each set of 3 adjacent digits sums to  multiple of 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"qg411d1jf2","ctcId":2603,"ctcDifficulty":"MEDIUM","title":"A Phistful of Circles","author":"Marty Sears","rules":"• Normal Sudoku Rules Apply.\n• A circled digit indicates exactly how many circles contain that digit.\n• Digits along a purple line do not repeat and form a consecutive sequence, but can be arranged in any order.\n• Adjacent digits along a green line must have a difference of at least 5.\n• Digits along a red line must alternate between odd and even.","solution":"271493568863521974954768321697152843542836719318974652126387495789245136435619287","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• A circled digit indicates exactly how many circles contain that digit. • Digits along a red line must alternate between odd and even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"ga32uqsobl","ctcId":2604,"ctcDifficulty":"MEDIUM","title":"Sydney Harbour Bridge","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along an orange line have a difference of at least four.\nBox borders divide the blue lines into segments whose values have the same sum. Different lines may have different sums.\nDigits along the purple line are a set of consecutive digits in any order with no repeats.\nCells separated by an X sum to ten. Not all possible Xs are given.","solution":"457138926861592473329746815914865237285473691736921548192657384648319752573284169","constraints":["XV","dutch-whispers","region-sum-line","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"2zohak8sgm","ctcId":2606,"ctcDifficulty":"VERY HARD","title":"The Moving Finger","author":null,"rules":"Chaos construction: Place the digits 1 to 9 once each in every row, column, and region. Regions are orthogonally connected and must be located by the solver. \n\nRegion numbers: The digit in the top-left cell of a region (the leftmost cell in its highest row) is its region number. All region numbers are different.\n\nPointing Arrows: If a cell with the digit X in a region with the number N contains an arrow, then the cell X steps away in the indicated direction belongs to the region numbered N+1. Not all possible arrows are given.","solution":"967438125184692537356724918715943862879365241421879653238517496542186379693251784","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Regions are orthogonally connected and must be located by the solver. Region numbers: The digit in the top-left cell of a region (the leftmost cell in its highest row) is its region number. Pointing Arrows: If a cell with the digit X in a region with the number N contains an arrow, then the cell X steps away in the indicated direction belongs to the region numbered N+1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5"]}]},{"id":"2ba20kauml","ctcId":2607,"ctcDifficulty":"MEDIUM","title":"3D Illusions","author":null,"rules":"Normal sudoku rules apply. Neighbouring digits on a line must have a difference of at least 4.","solution":"618349725724158396395627481481932657257486913963715248846271539139564872572893164","constraints":["dutch-whispers"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"929l9v2qt5","ctcId":2609,"ctcDifficulty":"HARD","title":"SET","author":"ICHTUES","rules":"Normal sudoku rules apply. Digits along a marked diagonal cannot repeat. Digits along an arrow sum to the digit in that arrow’s circle. Cells with the same relative position within a 3x3 box must contain different digits. (Eg the middle-left position of r2c1, r2c4, r2c7, r5c1, r5c4, r5c7, r8c1,r8c4&r8c7 must all be different). Let a digit's entropy describe if it is low (123), medium (456), or high (789). Let its modularity be its remainder when divided by 3. Let a SET be a set of three digits such that their entropy and modularity are either all the same or all different. Some examples of SETs are: 789 (same entropy, different modularity), 258 (different entropy, same modularity), 168 and 348 (different entropy and different modularity). In this puzzle, the three rows and three columns of each box all form SETs.","solution":"936714258471582936258369471825471369693258714147936582582693147369147825714825693","constraints":["arrow","custom","diagonal","disjoint-groups"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In this puzzle, the three rows and three columns of each box all form SETs.","evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"2j457uhz0t","ctcId":2612,"ctcDifficulty":"HARD","title":"Three is a crowd","author":"Dying Flutchman","rules":"• Normal sudoku rules apply.\n• Digits in cages sum to the indicated value; some of the values have been replaced by question marks.\n• White dots connect consecutive digits.\n• Along purple lines, any consecutive group of three values (digits or cage totals) must sum to a multiple of three.","solution":"931468725574329861826571493387956214142837659695142378253694187719283546468715932","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Along purple lines, any consecutive group of three values (digits or cage totals) must sum to a multiple of three.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"uz0380wkfg","ctcId":2613,"ctcDifficulty":"HARD","title":"Red-Yellow-Green","author":"Sumanta (Anu)","rules":"Normal Sudoku rules apply.\n\nIn the thermometer shapes digits must strictly increase from the bulb towards the tip.\n\nAlong the green lines neighbouring digits must differ at least by 5. (Digits may repeat in these lines)\n \nEach purple lines contain a set of consecutive digits in any order. (354 is a valid arrangement)\n\nBlue line is just for decoration.","rulesClarified":"Normal Sudoku rules apply.\n\nThermometers: the digits strictly increase from the bulb towards the tip.\n\nGreen lines: two neighbouring digits along a green line differ by at least 5. Digits that are not neighbours along a green line may repeat.\n\nPurple lines: the digits of a purple line are consecutive values, all different, in any order. For example, 3, 5 and 4 in any order form a valid purple line.\n\nThe blue line is decoration and has no rule.","solution":"657439281913852746482617395725194638148376952369528174894263517271945863536781429","constraints":["german-whispers","renban","thermometer"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"j0e1hqfsp4","ctcId":2614,"ctcDifficulty":"HARD","title":"Stay in Your Box","author":"Marty Sears and Justin Vitanza","rules":"Normal sudoku rules apply.\n\nINVISIBLE LINES:\n- Every box contains an invisible 'index line' whose route must be determined.\n- The index lines are all 9 cells long, only move orthogonally (not diagonally), and don't cross any 3x3 box borders. They don't cross themselves, or pass through any black or green spots.\n\nDIAMONDS:\n- Each row, column and box contains exactly one hidden diamond, which lies at one end of its index line, and contains its box number. (Boxes are numbered 1-9 in normal reading order from top left to bottom right.)\n\nINDEXING:\n- The digit in position N along an index line (starting at the end with the diamond) indicates the position along the line where the digit N should be placed. Eg: if the 1st digit is a 3, then the 3rd digit will be a 1.\n\nSPOTS:\n- Digits separated by a black spot are in a 1:2 ratio.\n- Digits separated by a green spot have a difference of at least 5.","solution":"187349256246185937953276841518427693629853174734691582492718365375962418861534729","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Every box contains an invisible 'index line' whose route must be determined. - Each row, column and box contains exactly one hidden diamond, which lies at one end of its index line, and contains its box number. (Boxes are numbered 1-9 in normal reading order from top left to bottom right.) - The digit in position N along an index line (starting at the end with the diamond) indicates the position along the line where the digit N should be placed. Eg: if the 1st digit is a 3, then the 3rd digit will be a 1. - Digits separated by a green spot have a difference of at least 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c6","c8","c11"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"arxojcplun","ctcId":2616,"ctcDifficulty":"MEDIUM","title":"Ambiguity","author":"James Kopp","rules":"Normal sudoku rules apply.\nThe gray lines in the grid are either Renban lines or Region Sum Lines.\nRenban lines contain a set of non-repeating consecutive digits (not necessarily in order). \nBox borders divide the Region Sum Lines into segments whose values have the same sum. Different Region Sum Lines may have different sums.\nThe clues outside the grid show the sum of the first X digits from that direction, where X is the first of those digits.","rulesClarified":"Normal sudoku rules apply.\n\nThe grey lines in the grid are of two kinds: Renban lines and Region Sum Lines. Each grey line is one of these two kinds.\n\nRenban line: the digits along it are all different and form a run of consecutive digits, in any order.\n\nRegion Sum Line: the box borders cut the line into segments. The digits in each segment add up to the same total as the digits in every other segment of that same line. Different Region Sum Lines may have different totals.\n\nThe clues outside the grid are read from the edge they sit on. A clue above or below a column is read along that column from that edge; a clue left of or right of a row is read along that row from that edge. The clue is the sum of the first X digits read in that direction, where X is the value of the first digit read.","solution":"961387524823456791475192836532964178196873452748215369257641983319528647684739215","constraints":["region-sum-line","renban","x-sum"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Box borders divide the Region Sum Lines into segments whose values have the same sum.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Renban lines contain a set of non-repeating consecutive digits (not necessarily in order).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"muytgcj0ni","ctcId":2617,"ctcDifficulty":"MEDIUM","title":"Nemo","author":null,"rules":"Normal sudoku rules apply. Along a (slow) thermometer digits must increase or stay the same from the bulb to the tip.","solution":"687413259315792468942568713154239876863157924279684135598321647431876592726945381","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Along a (slow) thermometer digits must increase or stay the same from the bulb to the tip.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"ndfa904mjz","ctcId":2618,"ctcDifficulty":"HARD","title":"Kissing Zipper","author":"Twototenth","rules":"Normal sudoku rules apply. Purple lines are zipper lines: digits an equal distance from the line’s central cell must sum to the digit in that central cell. The grid contains nine 'doublers', one in each row, column, and 3x3 box; each digit from 1-9 is 'doubled' exactly once. Doubled digits count as twice their value for the purposes of the zipper lines.","solution":"386241759945873126172965843237498561859316274461527398594132687723689415618754932","constraints":["custom","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The grid contains nine 'doublers', one in each row, column, and 3x3 box; each digit from 1-9 is 'doubled' exactly once.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"zipper-line","type":"zipper-line","variant":"modified","modifiers":[],"params":null,"note":"Purple lines are zipper lines: digits an equal distance from the line’s central cell must sum to the digit in that central cell.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"8cs9gx5dfg","ctcId":2621,"ctcDifficulty":"VERY HARD","title":"Big Bad Wolf","author":"IcyFruit","rules":"Divide the grid into nine regions, each consisting of 9 orthogonally connected cells. Place a digit from 1-9 in every cell such that each digit appears exactly once in every row, column, and region.\nRegion boundaries divide the line into segments. \nThe digit in the Nth cell of a segment indicates the position of the digit N on that segment. Positions are counted starting from 1 at an end of the segment which much be determined. Different segments may count in different directions relative to the line.","solution":"839164275452987316713526948624718593548631729167495832291853467386279154975342681","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Region boundaries divide the line into segments.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"ir0498bsgu","ctcId":2622,"ctcDifficulty":"MEDIUM","title":"CALLERLAB 50th","author":"Jeremy Butler","rules":"Normal Sudoku Rules apply:  Each row, column, and 3x3 box must contain the digits 1-9 once each.\nThe colored squares are all ODD digits.\nGreater than and less than signs indicate one digit is higher or lower than the one next to it.\nEx.  8>6 or 3<7\nEach letter corresponds to a number and must be resolved","solution":"724138965691574283853692741175346829468921537239785614982417356517863492346259178","constraints":["custom","inequality","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each letter corresponds to a number and must be resolved","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"62l02qt79r","ctcId":2623,"ctcDifficulty":"MEDIUM","title":"I Heard You Like Cages","author":"Justin Vitanza","rules":"Normal sudoku rules apply.\n\nEach cage in the grid is either a killer cage or a look-and-say cage (or both), with each to be determined by the solver. Cage colors have no logical content.\n\nKiller Cages: Digits must not repeat within a cage and must sum to the number in the top-left corner.\nLook-and-Say Cages: The number in the top left corner says how many of a digit are in that cage. The ones place indicates the digit and the tens place indicates exactly how many times that digit appears. Digits may repeat in look-and-say cages if allowed by this and other rules. Example: If a look-and-say cage has the clue \"14\" then there is exactly one 4 in the cage.","solution":"631275489497836521528914736349751862865392174172468953214583697753649218986127345","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Each cage in the grid is either a killer cage or a look-and-say cage (or both), with each to be determined by the solver.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each cage in the grid is either a killer cage or a look-and-say cage (or both), with each to be determined by the solver.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"46bismbam8","ctcId":2624,"ctcDifficulty":"HARD","title":"Would you like that toasted?","author":"Justin Vitanza","rules":"Normal Sudoku Rules Apply\n\nCrunchy Sandwiches: Clues outside the grid indicate that the sum of the digits between 1 and 9 (exclusive) in the indicated row or column is strictly greater than (>) or less than (<) the given clue value.\n\nBulbless thermometers: Digits on a grey line must increase from the bulb end. Each grey line has a single bulb whose location must be determined by the solver but it will always occur at the end of a line (i.e. thermometers may branch but not at the bulb).","solution":"871432956642591837953678412526187394384259761719346285267913548195824673438765129","constraints":["sandwich","thermometer"],"constraintFacts":[{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"7wu3gxtfgz","ctcId":2625,"ctcDifficulty":"HARD","title":"The King","author":"Justin Vitanza","rules":"Normal Sudoku Rules Apply\n\nThe King's Law states that for a digit X, exactly X instances of the digit X are a king's move away from another instance of the digit X. However, two of the digits 1-9 (to be deduced) are rebellious and do not abide by this law. In fact, a rebellious digit is never a king's move away from another instance of itself.\n\nThe grid is partially covered with fog. Correctly placed digits will clear the fog around that cell.","rulesClarified":"Normal Sudoku rules apply.\n\nKing's Law: for a digit X that obeys the law, exactly X instances of the digit X are a king's move away from another instance of the digit X. A king's move is one step in any of the eight directions, orthogonal or diagonal.\n\nTwo of the digits 1 to 9 are rebellious. They do not obey the King's Law, and you must find which two they are.\n\nA rebellious digit is never a king's move away from another instance of itself.\n\nThe grid is partially covered with fog. Correctly placed digits will clear the fog around that cell.","solution":"398257416246813795751649382175964238634582971982371564819725643427136859563498127","fogLight":"R5C3","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The King's Law states that for a digit X, exactly X instances of the digit X are a king's move away from another instance of the digit X. However, two of the digits 1-9 (to be deduced) are rebellious and do not abide by this law.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"6gv40dsdo2","ctcId":2630,"ctcDifficulty":"MEDIUM","title":"Magic Eggs","author":"James Kopp","rules":"Normal sudoku rules apply.\nBox 1 is a magic square in which all the rows, columns and both diagonals sum to the same total.\nAdjacent digits along a green line have a difference of at least five.\nDigits along a purple line are a set of consecutive digits in any order with no repeats.\nDigits on the blue line are even. \nDigits on the orange line are odd.\nCells separated by black dots are in the ratio of 1 to 2. Not all possible black dots are shown.","solution":"618479253753621498294583617529316784841297536367854921936145872185762349472938165","constraints":["custom","even","german-whispers","kropki","odd","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Box 1 is a magic square in which all the rows, columns and both diagonals sum to the same total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"b0toeo9gzp","ctcId":2631,"ctcDifficulty":"MEDIUM","title":"Thermoregulators","author":"SSG","rules":"Normal sudoku rules apply.\n\nThermometers: Digits along a thermometer must strictly increase starting at the bulb end.\n\nConsecutive Count: The digit in a bulb counts the number of pairs of consecutive digits appearing on its thermometer.","solution":"824679315196534782753812469671293854249758136538461927365987241487125693912346578","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Consecutive Count: The digit in a bulb counts the number of pairs of consecutive digits appearing on its thermometer.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"shdh45cgrz","ctcId":2636,"ctcDifficulty":"HARD","title":"Pipe Down","author":"G","rules":"Apply chaos construction sudoku rules: place the digits 1-9 without repeats in each row, column, and 9 deduced regions of 9 orthogonally connected cells. Clues outside the grid indicate the first N cells pointing in that direction are in the same region - followed by a region border - where N is the first digit seen by the clue. Digits along green lines have a minimum difference of 5.","solution":"617283954546938217183527469492716583851472396369854721934165872275649138728391645","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Apply chaos construction sudoku rules: place the digits 1-9 without repeats in each row, column, and 9 deduced regions of 9 orthogonally connected cells. Clues outside the grid indicate the first N cells pointing in that direction are in the same region - followed by a region border - where N is the first digit seen by the clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"i7jrq9g9oz","ctcId":2637,"ctcDifficulty":"MEDIUM","title":"Indifferent Neighbours!","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. (ie Place the digits 1-9, once each, in every row, column and 3x3 box.) Cells separated by a single knight's move (in chess) cannot contain the same digit. In a 3x3 box every horizontal threesome is contains one digit from {1,2,3}, one from {4,5,6} and one from {7,8,9}. A positive diagonal is any diagonal going from South-West to North-East. When normal sudoku rules allow neighbouring digits on a positive diagonal to be equal they MUST be equal. eg r2c4, r3c3 and r4c2 must contain the same digit; r6c2 and r7c1 must contain the same digit; etc.","solution":"963742851527168349841953762419537628275816934638429517384295176752681493196374285","constraints":["antiknight","custom"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In a 3x3 box every horizontal threesome is contains one digit from {1,2,3}, one from {4,5,6} and one from {7,8,9}. When normal sudoku rules allow neighbouring digits on a positive diagonal to be equal they MUST be equal. eg r2c4, r3c3 and r4c2 must contain the same digit; r6c2 and r7c1 must contain the same digit; etc.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5"]}]},{"id":"r9d3orh23f","ctcId":2639,"ctcDifficulty":"HARD","title":"Different Delights","author":"ThePedallingPianist","rules":"Normal sudoku rules apply.\n\nFog of war: some of the grid is covered in fog. Enter correct digits to uncover more clues.\n\nDifferent Difference lines: no pair of adjacent digits on a beige line may have the same difference. For example, if a line has a 3 and 5 next to each other, it may not also contain a 7 and a 9 next to each other.\n\nX: digits separated by an X sum to 10.\nKropki: digits separated by a black dot are in a 1:2 ratio.\n\nNot all possible Xs, black dots or difference lines are given. And thank goodness for that.","solution":"719562483425783169683914752248359617976128534531647928862475391197836245354291876","fogLight":"R1C1,R2C1,R2C2,R1C2","constraints":["XV","custom","fog","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Different Difference lines: no pair of adjacent digits on a beige line may have the same difference.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"w12tyqmvs0","ctcId":2640,"ctcDifficulty":"HARD","title":"Goldilocks and the Renbans","author":"Qodec","rules":"- Sudoku: Each row, column, and region indicated by thick borders in the grid must contain the digits 1 to 9 once each.\n- Killer cages: An area surrounded by a dashed line is a 'killer cage'. Digits in a cage cannot repeat, and they sum to the number in the upper left corner.\n- Renban: Digits along purple lines are a set of non-repeating consecutive digits in some order.","solution":"762543819531698427948127536217954368359286741486371952194765283675832194823419675","constraints":["cage","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"lf0k2bgpzu","ctcId":2641,"ctcDifficulty":"VERY HARD","title":"Kurodoku","author":"Malrog & yttrio","rules":"Chaos Construction: Place the digits from 1 to 9 exactly once in every row, column, and region. Regions consist of a set of nine orthogonally connected cells and must be determined by the solver.\n\nShade two groups of orthogonally connected cells in each region. These groups can consist of a single cell or multiple cells. Both of a region's groups must have the same size and shape, but may be rotated or reflected. Shaded groups may not be orthogonally adjacent.\n \nCells with arrows are not shaded, and indicate the size of a group of shaded cells which occupies the adjacent cell in the indicated direction(s). (Note: a 2 in a cell with two arrows would indicate that there was a region of size 2 in BOTH directions.)\n\nFor each region whose shaded groups consist of multiple cells, one shaded group must contain a set of consecutive digits in any order, and adjacent digits within the other shaded group must differ by at least 5. The solver must determine which is which.","rulesClarified":"Chaos Construction: Place the digits 1 to 9 exactly once in every row, column and region.\n\nRegions consist of nine orthogonally connected cells. The solver must determine the regions.\n\nShade two groups of orthogonally connected cells in each region. A group can be a single cell or several cells.\n\nThe two shaded groups in a region must be the same size and shape. One may be a rotation or reflection of the other.\n\nShaded groups may not be orthogonally adjacent to each other.\n\nCells with arrows are not shaded. Each arrow points to the adjacent cell in its direction. The number in an arrow cell is the size of the shaded group that occupies that adjacent cell.\n\nA cell with two arrows gives the size in both directions. A 2 in a cell with two arrows means there is a shaded group of size 2 in each of the two directions.\n\nFor each region whose shaded groups consist of multiple cells, one shaded group must contain a set of consecutive digits in any order, and adjacent digits within the other shaded group must differ by at least 5.\n\nThe solver must determine which group is which.","solution":"943562817286914735175849623432675189597281364769138542651327498328456971814793256","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade two groups of orthogonally connected cells in each region. Cells with arrows are not shaded, and indicate the size of a group of shaded cells which occupies the adjacent cell in the indicated direction(s). For each region whose shaded groups consist of multiple cells, one shaded group must contain a set of consecutive digits in any order, and adjacent digits within the other shaded group must differ by at least 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c7","c9"]}]},{"id":"eol0opcd7y","ctcId":2643,"ctcDifficulty":"VERY HARD","title":"Dueling Dragons","author":"IcyFruit","rules":"Place a digit from 1-9 once each in every row, column, and cage.\nIf and only if adjacent digits do not sum to a prime number, shade the boundary between them. Shaded boundaries must divide the grid into exactly 2 regions. There may be shaded boundaries that lie within a region without fully dividing it.\nA digit in a cell with one or more arrows indicates the total number of shaded boundaries in the directions of all arrows combined.","solution":"385492167216735498749123685834956712167589243952814376493267851521678934678341529","constraints":["custom","region"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If and only if adjacent digits do not sum to a prime number, shade the boundary between them. Shaded boundaries must divide the grid into exactly 2 regions. A digit in a cell with one or more arrows indicates the total number of shaded boundaries in the directions of all arrows combined.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"e27trjd6zv","ctcId":2645,"ctcDifficulty":"VERY HARD","title":"Holographic Principle","author":"Shintaro Fushida-Hardy","rules":"The digits 1 to 9 occur exactly once each in every row, column, and region. Regions cannot overlap and each consists of nine orthogonally-connected cells. The region borders must be deduced. A digit in a cell with arrow(s) gives the total number of cells in the same region as the arrow cell in all indicated directions combined (NB this count includes the arrow cell itself.) Cells in different regions to the arrow cell immediately block vision (and therefore prevent any cells further along the arrow’s path in that direction from contributing to the arrow cell’s count).","solution":"518936724196742583473815692785421369239674851851293476942568137367189245624357918","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The region borders must be deduced. A digit in a cell with arrow(s) gives the total number of cells in the same region as the arrow cell in all indicated directions combined (NB this count includes the arrow cell itself.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"7yx3e6616s","ctcId":2647,"ctcDifficulty":"MEDIUM","title":"Arrow vs Thermo","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. (ie Place the digits 1-9, once each, into every row, column and 3x3 box). Along a thermometer, digits must increase from the bulb end. Digits along an arrow must sum to the digit in that arrow's circle.","solution":"482956371619473825735281946846392517127845693593617482374529168961738254258164739","constraints":["arrow","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"k1h02y7ke0","ctcId":2648,"ctcDifficulty":"HARD","title":"Bishopsgate","author":"Cris Moore","rules":"Normal Sudoku rules apply. There is a bishop's constraint on the white squares of the checkerboard: the cells on each white diagonal are different. (Please note that playing in Dark Mode switches the white and black squares!)\n\nCells connected by a V or X sum to 5 or 10 respectively. Cells connected by a white dot are consecutive.","solution":"295614783813795426476823951729361845538249617164578392947132568381956274652487139","constraints":["XV","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There is a bishop's constraint on the white squares of the checkerboard: the cells on each white diagonal are different.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"04q6z7ds83","ctcId":2650,"ctcDifficulty":"VERY HARD","title":"When It's Time to Parity We Will Parity Hard","author":"Calvinball and ChinStrap","rules":"Normal sudoku rules apply.\n\nParity Mirror: The diagonal from r1c1 to r9c9 acts as a parity mirror. Each cell has the same parity as the cell reflected in the mirror, i.e. if r2c6 is even, r6c2 is also even.\n\nIndex Lines: The digit in the Nth cell along a teal line (starting from the diamond) indicates the position along the line where the digit N appears. For example, if a diamond cell contains a 3, the third cell along that line must have a 1.","solution":"278493165319658472654172983427315896935786214186924357743861529892537641561249738","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Parity Mirror: The diagonal from r1c1 to r9c9 acts as a parity mirror. Index Lines: The digit in the Nth cell along a teal line (starting from the diamond) indicates the position along the line where the digit N appears.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"nktjmzm64k","ctcId":2651,"ctcDifficulty":"MEDIUM","title":"Manta","author":"IcyFruit","rules":"Normal sudoku rules apply.\nOn purple lines, digits an equal distance from the center of the line must sum to the digit at the center. The center of the line is marked with a dot.\nOn blue lines, each set of 3 digits sums to a multiple of 5.","solution":"591874236746312895832965174628531947359487621417629358164253789275198463983746512","constraints":["custom","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On blue lines, each set of 3 digits sums to a multiple of 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"e37gpta782","ctcId":2652,"ctcDifficulty":"MEDIUM","title":"You Make Me Quiver","author":"Die Hard","rules":"Normal sudoku rules apply. Digits on an arrow sum to the digit in the attached circle.","solution":"415278936276539481983461275841725693697314528532896147754182369168943752329657814","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"d21nrto778","ctcId":2653,"ctcDifficulty":"VERY HARD","title":"Clashing Chameleons","author":null,"rules":"Normal Sudoku rules apply.\n\nShade the boundary between adjacent digits if and only if they sum to an even number. Shaded boundaries must divide the grid into exactly 2 regions. There may be shaded boundaries that lie within a region without fully dividing it, as allowed by other rules.\n\nA digit in a cell with one or more arrows indicates the total number of shaded boundaries in the directions of all arrows combined.","rulesClarified":"Normal Sudoku rules apply.\n\nFor every pair of adjacent digits, look at the boundary between them. Shade that boundary if and only if the two digits sum to an even number. Do not shade any other boundary.\n\nThe shaded boundaries must divide the grid into exactly two regions. A shaded boundary may also lie inside a region without splitting it, when the other rules allow it.\n\nA digit in a cell with one or more arrows gives the total number of shaded boundaries in the directions of all of that cell's arrows combined.","solution":"587492361692317548341685279416853792938726415275941683754138926829564137163279854","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shade the boundary between adjacent digits if and only if they sum to an even number. A digit in a cell with one or more arrows indicates the total number of shaded boundaries in the directions of all arrows combined.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5"]}]},{"id":"y85zt1ul4o","ctcId":2654,"ctcDifficulty":"HARD","title":"Winkelmesser","author":"Myxo","rules":"Sudoku: Place the digits 1-9 exactly once in each row, column and box.\n\nThermo: Digits along a grey thermometer must strictly increase from bulb to tip.","solution":"543196872917482653826573914734961285698725431251348769465237198382619547179854326","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"65113ete79","ctcId":2655,"ctcDifficulty":"MEDIUM","title":"Hungry Hungry Hippos","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nThe four hungry hungry hippos on the edges of the grid are fighting to eat all of the large circles in the grid. If a circle is entirely within the colored territory of a single hippo, that circle will be eaten by that hippo. If a circle is on the border between multiple hippos' territories, which hippo eats that circle must be determined. A number on a hippo shows the sum of all circles that it eats. A digit on a circle indicates how many circles contain that digit.\n\nDigits separated by a small white dot are consecutive. These dots are too small for the hippos to care about, so they are not eaten. Not all possible dots are shown.","solution":"284193657135627489769548321871364295693285714542719836926871543318456972457932168","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The four hungry hungry hippos on the edges of the grid are fighting to eat all of the large circles in the grid. A digit on a circle indicates how many circles contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"gsm8ktttzl","ctcId":2656,"ctcDifficulty":"HARD","title":"Modds and Mevens","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nModular Lines: Every group of 3 cells along a teal line must contain one digit from each modulo 3 group (1, 4, 7), (2, 5, 8), and (3, 6, 9).\n\nOdd Lots: A digit in a circle counts the number of odd digits on its line.\n\nEven Lots: A digit in a square counts the number of even digits on its line.\n\nLittle Killer: A clue outside the grid gives the sum of the digits along the indicated diagonal.","solution":"918672345324951687567834291485367912631295874279148536743586129196723458852419763","constraints":["custom","little-killer","modular-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Odd Lots: A digit in a circle counts the number of odd digits on its line. Even Lots: A digit in a square counts the number of even digits on its line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jm86sbi0bb","ctcId":2657,"ctcDifficulty":"HARD","title":"Fillomino Whispers","author":"Die Hard","rules":"𝗙𝗶𝗹𝗹𝗼𝗺𝗶𝗻𝗼. Divide the grid into regions of orthogonally connected cells. Regions can be upto 9 cells large. Fill each region with the number of cells it contains (eg: fill any 7-cell regions with seven 7s, etc). \n\n𝗔𝗻𝘁𝗶 𝗥𝗼𝘄/𝗖𝗼𝗹𝘂𝗺𝗻. Except for the given 1 in R3C1, the digit N cannot appear in row N or column N. \n\n𝗚𝗲𝗿𝗺𝗮𝗻 𝗪𝗵𝗶𝘀𝗽𝗲𝗿𝘀. Orthogonally adjacent digits in different regions must differ by at least 5.","solution":"772288822777718177172288827818822827888199277282919271282999916717229166777771666","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into regions of orthogonally connected cells. Fill each region with the number of cells it contains (eg: fill any 7-cell regions with seven 7s, etc). Except for the given 1 in R3C1, the digit N cannot appear in row N or column N.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"kwf3g2ne92","ctcId":2658,"ctcDifficulty":"HARD","title":"Whispering Internal Loop Skyscrapers","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nDraw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally.\n\nThe loop acts as a German Whispers line (i.e., adjacent digits on the loop must have a difference of at least 5).\n\nInternal Loop Skyscrapers: Each cell on the loop represents a skyscraper with a height equal to its value (non-loop cells are not skyscrapers). A digit in a clued cell gives the number of skyscrapers visible in the indicated direction (not including the cell itself), where skyscrapers block the view of skyscrapers with the same or lower height behind them.  The clued cell may or may not be on the loop.","solution":"496572183572381649183964572741625938265839417839147256354796821917258364628413795","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop of orthogonally connected cells. A digit in a clued cell gives the number of skyscrapers visible in the indicated direction (not including the cell itself), where skyscrapers block the view of skyscrapers with the same or lower height behind them.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"6dugnv08rk","ctcId":2659,"ctcDifficulty":"HARD","title":"Mischief","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nThe grid is covered in fog. Entering a correct digit will clear the fog in that cell, and maybe some others too. No guessing is required.\n\nSpots divide lines into segments. A 'segment total' is the sum of the digits in that segment. Digits may not repeat within a segment.\n\nLINE RULES:\n\n• EQUAL SEGMENT LINE: Along a BLUE LINE, each segment has the same total.\n• SEGMENT RENBAN : Along a PINK LINE, all the individual segment totals form a non-repeating consecutive sequence, but the segments can appear in any order (eg: 11, 13, 10, 9, 12.)\n• SEGMENT NABNER: Along a yellow line, any two segment totals anywhere on the line may not be consecutive or the same (eg: if there is a segment whose cells sum to 12, then no other segment may have a total of 11, 12 or 13.)\n\nSHENANIGANS: One of the digits 1-9 (to be determined) is the 'mischief digit.' Every line follows one of the three line rules above, but any line containing the mischief digit has been painted the wrong colour. (Any line NOT containing the mischief digit is the correct colour.)","solution":"897641532512739846634825791785964213963217485421583967149372658376458129258196374","fogLight":"R2C6,R2C7,R2C8,R2C9,R3C9,R4C9,R5C9,R6C9,R7C9,R8C9,R9C9,R9C8,R9C7,R9C6,R9C5,R9C4,R9C3,R9C2","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Spots divide lines into segments. • EQUAL SEGMENT LINE: Along a BLUE LINE, each segment has the same total. • SEGMENT RENBAN : Along a PINK LINE, all the individual segment totals form a non-repeating consecutive sequence, but the segments can appear in any order (eg: 11, 13, 10, 9, 12.) • SEGMENT NABNER: Along a yellow line, any two segment totals anywhere on the line may not be consecutive or the same (eg: if there is a segment whose cells sum to 12, then no other segment may have a total of 11, 12 or 13.) SHENANIGANS: One of the digits 1-9 (to be determined) is the 'mischief digit.'","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c9","c10","c11","c12"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ck24rsi50z","ctcId":2660,"ctcDifficulty":"MEDIUM","title":"Internal X-Sum Yin Yang","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nYin Yang: Shade some cells such that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2x2 area is fully shaded or fully unshaded.\n\nSmall numbers in the corners of cells are internal X-Sum clues.  The digit in a cell with a clue gives the total number of cells (including itself) of the same shading as itself seen in all horizontal/vertical directions combined (cells of the opposite shading block the vision).  Those cells sum to the number given by the clue.  Digits may repeat within a sum if allowed by other rules.","solution":"678921345234875961915643278146752893897136452352498617429317586763584129581269734","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Small numbers in the corners of cells are internal X-Sum clues.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"r7nwd76xu3","ctcId":2662,"ctcDifficulty":"VERY HARD","title":"Abatement","author":"dumediat","rules":"Normal sudoku rules apply.\nAnti-Diagonal: Each of the main diagonals may only contain 3 distinct digits.\nQuadruples: Digits in a Quadruple circle must be placed at least once in the four cells touching that circle.\nThe cell with the gray circle must contain an odd digit.","solution":"746238519538169724129547638384752196617894352295613847472381965863925471951476283","constraints":["custom","odd","quadruple"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Anti-Diagonal: Each of the main diagonals may only contain 3 distinct digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"n045ji0xsw","ctcId":2663,"ctcDifficulty":"HARD","title":"Throuple Island","author":"Belamis","rules":"Normal Sudoku rules apply.\n-Kropki: Digits in cells separated by a white dot are consecutive. Digits in cells separated by a black dot have a 1:2 ratio.\n-Divide the grid into islands of one or more orthogonally connected cells such that no two islands touch each other orthogonally.\n-All non-island cells are in the ocean which must be a contiguous region of orthogonnally connected cells that never completely fills a 2x2 area.\n-Each black dot connects 2 island cells.\n-Each white dot connects an ocean and island cell.\n-Throuple Island: Each island contains exactly 3 different digits (With potential repeats), with the highest digit equal to the islands size.","rulesClarified":"Normal Sudoku rules apply.\n\nKropki: the two digits in cells separated by a white dot are consecutive.\n\nThe two digits in cells separated by a black dot have a 1:2 ratio, so one is double the other.\n\nIslands: divide the grid into islands. Each island is one or more orthogonally connected cells, and no two islands touch each other orthogonally.\n\nOcean: every cell that is not in an island is in the ocean. The ocean must be one contiguous region of orthogonally connected cells, and it must never completely fill a 2x2 area.\n\nEach black dot connects two island cells.\n\nEach white dot connects one ocean cell and one island cell.\n\nThrouple Island: the size of an island is its number of cells. Each island contains exactly three different digits, though a digit may appear in more than one cell of the same island. The highest of those three digits equals the island's size.","solution":"213965487579384216864712953396528741742691538185473692451236879928147365637859124","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"-Divide the grid into islands of one or more orthogonally connected cells such that no two islands touch each other orthogonally. -All non-island cells are in the ocean which must be a contiguous region of orthogonnally connected cells that never completely fills a 2x2 area. -Each black dot connects 2 island cells. -Each white dot connects an ocean and island cell. -Throuple Island: Each island contains exactly 3 different digits (With potential repeats), with the highest digit equal to the islands size.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6","c7","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"frb3c5cxkr","ctcId":2664,"ctcDifficulty":"MEDIUM","title":"Smallest Chaotic Killer","author":"Belamis","rules":"Digits do not repeat in cages, and sum to the small clue in the top left corner of the cage. Divide the grid into regions, each consisting of nine orthogonally connected cells. Each row, column and region contains the digits 1-9 once each. The smallest digit in each cage counts the number of different regions that enter that cage.","solution":"784526391395168274251439786918647532637285419423971658176394825542813967869752143","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The smallest digit in each cage counts the number of different regions that enter that cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"7ipjii8013","ctcId":2665,"ctcDifficulty":"MEDIUM","title":"Regional Constraints","author":"Belamis","rules":"Normal Sudoku rules apply.\nRenban: Purple lines contain a non-repeating set of consecutive digits in any order.\nKiller: Digits do not repeat in cages, and sum to the small clue in the top left corner if given.\nThermo: Digits along a thermometer must increase from the bulb to the tip.\nKropki: Digits in cells separated by a black dot have a 1:2 ratio.\nGerman Whispers: Along green lines, digits must differ from their neighbors by at least 5.\nConstraint Regions: Each constraint type may contain no repeated digits anywhere in the puzzle. E.g. ALL renban cells must contain no repeated digits, ALL cells connected by a kropki dot must contain no repeated digits etc.","solution":"521684397843179526697235148158346279469752813732918654976821435314567982285493761","constraints":["cage","german-whispers","kropki","renban","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"3w7wprj07z","ctcId":2666,"ctcDifficulty":"MEDIUM","title":"Foggy Regional Constraints","author":"Belamis","rules":"Sudoku: Normal Sudoku rules apply.\nDynamic Fog: The grid is partially covered in dynamic fog. Correctly placed digits may remove fog from \nother cells.\nGerman Whispers: Along green lines, digits must differ from their neighbors by at least 5.\nKiller: Digits do not repeat in cages, and sum to the small clue in the top left corner if given.\nRenban: Purple lines contain a non-repeating set of consecutive digits in any order.\nParity: Along a peach line, adjacent digits must alternate between odd and even.\nKropki: Digits in cells separated by a black dot have a 1:2 ratio.\nConstraint Regions: Each constraint type may contain no repeated digits anywhere in the puzzle. E.g. ALL renban cells must contain no repeated digits, ALL cells connected by a kropki dot must contain no repeated digits etc.","solution":"175963428624851793938472165859127634742386951316549872283794516491635287567218349","fogLight":"R7C1,R7C2,R7C3,R9C8,R9C9,R2C7,R3C7,R4C7","constraints":["cage","custom","fog","german-whispers","kropki","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Killer: Digits do not repeat in cages, and sum to the small clue in the top left corner if given. Parity: Along a peach line, adjacent digits must alternate between odd and even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c8"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"gavbek5s69","ctcId":2667,"ctcDifficulty":"MEDIUM","title":"Regional Constraint Rally","author":"Belamis","rules":"Normal Sudoku rules apply.\nKropki: Digits in cells separated by a black dot have a 1:2 ratio (ie one digit will be double the other).\nKiller: Digits do not repeat in cages, and sum to the small clue in the top left corner if given.\nThermo: Digits along a thermometer must increase from the bulb to the tip.\nDutch Whispers: Along orange lines, digits must differ from their neighbors by at least 4.\nGerman Whispers: Along green lines, digits must differ from their neighbors by at least 5.\nParity: Along a red line, adjacent digits must alternate between odd and even. \nConstraint Regions: Each constraint type may contain no repeated digits anywhere in the puzzle. E.g. If one Thermo contains a 5, then no other Thermo may contain a 5 etc.\nFog of War: The grid is partially covered in fog. Correctly placing digits will clear the fog around that cell. No guessing is required.","solution":"912487563473561892568329417831974625257618349694253781386195274125746938749832156","fogLight":"R8C2,R8C7,R7C9,R4C7","constraints":["cage","custom","dutch-whispers","fog","german-whispers","kropki","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Parity: Along a red line, adjacent digits must alternate between odd and even. Constraint Regions: Each constraint type may contain no repeated digits anywhere in the puzzle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"3f7o01c1ws","ctcId":2669,"ctcDifficulty":"MEDIUM","title":"Creatures in the Fog","author":"Br1312te","rules":"Normal Sudoku rules apply, but strange things are afoot..\n\nCreatures of the night have invaded the land! Each row, column and box contains one creature, marked by a coloured dot. All creatures are marked.\n\nCells containing a creature index either the row, column or box number (read in normal reading order) they're placed in. Each number assigned to a creature is unique and can't be repeated.\n\nZombies: marked by a green dot, zombies have an infectuous bite. Orthogonally adjacent cells are even when the zombie's number is even, or odd when the zombie's number is odd.\n\nPoltergeists: marked by a grey dot, poltergeists throw everything into disarray. Orthogonally adjacent cells are either all higher than the poltergeist's number, or all lower.\n\nHeadless Horsemen: marked by an orange dot, horsemen have a knight's reach. Cells a chess-knight's move away from the horseman can't contain the same digit as the horseman's number.\n\nVampires: marked by a red dot, vampires suck the power from their victims. Orthogonally adjacent cells sum up to the vampire's number.\n\nFog: the land is covered in fog. Putting in correct digits will lift the fog. No guessing is required. The monster under your bed will know if you cheat!\n\nLove, Brigitte","solution":"913675842475823961286149753648917325321586479597432186152794638834261597769358214","fogLight":"R8C8,R6C9,R4C2","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each row, column and box contains one creature, marked by a coloured dot. Cells containing a creature index either the row, column or box number (read in normal reading order) they're placed in. Each number assigned to a creature is unique and can't be repeated. Zombies: marked by a green dot, zombies have an infectuous bite. Poltergeists: marked by a grey dot, poltergeists throw everything into disarray. Headless Horsemen: marked by an orange dot, horsemen have a knight's reach. Vampires: marked by a red dot, vampires suck the power from their victims.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5","c6","c7","c9","c11","c13"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c15"]}]},{"id":"th3wjsiv41","ctcId":2670,"ctcDifficulty":"HARD","title":"Sator Square","author":"Br1312te","rules":"Normal Sudoku rules apply.\n\nMagic Squares: red cages are magic squares where the row, column and main diagonals all add up to the same number. Digits in a magic square cannot repeat. \n\nDutch Whisper Lines: two cells connected by an orange line must have a difference of at least 4.\n\nFog: the grit is partly covered in fog. Placing correct digits will clear the fog. No guessing is required.\n\nLove, Brigitte","solution":"724815396983467251615932847867291435152346789439578162296183574371654928548729613","fogLight":"R1C1,R1C2,R1C3,R1C4,R1C5,R1C6,R1C7,R1C8,R1C9,R2C1,R2C2,R2C3,R2C4,R2C5,R2C6,R2C7,R2C8,R2C9,R3C1,R3C2,R3C3,R3C4,R3C5,R3C6,R3C7,R3C8,R3C9,R4C1,R4C2,R4C3,R4C4,R4C5,R4C6,R4C7,R4C8,R4C9,R5C1,R5C2,R5C3,R5C4,R5C5,R5C6,R5C7,R5C8,R5C9,R6C1,R6C2,R6C3,R6C4,R6C5,R6C6,R6C7,R6C8,R6C9,R7C4,R7C5,R7C6,R7C7,R7C8,R7C9,R8C4,R8C5,R8C6,R8C7,R8C8,R8C9,R9C4,R9C5,R9C6,R9C7,R9C8,R9C9","constraints":["custom","dutch-whispers","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Magic Squares: red cages are magic squares where the row, column and main diagonals all add up to the same number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"6pnb3dipkp","ctcId":2671,"ctcDifficulty":"MEDIUM","title":"BoogieigooW","author":"Br1312te","rules":"Normal Sudoku rules apply.\n\nPalindromes: digits on a grey palindrome line read the same forwards and backwards. The lines do not bend, diverge or cross each other.\n\nFog: the grid is partially covered in fog. Placing correct digits will clear the fog. No guessing is required.\n\nLove, Brigitte","solution":"318465972456729381729183546834972165691354827275816439167538294982641753543297618","fogLight":"R1C1,R1C2,R1C3,R1C4,R1C5,R1C6,R1C7,R1C8,R1C9,R2C1,R2C2,R2C3,R2C4,R2C5,R2C6,R2C7,R2C8,R2C9,R3C1,R3C2,R3C3,R3C4,R3C5,R3C6,R3C7,R3C8,R3C9,R4C1,R4C2,R4C3,R4C4,R4C5,R4C6,R4C7,R4C8,R4C9,R5C1,R5C2,R5C3,R5C4,R5C5,R5C6,R5C7,R5C8,R5C9,R6C1,R6C2,R6C3,R6C4,R6C5,R6C6,R6C7,R6C8,R6C9,R7C1,R7C2,R7C3,R7C4,R7C5,R7C6,R8C1,R8C2,R8C3,R8C4,R8C5,R8C6,R9C1,R9C2,R9C3,R9C4,R9C5,R9C6","constraints":["fog","palindrome"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"tom2r4079i","ctcId":2674,"ctcDifficulty":"HARD","title":"Penghu County","author":"Myxo","rules":"Sudoku: Place the digits 1-9 exactly once in each row, column and box.\n\nRegion Sum Lines: Box borders divide blue lines into segments. The digits on each segment of the same line must sum to the same total.\n\nArrows: The sum of the digits along an arrow must equal the digit in the attached circle.","solution":"271986534859734261634215978916547823483192657725368149547821396192673485368459712","constraints":["arrow","region-sum-line"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"yn92b7aepi","ctcId":2675,"ctcDifficulty":"HARD","title":"United King-dom - douze points","author":"olima","rules":"Normal Sudoku rules apply. Digits a King's move (in chess) apart must be different. Black dots indicate digits in a 1:2 ratio, white dots consecutive digits. Not all dots are necessarily given.","solution":"182976453594183276376254189625318947918647532437529861869431725753892614241765398","constraints":["antiking","kropki"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"0o823lt42s","ctcId":2677,"ctcDifficulty":"HARD","title":"Square of Squares","author":"Michael Lefkowitz","rules":"LATIN SQUARE - Place the digits 1-9 once each in every row and column. LATIN SQUARES - Subdivide the grid into smaller latin squares, which can be any size except 1×1. An N×N latin square contains exactly N unique digits selected from 1 to 9 (such that those N unique digits do not repeat in any row/column of their latin square). Latin squares with the same size may not have the same digit in the same relative position. (Eg if a 4×4 latin square has a 7 in its upper left corner, no other 4×4 latin square may have a 7 in its upper left corner). Digits on an arrow sum to the digit in the attached circle.","rulesClarified":"The whole grid is a Latin square: place the digits 1 to 9 once each in every row and column.\n\nThe grid is also subdivided into smaller Latin squares. Each may be any size except 1×1.\n\nAn N×N Latin square holds N different digits from 1 to 9. Each of those digits appears exactly once in every row and every column of that square.\n\nLatin squares of the same size may not have the same digit in the same relative position. For example, if one 4×4 Latin square has a 7 in its top-left corner, no other 4×4 Latin square may have a 7 in its top-left corner.\n\nArrows: the digits along an arrow add up to the digit in its circle. The circle's own cell is not part of its arrow.","solution":"379145682793514268937451826826793451682937145268379514514268937451826379145682793","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"LATIN SQUARES - Subdivide the grid into smaller latin squares, which can be any size except 1×1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"g21db32fo4","ctcId":2678,"ctcDifficulty":"MEDIUM","title":"Stepped Thermos","author":"Aad van de Wetering","rules":"Normal sudoku rules apply (ie place the digits 1-9, once each, into every row, column and 3x3 box.) Along a thermometer, digits must increase from the bulb end. Any horizontal or vertical threesome within a 3x3 box must not consist of three consecutive digits in some order.","solution":"541627893982531674376984521625493718137865942498172356813259467754316289269748135","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any horizontal or vertical threesome within a 3x3 box must not consist of three consecutive digits in some order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"nlvnqdwjsr","ctcId":2681,"ctcDifficulty":"HARD","title":"It Takes Two","author":"ChinStrap and Calvinball","rules":"Normal sudoku rules apply. Place the digits 1-9 once in every row, column, and box.\n\nTouching Twos:  Any cell that is orthogonally adjacent to a cell containing a digit 2 also has a value of 2.\n\nKiller Cages: Values in a cage sum to the value in the top left corner.  Digits may not repeat in a cage, but values may.\n\nNabner Lines: Values on a yellow line may not be the same or consecutive with any other value on the line.","solution":"459176238263589714817342569391758642748621395625493871974835126536214987182967453","constraints":["cage","custom","nabner-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Killer Cages: Values in a cage sum to the value in the top left corner.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Touching Twos:  Any cell that is orthogonally adjacent to a cell containing a digit 2 also has a value of 2.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"nabner-line","type":"nabner-line","variant":"modified","modifiers":[],"params":null,"note":"Nabner Lines: Values on a yellow line may not be the same or consecutive with any other value on the line.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]}]},{"id":"0tmwonfa8x","ctcId":2683,"ctcDifficulty":"HARD","title":"Rainbow Sandwich","author":"Myxo","rules":"• Normal Sudoku rules apply. Place the digits 1-9 in each row, column and box without repetition.\n• Rainbow Sandwiches: Shade some cells of the grid in two different colors, such that there is exactly one cell of each color in every row, column and box. Digits don't repeat within the same color. Clues outside the grid indicate the sum of the digits between the two colored cells in that row or column.","solution":"254837961867912345319654278572196834183475629946283157795361482431528796628749513","constraints":["custom","sandwich"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Rainbow Sandwiches: Shade some cells of the grid in two different colors, such that there is exactly one cell of each color in every row, column and box. Digits don't repeat within the same color. Clues outside the grid indicate the sum of the digits between the two colored cells in that row or column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"mm2lcvh3w1","ctcId":2684,"ctcDifficulty":"VERY HARD","title":"Below Zero","author":"James Kopp","rules":"Normal sudoku rules apply. \nOne digit from 1-9 (to be determined) has been rendered 'negative' and always has its negative value on any line or V that it appears on. \nRegion Sum: The 3x3 box borders divide blue lines into segments with digits that sum to the same value.\nGerman Whispers: Adjacent digits on a green line have values that differ by at least 5.\nCells separated by a V have values that sum to 5. Not all possible Vs are necessarily given.","solution":"163278549498561327725943186637185294981426753254739618516394872342817965879652431","constraints":["XV","custom","german-whispers","region-sum-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"Cells separated by a V have values that sum to 5.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"One digit from 1-9 (to be determined) has been rendered 'negative' and always has its negative value on any line or V that it appears on.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"German Whispers: Adjacent digits on a green line have values that differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Region Sum: The 3x3 box borders divide blue lines into segments with digits that sum to the same value.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"mdphj3roxm","ctcId":2685,"ctcDifficulty":"VERY HARD","title":"Crystalline Entity","author":"IcyFruit","rules":"Normal sudoku rules apply.\n\nA digit in a circle indicates the number of times that digit appears in either a circle or a square.\n\nDigits along an arrow sum to the digit in the attached circle.","solution":"514768923287391645369542781946127538175483296832956417658239174491875362723614859","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle indicates the number of times that digit appears in either a circle or a square.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"2ceyxwgi0w","ctcId":2686,"ctcDifficulty":"MEDIUM","title":"Arrow Of Arrows","author":"Aad van de Wetering","rules":"Normal sudoku rules apply (ie place the digits 1-9, once each, into every row, column and 3x3 box). Digits along an arrow must sum to the digit in that arrow's circle.","solution":"259684371163759824478231956791463285832195647645827139526948713387516492914372568","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9NpbhqmLH3","ctcId":2690,"ctcDifficulty":"HARD","title":"Snuggie","author":"Chefofdeath","rules":"Normal sudoku rules apply. Neighbouring digits along a green line must have a difference of at least 5. Digits along a purple line must form a set of non-repeating consecutive digits in any order. Digits separated by a V must sum to 5.","solution":"985713642361428957472695831546179328897236415213584796638951274124367589759842163","constraints":["XV","german-whispers","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"y3iozmwgi4","ctcId":2691,"ctcDifficulty":"VERY HARD","title":"String Theory","author":"Chefofdeath","rules":"Normal Sudoku rules apply.\n\nRenban: Digits on a purple (REN) line form a set of non-repeating consecutive digits in any order.\n\nEntropic Lines: Along a peach (ENT) line, no digit can be within 2 cells of a digit of the same entropic class [High (789), Middle (456), or Low (123)].","solution":"691752384573684192248913675762835419985146723134279856859361247416527938327498561","constraints":["entropic-line","renban"],"constraintFacts":[{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hc775p3w0o","ctcId":2693,"ctcDifficulty":"HARD","title":"The Lattice","author":"James Kopp","rules":"Normal sudoku rules apply.\nDigits along the gray lines must have values in between the values of the digits in the attached circles.\nThe sum of the digits along each red line is equal to the sum of the digits in the attached circles. \nCells separated by an V sum to five. Not all possible Vs are necessarily given.","solution":"486931257539672184712584936854196723923748561671253849267315498398427615145869372","constraints":["XV","between-line","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"between-line","type":"between-line","variant":"modified","modifiers":[],"params":null,"note":"Digits along the gray lines must have values in between the values of the digits in the attached circles.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits along each red line is equal to the sum of the digits in the attached circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"zmckmtohx1","ctcId":2694,"ctcDifficulty":"VERY HARD","title":"Ophidiophobia","author":"Marty Sears","rules":"Normal sudoku rules apply. Draw 4 snakes, moving orthogonally through the grid. Snakes may not move diagonally, branch, enter cages, cross themselves, or share cells with each other. But they may touch themselves and each other in any way they like.\n\nEach circled digit lies at one end of a snake, and indicates how many marked 3x3 boxes that snake visits.\n\nDigits in a cage sum to the clue in the corner (if one is given.)\n\nDigits separated by an X sum to 10.\n\nDigits separated by a black dot are in a 1:2 ratio (one is double the other.)\n\nEach snake follows ONE AND ONLY ONE of the four rules below (breaking all the other rules at least once.) Each snake follows a different rule.\n\n• ALTERNATING PARITY: Digits along the snake alternate between odd and even.\n• GERMAN WHISPER: Adjacent digits have a difference of at least 5.\n• PALINDROME: The snake reads the same in either direction.\n• NON-VENOMOUS: No pair of adjacent digits anywhere along the snake sum to exactly the 'venom value'.\n\nThe venom value (which is the same for any snake) is to be deduced.","solution":"874259136156347289923816574241785963638192745795463821517624398482931657369578412","constraints":["XV","cage","custom","german-whispers","kropki","palindrome"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw 4 snakes, moving orthogonally through the grid. Each circled digit lies at one end of a snake, and indicates how many marked 3x3 boxes that snake visits. Each snake follows ONE AND ONLY ONE of the four rules below (breaking all the other rules at least once.) • ALTERNATING PARITY: Digits along the snake alternate between odd and even. • NON-VENOMOUS: No pair of adjacent digits anywhere along the snake sum to exactly the 'venom value'.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c9","c11","c14"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]}]},{"id":"jfpmjqq6pw","ctcId":2695,"ctcDifficulty":"MEDIUM","title":"Augen auf beim Rat(t)enkauf!","author":"olima","rules":"Normal Sudoku rules apply.\nDutch/German whispers: Adjacent digits on orange/green lines differ by at least 4/5.\nRenban: Purple lines contain a set of distinct and consecutive digits in any order.\nThermos: Digits increase on a thermo from the bulb.\nParity: Adjacent digits on a red line differ in parity.\nKropki Pairs: Black dots indicate digits in a 1:2 ratio, white dots consecutive digits. Not all dots are necessarily shown.","solution":"361879542897542631452136789978413256614257893523698417246381975735924168189765324","constraints":["custom","dutch-whispers","german-whispers","kropki","renban","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Parity: Adjacent digits on a red line differ in parity.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"5idku2te8l","ctcId":2697,"ctcDifficulty":"MEDIUM","title":"Foggy Killer","author":"Visumation","rules":"Normal sudoku rules apply. All cages have a small “clue” in the leftmost cell of the top row that the cage occupies. Digits in a cage must not repeat and must sum to that cage’s clue. Digits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio (ie one digit must be double the other). The grid is partially covered in fog. The fog will clear from surrounding cells when a digit is placed correctly. No guessing is required.","solution":"347259186189346275265871394436798512918562437572413968723184659894635721651927843","fogLight":"R1C1,R1C2,R2C1,R3C1,R3C2,R3C4,R7C3,R8C3,R8C9,R9C8,R9C9,R4C7,R4C8","constraints":["cage","fog","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]}]},{"id":"4fimlq2cm2","ctcId":2699,"ctcDifficulty":"HARD","title":"Unique Under the Fog","author":"Visumation","rules":"Normal sudoku rules apply. 1) Digits on a purple Renban (RB) line form a non-repeating set of consecutive digits. 2) The 3x3 box borders divide blue Region Sum (RS) lines into segments with the same sum. 3) Neighbouring digits on a green German Whisper (GW) line must have a difference if at least 5. 4) Neighbouring digits on a red line (P) must alternate parity. 5) Digits separated by a black dot are in a 1:2 ratio (ie one digit must be double the other). 6) Digits separated by a white dot are consecutive. 7) Cells with a grey square contain an even digit. Each constraint type may contain no repeated digits anywhere in this puzzle. Eg. If one renban line contains a 5, then no other renban line may contain a 5. Additionally the grid is partially covered in fog. Placing a correct digit may clear fog somewhere in the grid.","rulesClarified":"Normal sudoku rules apply.\n\nPurple Renban lines: the digits on each purple line form a set of consecutive digits, with no digit repeated on that line.\n\nBlue Region Sum lines: the borders of the 3x3 boxes cut each blue line into segments. The segments of one blue line all have the same digit sum. The sum is not given.\n\nGreen German Whisper lines: neighbouring digits on a green line differ by at least 5.\n\nRed lines (P): neighbouring digits on a red line alternate between odd and even.\n\nBlack dot: the two digits either side of a black dot are in a 1:2 ratio, so one digit is double the other.\n\nWhite dot: the two digits either side of a white dot are consecutive.\n\nGrey square: the digit in a grey-square cell is even.\n\nEach of these seven constraint types may not repeat a digit across all of its cells. For example, if one purple Renban line contains a 5, no other purple Renban line may contain a 5.\n\nFog: the grid is partly covered in fog. Placing a correct digit may clear fog somewhere in the grid.","solution":"934271865126859743785364912412936578357128694869547321298715436671483259543692187","fogLight":"R1C3,R2C3,R3C3,R6C3,R7C3,R6C7,R6C8,R6C9,R6C4,R1C7,R2C7,R3C7","constraints":["custom","even","fog","german-whispers","kropki","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"4) Neighbouring digits on a red line (P) must alternate parity.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"sq3rfco0oe","ctcId":2700,"ctcDifficulty":"HARD","title":"Unique Under the Fog 4.0","author":"Visumation","rules":"Normal sudoku rules apply. A) Neighbouring digits on a green German Whisper (GW) line must have a difference of at least 5. B) Neighbouring digits on an orange Dutch Whisper (DW)  line must have a difference of at least 4. C) Digits on an arrow sum to the digit in that arrow’s circle. D) Along purple zipper (Z) lines, pairs of digits equidistant from the centre of the line have the same sum. On odd-length zipper lines, this sum is the value of the digit in the central position. E) Digits in a cage may not repeat and must sum to the clue in the top left of that cage (if given). Each constraint type may contain no repeated digits anywhere in this puzzle. Eg. If 2 appears on a GW line then no other 2 may appear on any GW line in the puzzle. Additionally the grid is partially covered in fog. Placing a correct digit may clear fog somewhere in the grid.","solution":"178265349965438712423197856592743681317586294846912537281374965659821473734659128","fogLight":"R9C1,R2C9,R1C9,R9C9,R9C2,R1C1,R2C1,R5C1,R6C1,R1C6,R1C5,R5C9,R6C9,R3C9,R9C4,R2C2","constraints":["arrow","cage","custom","dutch-whispers","fog","german-whispers","zipper-line"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each constraint type may contain no repeated digits anywhere in this puzzle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"3dnyh2rdg2","ctcId":2701,"ctcDifficulty":"MEDIUM","title":"Unique Under the Fog 5.0","author":"Visumation","rules":"Normal sudoku rules apply. \n\nConstraints: A) Digits on an arrow sum to the digit in that arrow’s circle; B) Neighbouring digits on a green German Whisper line (GW) must have a difference of at least 5; C) Digits on a purple Renban line (RB) form a non-repeating set of consecutive digits; D) Grey Ten-lines (T) must be divided into non-overlapping segments each of which sums to 10; E) Digits separated by a black dot are in a 1:2 ratio (ie one is double the other). Each constraint type may contain no repeated digits anywhere in the puzzle. Eg. If one renban line contains a 5, then no other renban line may contain a 5. \n\nDigits cannot repeat on the positive (SW-NE) diagonal. Digits cannot repeat on the negative (NW-SE) diagonal. Digits cannot repeat in cells with blue squares. Cells with an opaque grey circle contain odd digits. Additionally the grid is partially covered in fog. Placing a correct digit may clear fog somewhere in the grid.","solution":"153974286962853147847216593385467912694182735721395468479628351518739624236541879","fogLight":"R1C1,R2C2,R2C8,R1C9,R3C3,R5C4,R4C5,R5C6,R7C3,R8C2,R9C1,R7C7,R8C8,R9C9,R3C7","constraints":["arrow","custom","diagonal","fog","german-whispers","kropki","odd","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Constraints: A) Digits on an arrow sum to the digit in that arrow’s circle; B) Neighbouring digits on a green German Whisper line (GW) must have a difference of at least 5; C) Digits on a purple Renban line (RB) form a non-repeating set of consecutive digits; D) Grey Ten-lines (T) must be divided into non-overlapping segments each of which sums to 10; E) Digits separated by a black dot are in a 1:2 ratio (ie one is double the other).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7","c8"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"39lodiqwrj","ctcId":2702,"ctcDifficulty":"MEDIUM","title":"Bound Together","author":"Black_Doom","rules":"Normal sudoku rules apply.\nBetween Lines: digits along a line must have values strictly between the digits in the attached circles.","solution":"165789432742361985398542176413278659286953741957416328671835294539124867824697513","constraints":["between-line"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"pFpBDB3fpR","ctcId":2703,"ctcDifficulty":"MEDIUM","title":"Killer in the Mist","author":"Flinty","rules":"Normal sudoku rules apply. Most of the grid is covered in fog. Placing correct digits will clear the fog from the surrounding cells. No guessing is required. Digits in cages must sum to the small clue in the top-left corner of the cage. Digits cannot repeat within a cage. All cages are exactly 3 cells in size, and do not overlap / share cells.","solution":"487692135631574829925831647753126498892745316164389752316257984279418563548963271","fogLight":"R1C4,R1C5,R1C6,R2C4,R2C5,R2C6,R3C4,R3C5,R3C6","constraints":["cage","fog"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"20vtk6jbbz","ctcId":2704,"ctcDifficulty":"MEDIUM","title":"Thripple The Fun","author":"Flinty","rules":"Normal Sudoku Rules Apply.\n\nThripper Lines - They're like Zipper lines but there are three legs rather than two, where digits an equal distance from the centre of a Thripper line sum together to the same total, which is the value of the digit placed in the line's centre (highlighted with a bump).\n\nE.g. R3C1 + R3C2 + R5C1 = R4C1.","solution":"478561293592738641613249875935874162286195734147623589351487926864952317729316458","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Thripper Lines - They're like Zipper lines but there are three legs rather than two, where digits an equal distance from the centre of a Thripper line sum together to the same total, which is the value of the digit placed in the line's centre (highlighted with a bump).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"z1xpy7lrl5","ctcId":2705,"ctcDifficulty":"MEDIUM","title":"Thermal Equilibrium","author":"Flinty","rules":"1. Normal Sudoku Rules\n2. Digits may not repeat along the indicated diagonals.\n3. Thermometers:  Digits on a thermometer strictly increase from the bulb to the tip.\n4. The total value of all digits on each thermo is the same, and must be deduced by the solver.","solution":"123596487589714623674823951736945218241638795895172364918367542362451879457289136","constraints":["custom","diagonal","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"4. The total value of all digits on each thermo is the same, and must be deduced by the solver.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"0zhq0og7uz","ctcId":2706,"ctcDifficulty":"MEDIUM","title":"Outbreak!!","author":"Flinty","rules":"Normal sudoku rules apply (ie Place the digits 1-9 so that they do not repeat in any row, column, or 3x3 box). Zombie Cages:  Digits in cages must sum to the number in the initial top-left corner, and digits cannot repeat within a cage. ALL cages must grow by at least one orthogonally connected cell (and could grow by more than one!). Different cages cannot share cells.","solution":"329641578861573249745298316218956437597384621634127895953762184472815963186439752","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Zombie Cages:  Digits in cages must sum to the number in the initial top-left corner, and digits cannot repeat within a cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"ALL cages must grow by at least one orthogonally connected cell (and could grow by more than one!). Different cages cannot share cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"pdhr2gqlhe","ctcId":2707,"ctcDifficulty":"MEDIUM","title":"Dutch Flat Mates (Counting Circles)","author":"Flinty","rules":"Normal Sudoku rules apply.\n\nDigits may not repeat along the indicated diagonals.\n\n5s live in Dutch Flats = All 5s in the grid must have a '1' directly above it or a '9' directly below it. It may have both, but it doesn't need both.\n\nCounting Circles = If a digit is in a Circle, exactly that many instances of that digit must appear in Circles.\n5s live in Dutch Flats, they don't live in Circles.","solution":"193764582574128963682593417365971248749682351821345796417839625256417839938256174","constraints":["counting-circle","custom","diagonal"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"5s live in Dutch Flats = All 5s in the grid must have a '1' directly above it or a '9' directly below it.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"sz7ay5iw6l","ctcId":2708,"ctcDifficulty":"HARD","title":"Bliss","author":"Florian Wortmann","rules":"Normal sudoku rules apply (ie place the digits 1-9 once each in every row, column, and 3x3 box). \n\nThe 3x3 box borders divide each blue line into segments. The digits on each segment of the same line must sum to the same total. (Eg r2c7=r2c6+r3c5=r4c5).","solution":"534871926196452873287369451752983614841726395369145287978614532615238749423597168","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"2od7bk8x77","ctcId":2709,"ctcDifficulty":"MEDIUM","title":"Diamond Heist","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nEscape from the diamond vault by finding a path from the ventilation shaft (r9c9) to the door (r2c1). Your path may only move orthogonally, and may not visit any cell more than once. You may not pass through any coloured display plinths. Also, stepping on any floor tiles with an even digit will trigger the alarms, so don't do that.\n\nThe digit on a diamond equals the sum of the digits on all the keys that match its plinth colour (and letter). No two diamonds have the same digit.\n\nDiscover these diamond digits to steal them, and find the path to escape the room. You have 45 minutes!","solution":"846193752973542618125876934264719385517368249398425176752681493439257861681934527","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Escape from the diamond vault by finding a path from the ventilation shaft (r9c9) to the door (r2c1). You may not pass through any coloured display plinths. Also, stepping on any floor tiles with an even digit will trigger the alarms, so don't do that. The digit on a diamond equals the sum of the digits on all the keys that match its plinth colour (and letter). No two diamonds have the same digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c5","c6","c7"]}]},{"id":"dx1ord506o","ctcId":2710,"ctcDifficulty":"MEDIUM","title":"Staples","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Each grey line is a bulb-less thermometer.  Along a thermometer, digits must increase from the bulb to the tip. The solver must deduce where each thermometer's bulb is - it will always be at one end of the line.","solution":"214358697379642158865971324921587463438196275657423981596834712142765839783219546","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Each grey line is a bulb-less thermometer.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"pdywima58n","ctcId":2711,"ctcDifficulty":"HARD","title":"FEEDING FRIENDSy: It's Not Pea-sy Being Green","author":"sujoyku","rules":"Fill the grid with the digits 1-9 so that digits don't repeat in a row, column or 3x3 box (marked with dotted lines).\n______________________________\n\n#FRIENDSHIPGOALS:\nMarty! Croakz the Frog has noticed a delicious fly whirring around the pond; if that darn delicacy could only hold still for a second… help Croakz to chase the fly by drawing his path from water lily to water lily!\n\nThe path must not visit any cell more than once, cross itself or pass through any sharp rocks (the thick grey walls). As well as moving orthogonally, Croakz may move diagonally — if there's a 2x2 space in which to do so — but may never pass diagonally through rounded rock on the corner of a cell.\n______________________________\n\nWATER LILIES:\nThe grid contains nine (9) water lilies that must ALL be part of the path (of which you must determine the order). No water lily may contain the same digit.\n\nTWIGS: \nDigits separated by a brown, leafy twig sum to 5. Not all possible twigs have been given.\n\nLEAVES:\nDigits separated by a large, green leaf have a difference of at least 5. Not all possible leaves have been given.\n\nFROG EGG: \nDigits separated by a round frog egg have a 1:2 ratio (one is double the other). Not all possible frog eggs have been given.\n______________________________\n\nTRIALS and TRAILS:\nIn this test of friendship, water lilies divide Croakz' path into \"split pea\" segments.\n\nA segment between two water lilies must sum to a two-digit number formed by both digits. For example, if the water lilies containing the digits 1 and 2 are joined by a segment, that segment must sum to either 12 or 21.\n\nThe segment from Croakz' starting position to the first water lily must sum to the digit on that water lily — this includes the digit on Croakz' starting position itself. Good luck!","rulesClarified":"Normal sudoku rules apply: each row, column and 3x3 box (marked with dotted lines) holds the digits 1 to 9 once each.\n\nCroakz the Frog has noticed a delicious fly whirring around the pond. Help him chase it by drawing his path from water lily to water lily.\n\nThe path must not visit any cell more than once, cross itself, or pass through a sharp rock (the thick grey walls).\n\nCroakz moves orthogonally. He may also move diagonally, but only where there is a 2x2 space to do so, and he may never pass diagonally through a rounded rock on the corner of a cell.\n\nThe grid contains nine water lilies, and all nine must be on the path. You must find the order in which he visits them.\n\nNo water lily may contain the same digit.\n\nDigits on either side of a brown, leafy twig sum to 5. Not all possible twigs are given.\n\nDigits on either side of a large, green leaf have a difference of at least 5. Not all possible leaves are given.\n\nDigits on either side of a round frog egg have a 1:2 ratio: one is double the other. Not all possible frog eggs are given.\n\nThe water lilies divide Croakz' path into segments. A segment between two water lilies must sum to a two-digit number formed by both digits. For example, if the lilies containing 1 and 2 are joined by a segment, that segment must sum to 12 or 21.\n\nThe segment from Croakz' starting position to the first water lily must sum to the digit on that water lily. The digit on his starting cell is included in this sum.","solution":"386241759941576832572398416135782964264915387897634521629453178413867295758129643","constraints":["XV","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"Digits separated by a brown, leafy twig sum to 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c13"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Croakz the Frog has noticed a delicious fly whirring around the pond; if that darn delicacy could only hold still for a second… help Croakz to chase the fly by drawing his path from water lily to water lily! The grid contains nine (9) water lilies that must ALL be part of the path (of which you must determine the order). Digits separated by a large, green leaf have a difference of at least 5. A segment between two water lilies must sum to a two-digit number formed by both digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c10","c16","c24"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Digits separated by a round frog egg have a 1:2 ratio (one is double the other).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c19"]}]},{"id":"2n7efk46a1","ctcId":2713,"ctcDifficulty":"MEDIUM","title":"I'm Blue","author":"sujoyku","rules":"- Normal sudoku rules apply, i.e. each row, column, and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- Region Sum Lines: Box borders divide the blue lines into segments with the same sum. (Different lines may have different sums.)","solution":"145269783628371459793458162314596827579812634862734591437985216951627348286143975","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"fsq3l4xjbi","ctcId":2715,"ctcDifficulty":"HARD","title":"Big Waves (Are Coming)","author":"Mr.Menace","rules":"- Normal sudoku rules apply.\n- Lines are special region sum lines. Box borders divide the line in segments where digits on every segment on a line have the same sum. Additionally, digits on such line may not repeat.","solution":"674852931283691754915437628748265193362149875159378462521786349837924516496513287","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"44t9pol5x3","ctcId":2716,"ctcDifficulty":"MEDIUM","title":"Unique Under The Fog 3.0","author":"Visumation","rules":"Normal sudoku rules apply. \n\nEach unique clue type listed below cannot contain more than one instance of each of the digits 1-9. \n\nClue types: a) Neighbouring digits on a green German Whisper (GW) line must have a difference of at least 5; b) Every set of three sequential cells on a mint modular (MO) line must contain one digit from (1,4,7), one digit from (2,5,8), and one digits from (3,6,9); c) Neighbouring digits on an orange Dutch Whisper (DW) line must have a difference of at least 4. (DW); d) Neighbouring digits on a red parity (P) line must alternate parity (odd/even); e) Digits in a cage may not repeat and must sum to the clue in the top left of that cage (if given); f) Digits separated by a black dot are in a 1:2 ratio (ie one digit is double the other); g) Cells with a grey square contain an even digit; h) Cells with a grey circle contain an odd digit.\n\nAdditionally the grid is partially covered in fog. Placing a correct digit may clear fog somewhere in the grid.","solution":"246518973538927164197634528872365419364791285951482637415876392723149856689253741","fogLight":"R5C5,R5C2,R2C5,R5C8,R8C5,R8C2,R9C8,R7C1","constraints":["cage","custom","dutch-whispers","even","fog","german-whispers","kropki","modular-line","odd"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each unique clue type listed below cannot contain more than one instance of each of the digits 1-9. (DW); d) Neighbouring digits on a red parity (P) line must alternate parity (odd/even); e) Digits in a cage may not repeat and must sum to the clue in the top left of that cage (if given); f) Digits separated by a black dot are in a 1:2 ratio (ie one digit is double the other); g) Cells with a grey square contain an even digit; h) Cells with a grey circle contain an odd digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"odd","type":"odd","variant":"modified","modifiers":[],"params":null,"note":"(DW); d) Neighbouring digits on a red parity (P) line must alternate parity (odd/even); e) Digits in a cage may not repeat and must sum to the clue in the top left of that cage (if given); f) Digits separated by a black dot are in a 1:2 ratio (ie one digit is double the other); g) Cells with a grey square contain an even digit; h) Cells with a grey circle contain an odd digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"pc6ejr0nze","ctcId":2717,"ctcDifficulty":"MEDIUM","title":"Dutch Flat Mates: Pick-up Sticks","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nDUTCH FLAT MATES:\nEvery 5 in the grid must have a 1 directly above it or a 9 directly below it. It may have both, but it doesn't need both.\n\nDYNAMIC FOG:\nThe grid is covered in fog. Entering correct digits might clear fog somewhere in the grid.\n\nPICK-UP STICKS:\nA stick always has a lower total (the sum of its digits) than any stick which lies on top of it. Sticks that aren't grey have an additional rule:\n\n• A yellow ENTROPIC stick must contain one low digit (1, 2 or 3), one medium digit (4, 5 or 6), and one high digit (7, 8 or 9.)\n• A teal MODULAR stick must contain one digit from each of the sets (1,4,7), (2,5,8), and (3,6,9).\n• A pink RENBAN stick must contain a set of consecutive digits, arranged in some order.\n• Along an orange DUTCH WHISPER stick, adjacent digits on must have a difference of at least 4.\n• Along a red PARITY STICK, digits must alternate between odd and even.","solution":"678532914432916758519478623924153876781694235365287149847329561253861497196745382","fogLight":"R1C1,R2C1,R3C1,R3C2,R3C3,R2C3,R1C3,R1C2,R2C2","constraints":["custom","dutch-whispers","entropic-line","fog","modular-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every 5 in the grid must have a 1 directly above it or a 9 directly below it. A stick always has a lower total (the sum of its digits) than any stick which lies on top of it. • Along a red PARITY STICK, digits must alternate between odd and even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c9","c15"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]}]},{"id":"9c6on7okjr","ctcId":2718,"ctcDifficulty":"MEDIUM","title":"Friday The 13th (1980-2025)","author":"Jodawo","rules":"Normal Sudoku rules apply.\n\nKiller Cage: The numbers in the cage must sum to the total given in the upper left corner.\n\nVariant Sandwich Clues: The clues are the sum of the digits between the crusts. The crusts are determined by the row or column the clue is. For example, if the clue is in row 2 then the sandwich crusts are 2 and 8. If the clue is in column 7 then the sandwich crusts are 7 and 3. (Crust will sum to 10)\n\n***All sandwich filling are in their own Killer Cages***","solution":"876531942941276835235849716762384159453917628189625473594763281627158394318492567","constraints":["cage","custom","sandwich"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"***All sandwich filling are in their own Killer Cages***","evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"nk5f0ylrde","ctcId":2720,"ctcDifficulty":"MEDIUM","title":"X, Y and Z???","author":"Fenners","rules":"Normal 9x9 Sudoku rules apply.\n\nKiller Cages: Digits in cages with the same letter sum to the same value. These values are to be determined by the solver.\n\nKropki Dots: Digits separated by a white dot are consecutive.\n\nRenban Lines: Digits on a purple line form a set of non-repeating consecutive digits in any order.","solution":"932178465864953172157642389741286593596314827283597614379461258415829736628735941","constraints":["cage","kropki","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"atvcydetiu","ctcId":2721,"ctcDifficulty":"HARD","title":"Killer at large in the fog: #3","author":"Fenners","rules":"Hello again detective, it's been a while. We've been withholding this letter from the Zodiac for a while now, but even our best cryptographers don't know how to get started on it! Here are the rules we have, now it's over to you.\n\nNormal 9x9 Sudoku rules apply.\n\nDynamic Fog: The letter has been partially smudged this time and digits may or may not reveal more clues.\n\nArrows: Digits on the tail of an arrow sum to the digit in the bulb. All bulbs are visible from the start.\n\nIf a line heads towards a cell, it enters that cell. They are snipped so they can't been seen through smudge.\n\nGerman Whispers: Adjacent digits on a green line must differ by at least 5.\n\nParity Line: Adjacent digits on a red line must have an even and odd digit.\n\nEntropic Line: For every 3 adjacent digits on a peach line, one must be from the set {1, 2, 3}, one from {4, 5, 6} and one from {7, 8, 9}\n\nModular Line: For every 3 adjacent digits on a teal line, one must be from the set {1, 4, 7}, one from {2, 5, 8} and one from {3, 6, 9}.\n\nRegion Sum Line: Digits on a blue line must sum to the same value for each box it enters.\n\nFinally, the killers name will be revealed by the digits in \ncells with outlined boxes. Our heads were scrambled by this one! I Marvel at how letters could possibly be equated to digits???\n\nGood luck!","solution":"836147592721985634459623178582376941697412385314859726173264859265798413948531267","fogLight":"R1C1,R1C3,R1C5,R1C7,R1C9,R2C2,R2C4,R2C6,R2C8,R3C1,R3C3,R3C5,R3C7,R3C9,R4C2,R4C4,R4C6,R4C8,R5C1,R5C3,R5C5,R5C7,R5C9,R6C2,R6C4,R6C6,R6C8,R7C1,R7C3,R7C5,R7C7,R7C9,R8C2,R8C4,R8C6,R8C8,R9C1,R9C3,R9C5,R9C7,R9C9","constraints":["arrow","custom","entropic-line","fog","german-whispers","modular-line","region-sum-line"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Parity Line: Adjacent digits on a red line must have an even and odd digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]}]},{"id":"fl0kwpnejm","ctcId":2722,"ctcDifficulty":"MEDIUM","title":"Restricted? Where?","author":"Fenners","rules":"Normal 9x9 Sudoku Rules apply.\n\nAntiKnight: Digits a chess knights move apart cannot contain the same digit.\n\nRegion Sum: Digits on a blue line must sum to the same value each time the line enters and exits a 3x3 box.\n\nKropki: Digits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. Not all dots are given.","solution":"453718269218965473679234185742381956981652734536497812364879521895126347127543698","constraints":["antiknight","kropki","region-sum-line"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"5b9zqb4idr","ctcId":2723,"ctcDifficulty":"MEDIUM","title":"19 Crimes","author":"Fenners","rules":"Normal Sudoku rules apply.\n\nKiller Cages: Digits in cages do not repeat and sum to value in the upper left corner. All cages sum to 19.\n\nMarked diagonals: Digits cannot repeat along the positive and negative diagonal, marked with a blue line.\n\nGerman Whispers: Adjacent digits on a green line must differ by at least 5.","solution":"689237541571948362423516798192874653345691287867325419938462175754183926216759834","constraints":["cage","diagonal","german-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"imlvnekher","ctcId":2724,"ctcDifficulty":"MEDIUM","title":"Hidden Connection","author":"Fenners","rules":"Normal 9x9 Sudoku rules apply.\n\nKiller Cages: Digits in a cage sum to the clue in the top left corner.\n\nOn an index line, the digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears. Eg: 3214 would be a valid line; the 1st digit, 3, indicates that the 3rd digit is a 1, and so on.","solution":"516938742293174856784652139362781495859426371147395628438269517621547983975813264","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On an index line, the digit in the Nth cell along the line (starting from the diamond) indicates the position along the line where the digit N appears.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"jfyralmfoe","ctcId":2725,"ctcDifficulty":"HARD","title":"Breadcrumbs","author":"Belamis","rules":"Normal sudoku rules apply. \nThe grid is partially covered in fog. The first correctly placed digit on each constraint will remove fog from other cells.\nEach constraint type may contain no repeated digits anywhere in the puzzle. E.g. If one cell on a parity line contains a 5, then no other cell on a parity line may contain a 5. \nConstraints: \na) Along a red line, adjacent digits must alternate between odd and even; \nb) Digits do not repeat in cages, and sum to the small clue in the top left corner if given; \nc) digits in cells separated by a black dot have a 1:2 ratio (ie one is double the other); \nd) pairs of digits equidistant from the centre of a lavender zipper line must sum to the digit in the middle of that line (noted by a dot); \ne) digits along a thermometer increase from bulb to tip; \nf) a cell with arrows pointing inward must be smaller than all other cells that share its edge; and \ng) a digit in a grey square is even. \nEach listed constraint type appears at least once in the puzzle.","solution":"148793265352846971796251438983462157421375896567189342214537689635918724879624513","fogLight":"R6C2,R6C9,R8C9,R4C7,R5C2","constraints":["cage","custom","even","fog","kropki","minimum","thermometer","zipper-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each constraint type may contain no repeated digits anywhere in the puzzle. a) Along a red line, adjacent digits must alternate between odd and even;","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c7"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"minimum","type":"minimum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"rge5pbwzk4","ctcId":2726,"ctcDifficulty":"MEDIUM","title":"Pick-up Sticks (Blue)","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\n3x3 box borders divide a blue stick into segments. Each segment along a stick has the same sum. This segment sum can be different for different sticks.\n\nA stick always has a lower total (the sum of ALL its digits) than any stick which lies on top of it.","solution":"691342578724851693538967421183796245247135869965428137476513982812679354359284716","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A stick always has a lower total (the sum of ALL its digits) than any stick which lies on top of it.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"gx4a6r7xzq","ctcId":2727,"ctcDifficulty":"HARD","title":"Pointer Arrow Parity Loop","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nDraw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally.\n\nThe loop acts as a parity line: digits along the loop must alternate between even and odd digits.\n\nLoop Pointer Arrows:\n-- Digits along an arrow must sum to the digit in that arrow's bulb, and all bulbs are on the loop.\n-- Additionally, arrow tips point towards a cell containing the digit within the arrow's bulb, and this cell with the pointed-to digit is also on the loop.\n-- The digit in the arrow tip indicates the distance from the arrow tip to the pointed-to cell.  There may be other instances of the same digit between this cell and the arrow tip.","rulesClarified":"Normal Sudoku rules apply.\n\nDraw one loop: a one-cell-wide path of orthogonally connected cells that closes on itself. The loop may not touch itself, not even diagonally.\n\nParity: along the loop, digits alternate between even and odd. Each cell on the loop is the opposite parity from the cells next to it on the loop.\n\nPointer arrows: each arrow starts at a circled cell, its bulb, and runs through the cells drawn for that arrow to its tip. The bulb is on the loop.\n\nDigits along an arrow sum to the digit in that arrow's bulb.\n\nThe arrow tip points towards a cell that contains the same digit as the bulb, and that cell is on the loop. The digit in the arrow tip is the distance, in cells, from the tip to that cell. Other cells with the same digit as the bulb may lie between the tip and that cell.","solution":"856973214371824695429561378513498726298637451647152983764285139935716842182349567","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally. The loop acts as a parity line: digits along the loop must alternate between even and odd digits. -- Additionally, arrow tips point towards a cell containing the digit within the arrow's bulb, and this cell with the pointed-to digit is also on the loop. -- The digit in the arrow tip indicates the distance from the arrow tip to the pointed-to cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c7","c8"]}]},{"id":"g6riporqv1","ctcId":2728,"ctcDifficulty":"MEDIUM","title":"Co-op","author":"Math Pesto","rules":"Normal sudoku rules apply. Digits on an arrow sum to the digit in its circle.","solution":"925831476176924853834576291517463928348192765692785134763248519459317682281659347","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"xd3kuyn90z","ctcId":2729,"ctcDifficulty":"MEDIUM","title":"Cloister","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply.\n\nCHESS SUMS - A digit on a chess piece is the sum of the digits in cells the chess piece could move to in a single move. Bishops and kings can only move to cells in the same 3x3 box, but knights can jump into other boxes.\n\nDYNAMIC FOG - Fog covers part of the grid. Placing a correct digit will clear fog.","solution":"281349675476258139593716842847192356132564798659837421328675914915483267764921583","fogLight":"R9C1,R9C2,R8C2,R1C9,R2C9,R2C8,R7C3,R9C3,R8C4,R8C3,R7C4,R6C4,R9C4,R7C5,R6C5,R5C5,R9C5,R8C5,R8C6,R7C6,R6C7,R5C7,R4C7,R3C7,R4C6,R5C6,R6C6,R9C6,R9C7,R7C7,R3C8,R4C8,R5C8,R6C8,R7C8,R8C7,R9C8,R8C8,R3C9,R4C9,R5C9,R6C9,R7C9,R8C9,R9C9","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"CHESS SUMS - A digit on a chess piece is the sum of the digits in cells the chess piece could move to in a single move.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"8i5xr72ala","ctcId":2730,"ctcDifficulty":"MEDIUM","title":"Some Like It Hot","author":"James Kopp","rules":"Normal sudoku rules apply. Digits increase from the bulb to the end of each thermometer.","solution":"568917423471236985923458761712369854859724136634581279195672348347895612286143597","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"d7x6vy9n5s","ctcId":2731,"ctcDifficulty":"MEDIUM","title":"Is that a 3 in the corner?","author":"James Kopp","rules":"Normal sudoku rules apply. \nDigits along the gray lines must have values in between the values of the digits in the attached circles.\nAdjacent digits in each row of the puzzle have a difference of at least four.","solution":"948372615372615948615948372261594837837261594594837261159483726483726159726159483","constraints":["between-line","custom"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"modified","modifiers":[],"params":null,"note":"Digits along the gray lines must have values in between the values of the digits in the attached circles.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent digits in each row of the puzzle have a difference of at least four.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"uhbdfuaf2r","ctcId":2732,"ctcDifficulty":"HARD","title":"Top Right Boi","author":"Scojo","rules":"Oh no! Top Right Boi has become stranded far from his home in the top right corner of the grid! He must make his way from his starting location in the bottom left (ew!) all the way home. Luckily for Top Right Boi, he possesses a special power that will help him on his journey...\n\nNormal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nTop Right Boi's Path: Draw a path of orthogonally connected cells from Top Right Boi in row 9 column 1 to his home in row 1 column 9. The path may not touch itself, not even diagonally.\n\nOther than his starting position, Top Right Boi MUST NEVER visit the bottom left corner of any 3x3 box. Conversely, Top Right Boi MUST visit the top right corner of every 3x3 box before returning home. The 9 top right corner cells in the grid must all contain different digits. As the bottom left corner cells are lawless wastelands, there is no such restriction on their digits.\n\nAny cell Top Right Boi visits will have it's value modified to be equal to Top Right Boi's current value, regardless of the digit in that cell. When Top Right Boi visits a cell in the top right corner of a 3x3 box, his value changes to be the digit in that cell, and will remain as that value until the next top right corner cell he visits (For clarity, this means that all top right corner cells have their digits as their values). Because Top Right Boi is beginning his journey from the horrid bottom left of the grid, his value will be 0 until he reaches the first top right corner cell along the path. Cells not on the path retain the value of their digits.\n\nCages: Values in a cage must sum to the number in the top right corner of the cage. Digits may not repeat within a cage, but values may.\n\nKropki: If two values are separated by a black dot, one is double the other. If two values are separated by a white dot, they are consecutive.\n\nXV: If two values are separated by an X, they sum to 10. If two values are separated by a V, they sum to 5.\n\nNot all possible Kropkis or XVs are necessarily shown.","solution":"176489523942513876538276419654328197391657248827194365485961732219735684763842951","constraints":["XV","cage","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"XV: If two values are separated by an X, they sum to 10. If two values are separated by a V, they sum to 5.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c20","c21"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c16"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Top Right Boi's Path: Draw a path of orthogonally connected cells from Top Right Boi in row 9 column 1 to his home in row 1 column 9. Other than his starting position, Top Right Boi MUST NEVER visit the bottom left corner of any 3x3 box. Conversely, Top Right Boi MUST visit the top right corner of every 3x3 box before returning home. The 9 top right corner cells in the grid must all contain different digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c8","c9","c10"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Kropki: If two values are separated by a black dot, one is double the other. If two values are separated by a white dot, they are consecutive.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c18","c19"]}]},{"id":"yao1biwcxx","ctcId":2734,"ctcDifficulty":"HARD","title":"Knight Box","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Cells that share a border never contain consecutive digits. In every 3x3 box, digits separated by a single knight's move (in chess) have a greatest common divisor of 1. (So, for example, 2 and 4 could not be so separated as they have a divisor of 2.)","solution":"742836951368591427195274683951742836427368519683915274836159742519427368274683195","constraints":["custom","non-consecutive"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In every 3x3 box, digits separated by a single knight's move (in chess) have a greatest common divisor of 1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7v7lat2oxd","ctcId":2735,"ctcDifficulty":"MEDIUM","title":"Primal Roots","author":"Matt Tressel","rules":"Normal sudoku rules apply. Digits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. Not all possible dots are given. Prime digits (2,3,5,7) must NOT be orthogonally adjacent to each other. Square roots with single digit perfect squares MUST be orthogonally adjacent to their square. (all 2’s must be adjacent to a 4, and all 3’s must be adjacent to a 9)","rulesClarified":"Normal sudoku rules apply.\n\nDigits separated by a white dot are consecutive: they differ by exactly one.\n\nDigits separated by a black dot are in a 1:2 ratio: one is double the other.\n\nNot all possible dots are given. A place with no dot gives no information.\n\nPrime digits (2, 3, 5 and 7) may not sit orthogonally next to each other.\n\nEach 2 must sit orthogonally next to a 4, and each 3 must sit orthogonally next to a 9. This rule covers only 2s and 3s. It does not require a 4 or a 9 to touch a 2 or a 3.","solution":"518624793624793851397851264831562479762419385459387126983176542176245938245938617","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Prime digits (2,3,5,7) must NOT be orthogonally adjacent to each other. Square roots with single digit perfect squares MUST be orthogonally adjacent to their square. (all 2’s must be adjacent to a 4, and all 3’s must be adjacent to a 9)","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"m8j8rRQbTj","ctcId":2736,"ctcDifficulty":"MEDIUM","title":"Three Wishes","author":"Matt Tressel","rules":"Normal sudoku rules apply. Orthogonally connected cells within each region must differ by at least 3. Orthogonally connected cells between regions must differ by at least 4. The central digit in each 3x3 region is less than or equal to its region number.  (Regions are numbered in normal reading order.)","solution":"369471582714825936258369471693714825147258369582693714936147258471582693825936147","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Orthogonally connected cells within each region must differ by at least 3. Orthogonally connected cells between regions must differ by at least 4. The central digit in each 3x3 region is less than or equal to its region number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]}]},{"id":"qzcc0tx1yd","ctcId":2737,"ctcDifficulty":"HARD","title":"Kill Or Quads","author":"Matt Tressel","rules":"Normal sudoku rules apply.\n\nEach marked circle is either a Killer Quad OR a normal Quadruple, with each to be determined by the solver. \n\nKiller Quad: Digits surrounding a circle must sum to the indicated total.\n\nQuadruple: Digits marked in a circle must appear in its surrounding cells.","rulesClarified":"Normal sudoku rules apply.\n\nEach marked circle is either a Killer Quad or a Quadruple. You decide which kind each circle is.\n\nA circle sits at the shared corner of a 2x2 block of four cells. Those four cells are its surrounding cells.\n\nKiller Quad: the digits in its four surrounding cells sum to the number in the circle.\n\nQuadruple: each digit marked in the circle must appear among its four surrounding cells.","solution":"493178652861325794752649381279486135316957428548231967187593246925764813634812579","constraints":["custom","quadruple"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each marked circle is either a Killer Quad OR a normal Quadruple, with each to be determined by the solver. Killer Quad: Digits surrounding a circle must sum to the indicated total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"3gkoee7rau","ctcId":2738,"ctcDifficulty":"HARD","title":"Hyperextension","author":"Matt Tressel and ChinStrap","rules":"Normal sudoku rules apply.\n\nSilent Serial Killer: Digits may not repeat in cages. If the sum of a cage is a 1-digit number, that number must be in the cell pointed at by the cage's northwest corner. If the sum is a 2-digit number, it must be in the domino formed by that cell and the one to its left. (Example: if the sum of the cage in Box 3 was 9, then r1c6 would be 9. If it's sum was 12, then r1c5 would be 1 and r1c6 would be 2)\n\nTentropy Lines: Every set of 4 adjacent digits on a peach line must contain a digit from each of the X-pair (ten-pair) subsets of {1,9}, {2,8}, {3,7}, and {4,6}. A 5 may not appear on a tentropy line. Digits on a line may repeat if allowed by other rules.","solution":"758316294614982357923547681289461735367895412541723968176238549892654173435179826","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Tentropy Lines: Every set of 4 adjacent digits on a peach line must contain a digit from each of the X-pair (ten-pair) subsets of {1,9}, {2,8}, {3,7}, and {4,6}. A 5 may not appear on a tentropy line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8"]}]},{"id":"v3f32yjc6a","ctcId":2739,"ctcDifficulty":"HARD","title":"Highball","author":"Matt Tressel","rules":"Normal sudoku rules apply, and all clues are standard.\n\nGerman Whisper Lines: Adjacent digits along a green line must differ by at least 5.\n\nKiller Cages: Digits in a cage must sum to the value indicated in the top left corner.","solution":"168453927957182643342679581489231765523796418671845392295368174834917256716524839","constraints":["cage","german-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"a1yiqbbfh2","ctcId":2740,"ctcDifficulty":"VERY HARD","title":"Penumbra","author":null,"rules":"Normal Sudoku rules apply.\n\nShadow sums: A clue outside the grid gives the sum of all numbers in that row/column which are smaller than the number immediately before them, when reading from the direction of the clue.","rulesClarified":"Normal Sudoku rules apply.\n\nShadow sums. Each clue sits outside the grid, beside one row or one column, and gives the sum of some of the digits in that line. A clue above or below the grid belongs to the column it sits in. A clue left of or right of the grid belongs to the row it sits beside.\n\nRead that row or column starting from the side the clue is on. A digit counts when it is smaller than the digit immediately before it in that reading. The clue is the sum of the counted digits.","solution":"319564872752839146468172539974681325825493617631725498147256983583917264296348751","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shadow sums: A clue outside the grid gives the sum of all numbers in that row/column which are smaller than the number immediately before them, when reading from the direction of the clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"r6zqoxq6gz","ctcId":2741,"ctcDifficulty":"HARD","title":"Twisties","author":"BremSter","rules":"• Normal Sudoku rules apply. Place the digits 1-9 in each row, column and box without repetition.\n• Sandwich: The numbers outside the grid give the sum of the digits between the 1 and the 9 in that row or column.\n• Renban: Digits placed on purple lines must be a non-repeating set of consecutive digits, in any order.","solution":"561389274278154639493276158745693812986712543312845796859421367624537981137968425","constraints":["renban","sandwich"],"constraintFacts":[{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"k9rhoxxjvs","ctcId":2742,"ctcDifficulty":"HARD","title":"Counterproductive","author":"Marty Sears","rules":"Normal sudoku rules apply. A cage's product (the result of multiplying its digits together) exactly equals the number of cages with that product. Note: if a cage has only one digit, that digit is considered to be the cage's product.","solution":"318549726426873591759261438632984157891657342574312689943126875187495263265738914","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A cage's product (the result of multiplying its digits together) exactly equals the number of cages with that product.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"yvpjt47o16","ctcId":2743,"ctcDifficulty":"MEDIUM","title":"Because Two π's Are Better Than One","author":"Thomas Snyder","rules":"Standard Sudoku rules: Insert a number from 1 to 9 into each cell so that no number repeats in any row, column, or bold region.\n\nSome thermometer shapes are in the grid; numbers must be strictly increasing from the round bulb to the flat end.\n\nSome arrow shapes are in the grid; the sum of the numbers along the path of each arrow must equal the number in the circled cell. Numbers can repeat within an arrow shape.\n\nThe coloring is strictly to emphasize the theme.\n\nOriginally at https://gmpuzzles.com/blog as Wedding Gift #3","solution":"819542673526173498347698125938261547274935816165784239782316954491857362653429781","constraints":["arrow","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"8b7y7246mu","ctcId":2744,"ctcDifficulty":"MEDIUM","title":"Meta Unique-ish","author":"Fenners","rules":"Normal sudoku rules apply.\n\nMeta Unique-ish: No two instances of the same constraint type may share digits. So, although digits may repeat on a clue, they may NOT repeat across different occurrences of that clue type. Eg if an arrow has the digit X, X may repeat along that arrow, but X may not appear on any other arrow.\n\nClue types: \n\n1) Quadruples: In an orange circle, the question mark contains the set of all the (possibly repeating) digits appearing in the surrounding cells.\n\n2) Renban: Digits on a purple line form a set of non-repeating consecutive digits, in any order.\n\n3) Arrows: Digits along an arrow sum to the digit in that arrow's circle. \n\n4) White dot: Digits separated by a white dot are consecutive. \n\n5) Black dot: Digits separated by a black dot are in a 1:2 ratio (ie one digit is double the other).","solution":"981465732672839541345712689237581964869347125154926378713298456526174893498653217","constraints":["arrow","kropki","quadruple","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9","c10"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"xc7i2ozu0f","ctcId":2745,"ctcDifficulty":"MEDIUM","title":"Cheese, Wine & Bread","author":null,"rules":"Normal sudoku rules apply. All thermometers are slow thermos. Digits must increase or stay the same on each step from the bulb to the tip.","solution":"753981462482567931961324578614253789579148326238679145126735894345896217897412653","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"All thermometers are slow thermos.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"j6e5jfpw08","ctcId":2746,"ctcDifficulty":"HARD","title":"Given But Hidden","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nSome cells in the grid contain a given digit, and these have all been circled. A circled given digit indicates how many times that digit appears as a circled given digit in the grid.\n\nUnfortunately, most of these given digits are obscured by fog. Entering a correct digit will clear the fog in that cell, and maybe other cells too. No guessing is necessary.\n\nA black dot sits between two digits where one is double the other.\n\nThe two digit number to be discovered in the blue frame (reading left to right) will indicate the total number of circled given digits that exist in the grid.","rulesClarified":"Normal sudoku rules apply.\n\nSome cells in the grid contain a given digit, and each of these cells is circled. Most of these given digits are obscured by fog.\n\nEntering a correct digit clears the fog in that cell, and may clear the fog in other cells too. No guessing is necessary.\n\nA circled given digit tells you how many circled given digits in the whole grid show that same digit. The cell itself is counted.\n\nA black dot sits between two digits where one is double the other.\n\nThe two-digit number to be discovered in the blue frame, read left to right, gives the total number of circled given digits in the grid.","solution":"652317489793845126184962735219758364876134592435296871368521947527489613941673258","fogLight":"R9C8,R9C7,R9C6,R9C5,R5C1,R4C1,R3C1,R2C1,R6C1,R7C1,R9C4,R9C3,R8C1,R9C2,R1C2,R1C3,R1C4,R1C5,R1C6,R1C7,R1C8,R2C9,R3C9,R4C9,R5C9,R8C9,R7C9,R6C9,R5C5,R5C6","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A circled given digit indicates how many times that digit appears as a circled given digit in the grid. The two digit number to be discovered in the blue frame (reading left to right) will indicate the total number of circled given digits that exist in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c8"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"78ps2l3dox","ctcId":2747,"ctcDifficulty":"HARD","title":"10 x 10 = 100","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Each of the ten lines contains digits that sum to 10.","solution":"413629758867351429952847136629175843185934672734286915241568397578493261396712584","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each of the ten lines contains digits that sum to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"yvfa2jpnew","ctcId":2748,"ctcDifficulty":"VERY HARD","title":"Transfer Right By 2","author":"Justin Vitanza","rules":"Normal Sudoku rules apply.\n\nMod-3 Rows: Each row in the puzzle is a mod-3 line. That is, any set of three horizontally adjacent digits must contain one digit from (1,4,7), one digit from (2,5,8), and one digit from (3,6,9).\n\n159 Indexing: Digits in columns 1, 5, and 9 indicate the column in which the digits 1, 5, or 9 (respectively) appears in that row.\n\nRenban: Each purple line contains a set of consecutive digits in any order.\n\nLittle Killer: Digits along the positive diagonal sum to a value that is (strictly) less than 24.","solution":"219546873846273519573819246768492135195738462432165798984357621627981354351624987","constraints":["custom","little-killer","modular-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"159 Indexing: Digits in columns 1, 5, and 9 indicate the column in which the digits 1, 5, or 9 (respectively) appears in that row.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"2301tf6q1e","ctcId":2749,"ctcDifficulty":"MEDIUM","title":"The Mismatch","author":"Cane_Puzzles","rules":"Classic Sudoku rules apply.\n\nThe gray regions contain the same digits in the same arrangement without rotation or reflection.\n\nThe digits in a cage sum to the number given in the cage.","solution":"169432857827659314354817926248391765673548192591276483436985271912763548785124639","constraints":["cage","clone"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"fgtl60ohu1","ctcId":2750,"ctcDifficulty":"MEDIUM","title":"Indexpennant Day","author":"rockratzero","rules":"Normal Sudoku rules apply.\n-Region Sum Line: 3x3 box borders divide the blue line into segments. Digits on each segment along the blue line have the same sum. \n-Column Indexers (red colored cells in columns 3,5,7). The digit in a red cell gives the placement of that cell's column number in its row. (i.e. if row 6, column 5 contained a 9, that would place a 5 in row 6, column 9.)\n-Row Indexers (blue colored cells in columns 2,4,6). The digit in a blue cell gives the placement of that cell's row number in its column. (i.e. if row 6, column 4 contained a 9, that would place a 6 in row 9, column 4.)\n-Odd Stars. Digits in cells with Stars are Odd.","solution":"963872541124365879578914236756423198832791465419658723687549312245136987391287654","constraints":["custom","odd","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digit in a red cell gives the placement of that cell's column number in its row. (i.e. if row 6, column 5 contained a 9, that would place a 5 in row 6, column 9.) The digit in a blue cell gives the placement of that cell's row number in its column. (i.e. if row 6, column 4 contained a 9, that would place a 6 in row 9, column 4.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c7"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"r38cxr9nhu","ctcId":2751,"ctcDifficulty":"HARD","title":"Foggy Expeadition","author":"SamuPiano","rules":"𝗦𝘂𝗱𝗼𝗸𝘂: Normal sudoku rules apply.\n𝗙𝗼𝗴: The grid is partially covered in fog. Placing correct digits will clear fog from surrounding cells.\n𝗖𝗮𝘃𝗲: Shade some cells such that all unshaded cells form a single orthogonally connected region and all shaded cells are connected to the edge of the grid. Digits in circles either give the size of the shaded region in which it lies or the total number of unshaded cells which can be seen in all directions from the unshaded circled cell, including the cell itself. Shaded cells block vision.\n𝗟𝗶𝗻𝗲 𝗖𝗼𝘂𝗻𝘁: Some circled cells are endpoints of lines in the grid. All lines move orthogonally. Lines do not cross or branch, except at circled cells. The digit in a circle gives the total number of cells along each line attached to the circle of the same shading as the circled cell, including the endpoints.\n𝗦𝗽𝗹𝗶𝘁 𝗣𝗲𝗮𝘀: Digits along a line strictly between two circles must sum to a two-digit number, where the tens digit is in one circle and the ones digit is in the other.\n𝗫𝗩: Digits separated by an X sum to 10. Digits separated by a V sum to 5. Not all X or V are given.","solution":"812964573594173682367582419473628195189457236625319748931245867248796351756831924","fogLight":"R1C2,R3C1","constraints":["XV","custom","fog"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"𝗖𝗮𝘃𝗲: Shade some cells such that all unshaded cells form a single orthogonally connected region and all shaded cells are connected to the edge of the grid. Digits in circles either give the size of the shaded region in which it lies or the total number of unshaded cells which can be seen in all directions from the unshaded circled cell, including the cell itself. The digit in a circle gives the total number of cells along each line attached to the circle of the same shading as the circled cell, including the endpoints. 𝗦𝗽𝗹𝗶𝘁 𝗣𝗲𝗮𝘀: Digits along a line strictly between two circles must sum to a two-digit number, where the tens digit is in one circle and the ones digit is in the other.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c10","c11"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6oz1ae7e1l","ctcId":2752,"ctcDifficulty":"MEDIUM","title":"Flux Capacitor","author":"Scott Strosahl","rules":"Normal Sudoku rules apply.\n\nKiller Cages: Some cells are surrounded by dotted lines, called \"cages.\" Digits cannot repeat in a cage. The digits in a cage sum to the value in the top left.\n\nBetween Lines: There are circles in the grid connected by lines. The digits on the lines must be strictly in-between the digits filled in the circles, excluding the digits in the circles.\n\nFor the red and blue between lines, all circles connect across to both ends on the opposite side. (e.g. r4c3 connects to both r4c7 AND r6c7)","solution":"245378691913465827687291354728139465134756289569842173351687942496523718872914536","constraints":["between-line","cage"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"csdq2h21cv","ctcId":2753,"ctcDifficulty":"MEDIUM","title":"Cloud Atlas","author":"James Kopp","rules":"Normal sudoku rules apply.\nThe grid is covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area. \nOrthogonally adjacent cells cannot contain consecutive digits. \nAdjacent digits along a green line have a difference of at least five. \nThe digits along a grey arrow line sum to the digit in that arrow’s circle.","solution":"528473196196825374374691852852914637419736285637258419963582741741369528285147963","fogLight":"R4C5,R5C5,R2C4,R2C5,R2C6","constraints":["arrow","fog","german-whispers","non-consecutive"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"tMq37fgf63","ctcId":2754,"ctcDifficulty":"VERY HARD","title":"May the 4's Be With You","author":"Scott Williams","rules":"Normal sudoku rules apply. Identical digits cannot be a knight's move apart. Digits in cages cannot repeat and must add to the given total. Along the marked diagonal, digits must add to the given total.","solution":"341258679258679134679431258192346587486795312735182496923814765514967823867523941","constraints":["antiknight","cage","little-killer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"huv80pdliu","ctcId":2755,"ctcDifficulty":"HARD","title":"Bow Fishing","author":"Scott Williams","rules":"Normal Sudoku rules apply. Digits in a cage cannot repeat and must sum to the given total. Digits along an arrow must sum to the number in the circle. Digits along a thermometer strictly increase from the bulb to the tip.","solution":"584672193923185476617934528345827619192356847876491235468713952751269384239548761","constraints":["arrow","cage","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Digits along an arrow must sum to the number in the circle.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"1zta3rkwrq","ctcId":2756,"ctcDifficulty":"MEDIUM","title":"Thirty-Five","author":"Scott Williams","rules":"Normal Sudoku rules apply. A clue outside the grid gives the sum of the digits along the indicated diagonal. The middle 3x3 box is a magic square; each row, column, and diagonal of this box must all have the same sum. Digits along an arrow must sum to the digit in the arrow's bulb.","solution":"352819647478563219196742583725438196863951724941276835539187462617324958284695371","constraints":["arrow","custom","little-killer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The middle 3x3 box is a magic square; each row, column, and diagonal of this box must all have the same sum.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"JnpJ7TpdPd","ctcId":2757,"ctcDifficulty":"MEDIUM","title":"Prime Time","author":"Scott Williams","rules":"Normal sudoku rules apply. Digits on a red line must alternate between prime (2,3,5,7) and composite (4,6,8,9). The digit 1 is neither prime nor composite. The digits in each cage form a prime number when read rightwards or downwards. Digits in the circle must appear within the surrounding four cells. Digits in cells joined by a white dot must be consecutive and digits in cells joined by a black dot must be in a 2:1 ratio.","solution":"658721943132954867974836251243619785765348129819275436396487512421593678587162394","constraints":["custom","kropki","quadruple"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits on a red line must alternate between prime (2,3,5,7) and composite (4,6,8,9). The digits in each cage form a prime number when read rightwards or downwards.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"jrnrm1a25q","ctcId":2758,"ctcDifficulty":"MEDIUM","title":"Six Seven","author":"Scott Williams","rules":"Normal Sudoku rules apply. Identical digits cannot be a knight's move apart. Adjacent digits may not sum to 5 or 10. Box borders divide each blue line into segments with the same sum.","solution":"879562134365471892124398657718924365536817429942635718697243581251786943483159276","constraints":["XV","antiknight","region-sum-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Box borders divide each blue line into segments with the same sum.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"4yizx5451j","ctcId":2759,"ctcDifficulty":"MEDIUM","title":"Aced","author":"James Kopp","rules":"Normal sudoku rules apply. \nDigits do not repeat along a marked blue diagonal.\nAdjacent digits along an orange line have a difference of at least four.\nAll digits along a blue line must sum to the same total in each 3x3 box the line visits.\nThe central 3x3 box must form a magic square.","solution":"286941537395278641741563928578492316612357894934816275853124769469735182127689453","constraints":["custom","diagonal","dutch-whispers","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The central 3x3 box must form a magic square.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"All digits along a blue line must sum to the same total in each 3x3 box the line visits.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"z417emg43r","ctcId":2760,"ctcDifficulty":"HARD","title":"Cycles of Time and Tide","author":"zetamath","rules":"Normal sudoku rules apply. \nA black dot sits between two digits where one is double the other. Not all dots are necessarily given. \nThe single grey line is a palindrome ie its digits read the same forwards and backwards. \nBlue lines in the grid are Region Sum Lines ie The 3x3 box borders divide each blue line into segments; each segment along a line has the same sum. (NB Different lines may have different sums).\nFor example: r5c2+r5c3+r6c2+r6c3=r7c2+r8c2=r7c3+r8c3\nThe salmon coloured lines in the grid are entropic lines ie Any set of three sequential cells along an entropic line must contain a low digit (123), middle digit (456) and high digit (789). Digits may repeat on a line, if allowed by other rules.","solution":"631784295479512863852936174583691742916247358724853619148375926295168437367429581","constraints":["entropic-line","kropki","palindrome","region-sum-line"],"constraintFacts":[{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"o39fgip872","ctcId":2762,"ctcDifficulty":"HARD","title":"Hit Count","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nDigits may not repeat on a beige hitline. A circled digit on a hitline indicates how many digits match their position number along that line, starting at the end with the square (which is 'position 1'.) \n\nEg: If a line reads 97325, then the 2 would be circled because there are two digits in their correct positions: 3 is in the 3rd position, and 5 is in the 5th position.","solution":"294871635168523947357694218476932581935186472812457369721369854689745123543218796","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits may not repeat on a beige hitline. A circled digit on a hitline indicates how many digits match their position number along that line, starting at the end with the square (which is 'position 1'.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"97hj3g41ka","ctcId":2765,"ctcDifficulty":"MEDIUM","title":"Entwined","author":"Alaric Taqi A. (Crusader175)","rules":"• Normal sudoku rules apply.\n• All lines are both Index Lines and Entropic Lines.\n• Index Lines: The digit in the Nth cell along a line (starting from the diamond) indicates the position along the line where the digit N appears.\n• Entropic Lines: Any set of three sequential cells along a line must contain a low (1,2,3), middle (4,5,6), and high (7,8,9) digit.\n• Sum Dots: Digits around the brown diamond may repeat and must sum to the given total.","solution":"258147369936258471147369258369582714471936825825714936714693582582471693693825147","constraints":["custom","entropic-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Index Lines: The digit in the Nth cell along a line (starting from the diamond) indicates the position along the line where the digit N appears. • Sum Dots: Digits around the brown diamond may repeat and must sum to the given total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ozvhz71rzq","ctcId":2767,"ctcDifficulty":"HARD","title":"Chiaroscuro-doku","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nChiaroscuro: Shade some cells so that all groups of orthogonally connected shaded cells have an even number of cells and all groups of orthogonally connected unshaded cells have an odd number of cells. Two groups cannot have the same shape and size, counting rotations and reflections as the same.\n\nDigits cannot repeat within a Chiaroscuro group.\n\nA digit in a circled cell is equal to the size of the Chiaroscuro group which contains that cell.\n\nIf a cell has a given number in the upper left corner, then the digits in the Chiaroscuro group which contains that cell must sum to that number.","solution":"895263741732194658146785392489327516253618974617549283568931427374852169921476835","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Chiaroscuro: Shade some cells so that all groups of orthogonally connected shaded cells have an even number of cells and all groups of orthogonally connected unshaded cells have an odd number of cells. Two groups cannot have the same shape and size, counting rotations and reflections as the same. Digits cannot repeat within a Chiaroscuro group. A digit in a circled cell is equal to the size of the Chiaroscuro group which contains that cell. If a cell has a given number in the upper left corner, then the digits in the Chiaroscuro group which contains that cell must sum to that number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6"]}]},{"id":"5k5lcjymlk","ctcId":2768,"ctcDifficulty":"HARD","title":"Rod of Eternal Coherence","author":"Playmaker6174","rules":"Normal sudoku rules apply. \n\nDigits within a cage sum to the small number written in the top left of that cage. \n\nThe sum of the digits along the red line that has two circles as its endpoints must equal to the sum of two digits in both circles. \n\nAlong the green line, two adjacent digits have the difference of at least 5. \n\nAlong the grey palindrome line, digits form a sequence that reads the same backwards as it does forwards. \n\nAlong each teal line, the set of three sequential cells must contain one digit from set {1,4,7}, one digit from set {2,5,8} and one digit from set {3,6,9}. \n\nA black dot sits between two digits where one is double the other, while two digits connected by a white dot have difference of 1. Not all black dots and white dots are given.","solution":"529684317487139562136752894654927183912348756873516249295471638348265971761893425","constraints":["cage","custom","german-whispers","kropki","modular-line","palindrome"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits along the red line that has two circles as its endpoints must equal to the sum of two digits in both circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"miv6k9rwi0","ctcId":2769,"ctcDifficulty":"MEDIUM","title":"Bubbles","author":"Michael Lefkowitz","rules":"Normal sudoku rules apply. A digit in a small white circle indicates how many times that digit appears in small white circles in the puzzle. 3x3 box borders divide blue lines into segments; the digits on each segment must have the same sum.  (Different lines may have different sums.)","solution":"352179846761584329849362517984726153625431798137958264276845931498213675513697482","constraints":["counting-circle","region-sum-line"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"3x3 box borders divide blue lines into segments; the digits on each segment must have the same sum.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"3doylfz343","ctcId":2770,"ctcDifficulty":"HARD","title":"New York City","author":"ICHTUES","rules":"Normal sudoku rules apply. Each main diagonal must contain all of the digits 1 to 9, once each. In cages, digits must sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage.","solution":"715426983634981752982375461527618349348592176196734825871269534469853217253147698","constraints":["cage","diagonal"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"myzopzm5k3","ctcId":2771,"ctcDifficulty":"MEDIUM","title":"Three-Sums","author":"James Kopp","rules":"Normal sudoku rules apply. \nThe grid contains nine \"three-sums,\" one in each row, column, and 3x3 box. Each digit from 1-9 is a \"three-sum\" exactly once. “Three-sum” digits count as their nominal value increased by 3. For example, a “three-sum” 7 would have a value of 10.\nThe sum of the value of the digits on a line within a box (the line's 'region sum') must be the same for each box that line passes through.","solution":"895264371136798542247135896721843659369527184584916237652489713473651928918372465","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The grid contains nine \"three-sums,\" one in each row, column, and 3x3 box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"The sum of the value of the digits on a line within a box (the line's 'region sum') must be the same for each box that line passes through.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]}]},{"id":"fp82wljj36","ctcId":2779,"ctcDifficulty":"MEDIUM","title":"Jinxed Squad","author":"Secret Santa","rules":"Normal sudoku rules apply.\n\nQUARUPLES -  A digit inside a white circle must appear in one of the four cells surrounding that circle.\n\n159 INDEXING -  Digits in columns 1, 5, and 9 indicate the column in which the digit 1, 5, or 9 (respectively) appears in that row.","solution":"321986754594713862786542139138297645472165398965438271217359486853624917649871523","constraints":["custom","quadruple"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"159 INDEXING -  Digits in columns 1, 5, and 9 indicate the column in which the digit 1, 5, or 9 (respectively) appears in that row.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"1cwnilmrp0","ctcId":2780,"ctcDifficulty":"HARD","title":"Two Out of Three Ain't Bad","author":"FullDeck and Missing a Few Cards","rules":"**Sudoku, Cages, Ambiguous Lines**\n\n- Standard sudoku rules apply: The digits 1 through 9 appear in every row, column, and box.\n- Cages: Digits in cages must sum to the value shown in the upper left corner of the cage.\n- Ambiguous Lines: Each line in the puzzle is EXACTLY TWO of modular, entropic, or parity.\n- Modular Lines: Any set of three adjacent digits along a modular line has three different remainders when divided by 3\n- Entropic lines: Any set of three adjacent cells along an entropic line must contain a low digit (123), a middle digit (456), and a high digit (789).\n- Parity Lines: Digits along parity lines alternate odd/even.\n\nFor more of our puzzles, please visit https://missingdeck.net","solution":"183456729267893541954271836429568317578319462631724985745632198812947653396185274","constraints":["cage","custom","entropic-line","modular-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Ambiguous Lines: Each line in the puzzle is EXACTLY TWO of modular, entropic, or parity. - Parity Lines: Digits along parity lines alternate odd/even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c7"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"1imy136lv4","ctcId":2784,"ctcDifficulty":"HARD","title":"Spinning Top","author":"Phistomefel","rules":"1. Normal Sudoku rules apply.\n2. Renban: Pink lines must contain a set of consecutive, non-repeating digits in any order. \n3. German Whispers: The digits in adjacent cells along green lines must differ by at least 5. Digits can repeat on green lines if allowed by other rules.","solution":"796431258835267419142895637629318574513749826478526391364972185287154963951683742","constraints":["german-whispers","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"vt15nmht65","ctcId":2785,"ctcDifficulty":"HARD","title":"Parity Parity","author":"Justin Vitanza","rules":"Normal Sudoku rules apply.\n\nAnti-king: Cells that are diagonally adjacent may not contain the same digit.\n\nDynamic Fog: The grid is mostly covered in fog. Correctly placing digits will reveal the fog in that cell and possibly other cells.\n\nParity Parity: Beneath the fog is a checkerboard pattern of yellow and blue cells. Each digit appears in one of the colors exactly as many times as its value. For example, 7 will appear either exactly seven times in blue or exactly seven times in yellow.","solution":"429158763863279451175463289698324175217586934354917826982645317541732698736891542","fogLight":"R1C7,R2C7,R3C7,R4C7,R5C5,R5C6,R5C7,R6C7,R7C7,R8C7,R9C7","constraints":["antiking","custom","fog"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each digit appears in one of the colors exactly as many times as its value.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"gejf3uvo1y","ctcId":2787,"ctcDifficulty":"HARD","title":"War with Pythagoras","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\nAdjacent digits along a green line must differ by at least 5.\nEach pink line contains a set of consecutive, non-repeating digits, which can appear in any order.\nEach gray line consists of one or more contiguous groups of cells, each of which sums to 10. These groups of cells cannot overlap; every cell is part of exactly one group.\nLines may share endpoints, but otherwise don't overlap.","rulesClarified":"Normal Sudoku rules apply.\n\nGreen line: adjacent digits along a green line must differ by at least 5.\n\nPink line: a pink line holds a set of consecutive, non-repeating digits, which can appear in any order.\n\nGrey line: each grey line is made of one or more contiguous groups of cells. Each group's digits sum to 10. The group boundaries are not drawn; you choose them.\n\nThe groups do not overlap. Every cell of a grey line belongs to exactly one group.\n\nLines may share endpoints, but otherwise do not overlap.","solution":"634729815182536794975148263491382657826957431753461982568273149317694528249815376","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each gray line consists of one or more contiguous groups of cells, each of which sums to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"6i5it6u94z","ctcId":2788,"ctcDifficulty":"MEDIUM","title":"1080°","author":"Raumplaner & Qodec","rules":"- Normal Sudoku rules apply. \n- Quadruples: Digits in circles must appear at least once in the four surrounding cells.","solution":"587921463391456278642378519975842631813695742426137985734289156268514397159763824","constraints":["quadruple"],"constraintFacts":[{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"zbgub1jtmx","ctcId":2789,"ctcDifficulty":"MEDIUM","title":"Up to Something","author":"sujoyku","rules":"- Normal sudoku rules apply, i.e. each row, column, and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- Dynamic Fog: The grid is covered in fog. Correctly placing a digit will clear any fog in its own cell, and potentially clear fog in other cells too. No guessing is required.\n\n- Up to Given-sums: Each row, column, and 3x3 region contains exactly one given digit whose exact location is to be deduced. No two givens are identical digits, i.e. each of the digits 1 to 9 is given exactly once.\nA clue outside a row or column indicates the sum of all digits up to the given digit. (The given digit itself is not included in the sum.)\n\n- Arrows: Digits on an arrow sum to the digit in the circle from which the arrow emerges.\n\n- Kropki: Digits joined by a black dot have a 1:2 ratio. Digits joined by a white dot are consecutive. (Not all dots are given.)","rulesClarified":"Normal sudoku rules apply. Each row, column and 3x3 region contains the digits 1 to 9 once each.\n\nDynamic Fog: the grid is covered in fog. Correctly placing a digit clears the fog in its own cell, and may clear fog in other cells too. No guessing is required.\n\nUp to given-sums: each row, column and 3x3 region contains exactly one given digit, whose location you must deduce. No two givens are the same digit, so each of the digits 1 to 9 is given exactly once across the grid.\n\nA clue outside the grid sits at the end of a row or column. It sums the digits from that end up to the given digit of that row or column. The given digit itself is not included in the sum. A clue at the left or right end refers to its row; a clue above or below the grid refers to its column.\n\nArrows: the digits on an arrow sum to the digit in the circle the arrow leaves. The circle itself is not part of the sum.\n\nKropki: digits joined by a black dot have a 1:2 ratio. Digits joined by a white dot are consecutive. Not all dots are drawn, and a pair of cells with no dot gives you nothing from this rule.","solution":"694823175231657498785491263927534681548716932163289547416375829879142356352968714","fogLight":"","constraints":["arrow","custom","fog","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Up to Given-sums: Each row, column, and 3x3 region contains exactly one given digit whose exact location is to be deduced. No two givens are identical digits, i.e. each of the digits 1 to 9 is given exactly once. A clue outside a row or column indicates the sum of all digits up to the given digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"4otpj4l7xo","ctcId":2795,"ctcDifficulty":"HARD","title":"Heatstroke","author":"Emmett Cito","rules":"Normal sudoku rules apply. Along a thermometer, digits must increase from the bulb end.","solution":"135927864867341529429856137381674952754192386296583471648739215913265748572418693","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jzrbr86s3n","ctcId":2797,"ctcDifficulty":"MEDIUM","title":"Another Mismatch","author":"Cane_Puzzles","rules":"Normal sudoku rules apply (ie place the digits 1-9, once each, in every row, column and 3x3 box). The purple line contains a set of consecutive digits in any order. The digits in a cage sum to the small clue in the cage’s top left corner. Digits may not repeat in a cage.","solution":"951627384734918265628435917386571492279364158145892673567143829412789536893256741","constraints":["cage","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hewaby2tso","ctcId":2798,"ctcDifficulty":"HARD","title":"Unlikely Friends","author":"Phistomefel","rules":"Normal sudoku rules apply (Place the digits 1-9, once each, into every row, column and 3x3 box). Cells separated by a single knight's move (in chess) cannot contain the same digit.  The digits along a thermometer increase from the bulb end.","solution":"874913256159672348326845179947381625685729431231564987493157862562498713718236594","constraints":["antiknight","thermometer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"buum97646q","ctcId":2799,"ctcDifficulty":"HARD","title":"Lost in the Modhouse","author":"Kennet's Dad","rules":"Normal sudoku rules apply. \nThe grid is partially covered in fog; placing a correct digit will clear the fog in that cell and possibly elsewhere in the grid. Each of the following constraint types may contain no repeated digits anywhere in the puzzle. E.g., if a parity line contains a 5, then no other parity line cell in the puzzle  may contain a 5: \n1) Digits in a cage must sum to the total given; \n2) Digits joined by an X sum to 10; \n3) Adjacent digits along a red parity line (PR) must alternate between odd and even digits; \n4) A purple renban line (RB) must contain a set of consecutive digits in any order; \n5) A yellow nabner line (NB) must contain a set of nonconsecutive digits in any order; \n6) Any set of three digits along an orange entropic line (ENT) line must contain one digit from each of the following sets: 123; 456; 789; \n7) Any set of three digits along a teal modular line (MOD) must contain one digit from each of the following sets: 147; 258; 369; \n8) Pairs of digits equidistant from the centre of a pink zipper line (ZIP) must sum to the digit in the centre of that line, notated by a small circle. \nLines in the puzzle never intersect or share cells.","solution":"319256478274918563856437912785129634693784251421365789142573896967841325538692147","fogLight":"R6C2,R6C3,R6C6,R6C8,R2C6,R3C6,R8C6,R3C2,R2C3,R1C2,R2C1,R1C6,R6C1,R6C4,R4C6","constraints":["XV","cage","custom","entropic-line","fog","modular-line","nabner-line","renban","zipper-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each of the following constraint types may contain no repeated digits anywhere in the puzzle. 3) Adjacent digits along a red parity line (PR) must alternate between odd and even digits;","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c7"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]}]},{"id":"9rwnig6n8g","ctcId":2800,"ctcDifficulty":"HARD","title":"NOT ON","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nDraw a single snaking line connecting two particular cells (to be discovered) which forms a palindrome, ie; its sequence of digits reads the same in either direction. The palindrome line should pass through the centres of cells, and may move both orthogonally and diagonally, but may not branch or cross itself.\n\nARROWS: A digit on an arrow indicates how many cells it sees (in the indicated direction) that are NOT ON the palindrome. The arrow cell itself is not included in the count.\n\nCAGES: Digits in a cage do not repeat, and the clue in the top left corner indicates the total of any digits in the cage that are NOT ON the palindrome.","rulesClarified":"Normal sudoku rules apply.\n\nThe palindrome: draw one unbroken line through cell centres that links two cells (you must find which two). Each step of the line goes to a neighbouring cell, orthogonally or diagonally. The line may not branch or cross itself. Its digits read the same forwards and backwards.\n\nA cell is ON if its centre lies on the palindrome line. Every other cell is NOT ON.\n\nArrows: the digit on an arrow is how many NOT ON cells it sees in the direction the arrow points. The cell holding the arrow is not counted.\n\nCages: digits in a cage do not repeat. The number in a cage's top-left corner is the total of that cage's digits that are NOT ON the palindrome. Digits that are ON do not add to it.","solution":"769832514142956783583471629894317256257684391631529478915243867326798145478165932","constraints":["custom","palindrome"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"ARROWS: A digit on an arrow indicates how many cells it sees (in the indicated direction) that are NOT ON the palindrome. CAGES: Digits in a cage do not repeat, and the clue in the top left corner indicates the total of any digits in the cage that are NOT ON the palindrome.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c6"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"n5y2dw7hdb","ctcId":2802,"ctcDifficulty":"MEDIUM","title":"Square Threads","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Every 2-cell red or blue line can be read as a square number in one direction or the other (eg 25 or 52). The central grey cell is also a square number.","solution":"861723945432598176957614283523879614186245397794136852345961728679482531218357469","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every 2-cell red or blue line can be read as a square number in one direction or the other (eg 25 or 52). The central grey cell is also a square number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"c8kz188s7p","ctcId":2803,"ctcDifficulty":"HARD","title":"Pro-Diagonal","author":"Justin Vitanza","rules":"Latin Square rules apply.\n\nParity Parity: The grid is covered in a checkerboard pattern of yellow and blue cells. Each digit appears in one of the colors exactly as many times as its value. For example, 7 will appear either exactly seven times in blue or exactly seven times in yellow.\n\nAnti-Diagonal (Negative): Digits may not repeat along any negative diagonal (those going from the top left to the bottom right).\n\nAnti-Knight: Cells a knight’s move (in chess) apart cannot contain the same digit.\n\nOdd Circles: Digits in grey circles must be odd.","solution":"123456789234567891345678912456789123567891234678912345789123456891234567912345678","constraints":["antiknight","custom","diagonal","odd"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each digit appears in one of the colors exactly as many times as its value.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"modified","modifiers":[],"params":null,"note":"Anti-Diagonal (Negative): Digits may not repeat along any negative diagonal (those going from the top left to the bottom right).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"r3tfzi51qa","ctcId":2804,"ctcDifficulty":"HARD","title":"Unstable Seesaws","author":"Cane_Puzzles & Piatato","rules":"Classic Sudoku rules apply.\nDigits in adjacent cells separated by a white dot differ by exactly 1.\nAdjacent digits on a green line differ by 5 or more.\nThe digits in a cage sum to the small number given in the cage.","solution":"296784351341295876578163492483652917617839245952417683764528139829371564135946728","constraints":["cage","german-whispers","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jf0yny3xul","ctcId":2805,"ctcDifficulty":"HARD","title":"That's 3 in the corners","author":"Lithium-Ion","rules":"Normal Sudoku rules apply. Cells that are a king's move apart are not allowed to contain identical digit. The digit in the central cell of each box has to be less or equal than the box number. Boxes are numbered in normal reading order. Each horizontal 3x1 region that is completely contained in a single box has to sum to the same value. Each vertical 1x3 region that is completely contained in a single box has to sum to the same value. The digit in the top-left cell and the digit in the bottom-right cell of the grid must sum to 3.","solution":"267843159915627834483195672726438915348951267591276483834519726159762348672384591","constraints":["antiking","custom"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digit in the central cell of each box has to be less or equal than the box number. Each horizontal 3x1 region that is completely contained in a single box has to sum to the same value. Each vertical 1x3 region that is completely contained in a single box has to sum to the same value. The digit in the top-left cell and the digit in the bottom-right cell of the grid must sum to 3.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5","c6","c7"]}]},{"id":"rms66f3qkn","ctcId":2807,"ctcDifficulty":"HARD","title":"Geometry Exam #5","author":"Blashyrkh","rules":"Normal sudoku rules apply.\n\nDigits along an arrow sum to the number in the attached circle.\n\nDigits do not repeat along each of the indicated diagonals.","solution":"459781632276453891813962457168537924592814376734629185645378219981245763327196548","constraints":["arrow","diagonal"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"w4l55nhbav","ctcId":2808,"ctcDifficulty":"MEDIUM","title":"The Penrose Steps","author":"Fenners","rules":"Normal 9x9 Sudoku rules apply.\n\nPenrose Lines: On a pink line, a sequence of increasing digits repeats from the bulb end. The sequence must fully complete and repeat at least once (and, each time it repeats, it must repeat fully). For example, along a penrose line, digits could read: 137137137.","rulesClarified":"Normal 9x9 Sudoku rules apply.\n\nPenrose lines: each pink line starts at a bulb, which is the circle at its start cell.\n\nOn a pink line, a sequence of increasing digits repeats from the bulb end.\n\nThe sequence must fully complete and repeat at least once. Each time it repeats, it must repeat fully.\n\nFor example, along a penrose line, digits could read: 137137137.","solution":"852417963417963528963528174528174639174639285639285741285741396741396852396852417","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Penrose Lines: On a pink line, a sequence of increasing digits repeats from the bulb end.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7exqntdae5","ctcId":2810,"ctcDifficulty":"HARD","title":"Not All Who Wander Are Lost","author":"Allagem","rules":"Normal sudoku rules apply.\nEach line can be divided into one or more segments such that every segment in the grid sums to the same total. (For the avoidiance of doubt, this means that segments from both the 78-cell line and the 2-cell line have the same sum!) The digit in the grey square is even.","solution":"125784693384569712769123458258476931413892576976315284541637829897241365632958147","constraints":["custom","even"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each line can be divided into one or more segments such that every segment in the grid sums to the same total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"bpm965ze9a","ctcId":2811,"ctcDifficulty":"MEDIUM","title":"Terrace","author":"Qodec","rules":"- Sudoku: Each row, column, and region indicated by thick borders in the grid must contain the digits 1 to 9 once each.\n- Even: The cell with the gray square is even.\n- Dutch Flatmates: Every 5 must have a 1 directly above it or a 9 directly below it. It may have both, but it doesn't need both.\n- 159: Digits in column 1 indicate the column in which the digit 1 appears in that row (e.g. if r4c1 is a 6, r4c6 is a 1). The same is true of column 5 and the digit 5, and column 9 and the digit 9.\n- XV pairs: An X between two cells means that the digits in those cells must add up to 10. Not all possible X clues are necessarily given.","solution":"469178523823465917157329846798546132216983754534217698982654371371892465645731289","constraints":["XV","custom","even"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Dutch Flatmates: Every 5 must have a 1 directly above it or a 9 directly below it. It may have both, but it doesn't need both. - 159: Digits in column 1 indicate the column in which the digit 1 appears in that row (e.g. if r4c1 is a 6, r4c6 is a 1). The same is true of column 5 and the digit 5, and column 9 and the digit 9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"3qz1km5o1d","ctcId":2815,"ctcDifficulty":"MEDIUM","title":"Prison Break","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply. \n\nThe grid 'wraps around' (the top connects to the bottom, and the left edge to the right edge).\n\nDUTCH CELLMATES: Every digit in the grid needs to have a digit at least 4 greater in the cell below it, or a digit at least 4 smaller in the cell above it. It may have both, but doesn't need both.\n\nKILLER CAGES: Cages chained to each other have the same sum.","solution":"461725938835469271279813645614257389358694712792138456146572893583946127927381564","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The grid 'wraps around' (the top connects to the bottom, and the left edge to the right edge). KILLER CAGES: Cages chained to each other have the same sum.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5"]}]},{"id":"4ctb5mbrk8","ctcId":2816,"ctcDifficulty":"VERY HARD","title":"Twirled mermaid goes forklift","author":"olima","rules":"Normal Sudoku rules apply.\nEvery three-cell-segment of a teal modular line contains one digit from the groups 147, 258 and 369. The sum of the digits on a thin gray line equals the sum of the digits in the attached circles. Adjacent digits on a green line differ by at least 5. Purple lines contain a set of distinct consecutive digits in any order. Digits in cages do not repeat. Gray circles indicate odd and gray squares even digits. The digits on the MARKed diagonal sum to 60.","solution":"524981637768543192319726458472839516831652749956417283187294365293165874645378921","constraints":["custom","even","german-whispers","modular-line","odd","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits on a thin gray line equals the sum of the digits in the attached circles. Digits in cages do not repeat. The digits on the MARKed diagonal sum to 60.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c6","c8"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"odd","type":"odd","variant":"modified","modifiers":[],"params":null,"note":"Gray circles indicate odd and gray squares even digits.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Purple lines contain a set of distinct consecutive digits in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"u0cs9m2qmx","ctcId":2817,"ctcDifficulty":"EASY","title":"Lockout Lines turn 4","author":"Riffclown","rules":"• Normal Sudoku rules apply. Place the digits 1-9 in each row, column and box without repetition.\n\n• Lockout Lines: Digits on blue lines can not be between or equal to the digits in the diamonds at the ends of the line. The digits in the diamonds at the ends of a line must differ by at least 4. A diamond terminates a line segment.","solution":"381592674564817392729364815458639127136725948297481536673948251815273469942156783","constraints":["lockout-line"],"constraintFacts":[{"slug":"lockout-line","type":"lockout-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"82dowa2bt5","ctcId":2818,"ctcDifficulty":"HARD","title":"Inchworms","author":"dumediat","rules":"- Normal sudoku rules apply. Place the digits 1-9 in each row, column and box without repetition.\n- German whispers: Adjacent digits on a green line must have a difference of at least 5.\n- Odd/Even: Digits in gray circles must be odd, and digits in gray squares must be even.\n- Ratio pair: Digits separated by the black dot must be in a 1:2 ratio. Not all dots are given.\n- Renban: Digits placed on purple lines must be a non-repeating set of consecutive digits, in any order.\n- X pairs: Digits separated by an X must sum to 10. Not all X's are given.","solution":"174596283526348179389712564635187492297465318418239657843671925751924836962853741","constraints":["XV","even","german-whispers","kropki","odd","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"jvfdr3d0ag","ctcId":2819,"ctcDifficulty":"HARD","title":"Humidex","author":"shady moon","rules":"Normal sudoku rules apply. Each digit in column 1 indicates the position of the 1 in its row. (eg if R5C1 is a 6, then R5C6 is a 1 as the 1 must appear in the 6th position). Column 5 operates the same way for the digit 5; and column 9 for the digit 9. Each digit in row 1 indicates the position of the 1 in its column. (eg if R1C5 is a 6, then R6C5 is a 1). Row 5 operates the same way for the digit 5; and row 9 for the digit 9. On thermometers, digits must increase from the bulb end. Along the marked diagonal, digits must not repeat.","solution":"147693825829547613653821947218479536936258471475136298361982754794365182582714369","constraints":["custom","diagonal","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each digit in column 1 indicates the position of the 1 in its row. (eg if R5C1 is a 6, then R5C6 is a 1 as the 1 must appear in the 6th position). Column 5 operates the same way for the digit 5; and column 9 for the digit 9. Each digit in row 1 indicates the position of the 1 in its column. (eg if R1C5 is a 6, then R6C5 is a 1). Row 5 operates the same way for the digit 5; and row 9 for the digit 9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"xyrh6tfdyq","ctcId":2820,"ctcDifficulty":"MEDIUM","title":"Read between the cages","author":"shady moon","rules":"Normal Sudoku rules apply. Digits must not repeat in cages. Digits on thermometers increase from the bulb end. Digits on lines must be between the digits in the circles on each end. These lines also act as thermometers i.e. digits on lines must increase from the \"low\" circle to the \"high\" circle.","solution":"432179865519286734687534192743698251965412378821357649356841927174923586298765413","constraints":["between-line","cage","thermometer"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"These lines also act as thermometers i.e. digits on lines must increase from the \"low\" circle to the \"high\" circle.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3","c5"]}]},{"id":"p6660shn47","ctcId":2821,"ctcDifficulty":"HARD","title":"Spellbinding Square","author":"shady moon","rules":"Normal Sudoku rules apply. The central 3x3 box is a magic square (each row, column and diagonal in that box sum to the same number). Digits on the thermometer increase from the bulb end. Cells connected by a purple line sum to 10. In the cage, digits that are a (chess) king's move apart from other caged digits must not repeat and must not sum to 5, 10 or 15.","solution":"397241685652789431481635792735816249249357168168492573813574926976123854524968317","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The central 3x3 box is a magic square (each row, column and diagonal in that box sum to the same number). Cells connected by a purple line sum to 10. In the cage, digits that are a (chess) king's move apart from other caged digits must not repeat and must not sum to 5, 10 or 15.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c5"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"uwygvvt8nd","ctcId":2822,"ctcDifficulty":"VERY HARD","title":"Triple Point","author":"shady moon","rules":"Normal Sudoku rules apply. Lines contain digits in order with a constant difference (e.g. 1-2-3, 4-6-8, 7-4-1). Lines of the same colour cannot contain repeated digits. Cells separated by a black dot are in a 1:2 ratio (ie one digit will be double the other)","solution":"962715834485263917317948562159682473634157289278394156741526398896431725523879641","constraints":["custom","kropki","same-difference-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Lines of the same colour cannot contain repeated digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"e3zml763km","ctcId":2823,"ctcDifficulty":"HARD","title":"8/9/1990","author":"shady moon","rules":"Normal Sudoku rules apply. \n\nThe 3x3 box borders divide the blue line into segments. Along this blue line, each segment’s digits sum to the same total. \n\nThe sum of all digits on the blue line and pink line combined is 89 \n\nA black dot between two cells indicates that one digit is double the other. Not all black dots are given.","solution":"327984651684175293951632478716348529832597146495261387579413862148726935263859714","constraints":["custom","kropki","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of all digits on the blue line and pink line combined is 89","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"rj53fjf9jo","ctcId":2824,"ctcDifficulty":"MEDIUM","title":"How Far I'll Go","author":"MaizeGator","rules":"Normal sudoku rules apply: Place the digits 1-9, once each, into every row, column, and 3x3 box.\n\nNormal nurikabe rules apply: Shade some cells blue (representing water), such that all water cells are orthogonally connected, but water may not fully cover a 2x2 area. Shade the remaining cells green, which represent islands. Digits may not repeat within an island.\n\nEach island contains exactly one numbered clue, which gives the product of the sum of the digits on the island and the size (number of cells) of the island, e.g. an island filled with 346 is would have a \"39\" clue (13x3). A \"?\" may represent any single, double, or triple-digit number. \n\nA cell with arrow(s) may be land or water, and the digit gives the total number of island cells in the indicated directions combined, not including itself. Not all arrows are given.","solution":"759234681631598274284176593862349715495712836173865942326981457947653128518427369","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Normal nurikabe rules apply: Shade some cells blue (representing water), such that all water cells are orthogonally connected, but water may not fully cover a 2x2 area. Each island contains exactly one numbered clue, which gives the product of the sum of the digits on the island and the size (number of cells) of the island, e.g. an island filled with 346 is would have a \"39\" clue (13x3). A cell with arrow(s) may be land or water, and the digit gives the total number of island cells in the indicated directions combined, not including itself.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c7"]}]},{"id":"sm66vknq8l","ctcId":2828,"ctcDifficulty":"VERY HARD","title":"Beyond","author":"MaizeGator","rules":"Sudoku: Fill each cell with a digit 1-9 such that each digit appears exactly once in every row, column, and 3x3 box.\n\nNurikabe: Shade some cells (representing water) such that all shaded cells are orthogonally connected, but never fully cover a 2x2 area. Groups of orthogonally connected unshaded cells form islands. Two separate islands cannot touch one another orthogonally, but may touch diagonally.\n\nDigits may not repeat on an island.  Each island contains exactly one numbered clue, which gives the product of the sum of the digits on the island and the size (number of cells) of the island, e.g. an island filled with 346 is would have a '39' clue (13x3). A '?' may represent any number (not necessarily single-digit). \n\nA cell with arrow(s) may be land or water, and the digit gives the total number of island cells in the indicated directions combined, not including itself. Not all arrows are given.","solution":"689217543531469827427538916874192365196345782352876194768923451943651278215784639","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Nurikabe: Shade some cells (representing water) such that all shaded cells are orthogonally connected, but never fully cover a 2x2 area. Each island contains exactly one numbered clue, which gives the product of the sum of the digits on the island and the size (number of cells) of the island, e.g. an island filled with 346 is would have a '39' clue (13x3). A cell with arrow(s) may be land or water, and the digit gives the total number of island cells in the indicated directions combined, not including itself.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6","c8"]}]},{"id":"fawimvf33u","ctcId":2829,"ctcDifficulty":"HARD","title":"Stinky Stuffing","author":"the_cogito","rules":"Normal sudoku rules apply. Digits may not repeat along the indicated diagonal. Numbers outside the grid are simultaneously full rank clues and sandwich clues. A '?' can be any number. \n\nFull rank Each complete row and column can be read from both directions to form 36 distinct 9-digit numbers. The clues outside the grid give the rank of the 9-digit number read from that position when all the numbers are ranked from smallest (1) to highest (36). \n\nSandwich: A number outside the grid represents the sum of the digits sandwiched between the '1' and '9' in its respective row or column.","solution":"624178359357492816189653742461389275798526134532741968876935421945217683213864597","constraints":["custom","diagonal","sandwich"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Numbers outside the grid are simultaneously full rank clues and sandwich clues.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"b5azokaz10","ctcId":2830,"ctcDifficulty":"EASY","title":"You're Such a Square!","author":"Walking Writer","rules":"Normal sudoku rules apply. Digits along a diagonal cannot repeat. Digits separated by an X sum to ten. Digits separated by a V sum to five. Not all XV pairs are shown. Numbers in a cage must be a perfect square, and each perfect square can be used only one time.","solution":"974581236528637914163429758641798325387256149259314867812945673795163482436872591","constraints":["XV","custom","diagonal"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Numbers in a cage must be a perfect square, and each perfect square can be used only one time.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"rgws0916u4","ctcId":2831,"ctcDifficulty":"HARD","title":"More Piles of 15","author":"Cane_Puzzles","rules":"1) Classic Sudoku rules apply.\n2) Killer Sudoku rules apply: If a number is given at the left corner of a cage, the digits in the cage sum to that number. Digits cannot repeat in a cage.","solution":"736948152145326897829751436671432589394685271582197364467813925213579648958264713","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"D28Pt8pqfB","ctcId":2832,"ctcDifficulty":"EASY","title":"High Rise Window Washer","author":"Will Power","rules":"Normal sudoku rules apply. Neighbouring digits on the green line have a difference of at least 5. Digits do NOT repeat on the green line. Neighbouring digits on the orange line have a difference of at least 4. Digits may repeat on the orange line. A purple line contains a set of consecutive numbers in any order. The cage shows its sum.","solution":"574618293192573468683249571269134857347856129851792634936485712728361945415927386","constraints":["cage","dutch-whispers","german-whispers","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"modified","modifiers":["repeats-allowed"],"params":null,"note":"Digits may repeat along the orange line, unlike the green one.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"3ij3v3r73g","ctcId":2833,"ctcDifficulty":"MEDIUM","title":"Face Off at Center Ice","author":"Will Power","rules":"Normal sudoku rules apply. The central 3x3 box of the puzzle forms a magic square. Ie each 3-cell row, column and main diagonal of that 3x3 box must sum to the same total. Digits in cages sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage. Cells separated by a white dot must contain consecutive digits. Cells separated by an X must contain digits summing to 10. Cells separated by a V must contain digits summing to 5.","solution":"583429176674831259129576843738294561416753928295618734347985612951362487862147395","constraints":["XV","cage","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The central 3x3 box of the puzzle forms a magic square.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"jBfHFQHHp9","ctcId":2835,"ctcDifficulty":"EASY","title":"Major Diagonals Speed Run","author":"Will Power","rules":"Normal sudoku rules apply. Digits cannot repeat on marked diagonals. Digits joined by a white dot are consecutive. Digits joined by a black dot are in a ratio of 2:1.","solution":"149578263278963451365124879827631945956842137431759628512487396793216584684395712","constraints":["diagonal","kropki"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"f29kk6v182","ctcId":2836,"ctcDifficulty":"MEDIUM","title":"Crystallization of Arrows","author":"Will Power","rules":"Normal Sudoku rules apply. \n\nARROWS- Numbers on arrows sum to the number on the arrow's origin (circle or pill). Pills are read from left to right. Some circles and pills do not have an arrow.\n\nCRYSTALLIZATION- Pink pills are the sum of the two pills or circles below them.\n\nKROPKI PAIRS- Numbers with a white dot between them are consecutive. Numbers with a black dot between them are in a ratio of 2:1. Not all possible dots are shown.","solution":"218637549465192738937458621123586497754319286689724315542961873896273154371845962","constraints":["arrow","custom","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"CRYSTALLIZATION- Pink pills are the sum of the two pills or circles below them.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6","c7"]}]},{"id":"p1x3ugit3e","ctcId":2837,"ctcDifficulty":"EASY","title":"Consecutive Power Factory","author":"Will Power","rules":"Normal Sudoku rules apply. Numbers in circles and Pills are CONSECUTIVE powers (first power, second power, third power, etc.) of the number in the top circle in each of the three stacks. Numbers in pills are read from left to right. KILLER CAGES- Numbers in cages sum to the number in the top left corner of the cage. Numbers do not repeat in cages. KROPKI PAIR- Numbers with a white dot between them are consecutive. Not all possible dots are given.","solution":"582476931439815762167932584643791258925648173871253649356189427294367815718524396","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Numbers in circles and Pills are CONSECUTIVE powers (first power, second power, third power, etc.) of the number in the top circle in each of the three stacks.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"db59pt4nvp","ctcId":2842,"ctcDifficulty":"VERY HARD","title":"High Five","author":"Dubax","rules":"Normal sudoku rules apply. A clue outside the grid shows the sum of the digits between the 1 and the 9 in that row/column. No two 5s in the grid have the same digit in the cell immediately above.","solution":"951876423673142958824539716182394675496257831537681294345928167218765349769413582","constraints":["custom","sandwich"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No two 5s in the grid have the same digit in the cell immediately above.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qlc2250o3w","ctcId":2843,"ctcDifficulty":"HARD","title":"Carefully Balanced Weights and Measures","author":"HalfBakedLunatic (aka David Workman)","rules":"• Normal Sudoku Rules Apply\n• Box borders divide the blue Region Sum Lines into segments with the same sum\n• Gold Palindrome lines must read the same forwards or backwards","solution":"642983517718245396359671248234167859961358472875492631427516983196834725583729164","constraints":["palindrome","region-sum-line"],"constraintFacts":[{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"bupkl5df4h","ctcId":2844,"ctcDifficulty":"VERY HARD","title":"Magic Matryoshka","author":"Nahileon","rules":"Place the digits 1-9, once each, into every row, column and irregularly-shaped marked nine-cell region. Cells separated by a black dot contain two digits where one digit is double the other. A magic square is a square of NxN cells in which each row, column and both main diagonals sum to the same total. (In this puzzle digits CAN repeat in a magic square.) The entire 9x9 grid is a magic square. In the centre of the 9x9 magic square is a 7x7 magic square. In the centre of that is a 5x5 magic square. And in the very centre is a 3x3 magic square. The dotted lines clarify the positions of the magic squares.","rulesClarified":"Place the digits 1 to 9, once each, into every row, column and irregularly shaped nine-cell marked region.\n\nTwo cells separated by a black dot contain two digits, and one of the two digits is double the other. The dot sits on the border between the two cells.\n\nA magic square is a square block of N by N cells in which every row, every column and both main diagonals add up to the same total. The total is not given.\n\nDigits may repeat within a magic square. This does not relax the first rule: every row and every column of the whole grid still holds the digits 1 to 9 once each.\n\nThe whole 9 by 9 grid is a magic square. In its centre is a 7 by 7 magic square. In the centre of that is a 5 by 5 magic square, and in the very centre is a 3 by 3 magic square.\n\nThe dotted outlines show exactly where each of these squares sits.","solution":"786391425152437869279146538413528796697852314361285947835964172948673251524719683","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The entire 9x9 grid is a magic square. In the centre of the 9x9 magic square is a 7x7 magic square. In the centre of that is a 5x5 magic square. And in the very centre is a 3x3 magic square.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c7","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"5i6eemxl09","ctcId":2845,"ctcDifficulty":"MEDIUM","title":"Blue Frame","author":"Kaktuslav","rules":"Normal sudoku rules apply. The 3x3 box borders divide a blue line into segments. Each segment along a line has the same sum. (This segment sum can be different for different lines).","solution":"632978154157264893489135762924816537715392648863547219276453981398621475541789326","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"z44mcyjr8y","ctcId":2846,"ctcDifficulty":"MEDIUM","title":"Miracle Of Eleven","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Orthogonal neighbours (ie cells sharing an edge) are never consecutive. In the positive diagonals (ie diagonals sloping from SW to NE), the sum of neighbours is at most 11.","rulesClarified":"Normal sudoku rules apply.\n\nOrthogonal neighbours (cells sharing an edge) are never consecutive: two such cells never hold digits that differ by exactly 1.\n\nIn the positive diagonals (diagonals sloping from bottom-left to top-right), the sum of neighbours is at most 11.","solution":"752693184184275369369418527527936841841752693693184275275369418418527936936841752","constraints":["custom","non-consecutive"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In the positive diagonals (ie diagonals sloping from SW to NE), the sum of neighbours is at most 11.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qbg612qq8c","ctcId":2847,"ctcDifficulty":"MEDIUM","title":"Against the Odds","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along a green line have a difference of at least five.\nDigits increase from the bulb to the end of the thermometer.\nA digit in a square counts the number of odd digits (including itself) on its line or thermometer.","solution":"918236547657984132423751698892415763135867429764329851371542986589673214246198375","constraints":["custom","german-whispers","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a square counts the number of odd digits (including itself) on its line or thermometer.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"8opgiv0h40","ctcId":2848,"ctcDifficulty":"VERY HARD","title":"Myriapods: New Batch","author":"Marty Sears","rules":"⚠️ We can no longer contain them. The new batch of eggs looks set to hatch within days. Please urgently review studies 1-8 in order to gain vital understanding about these bizarre creatures. All we currently know is that they're always at least two cells long, and seem incapable of moving diagonally.\n\nNormal sudoku rules apply.\n\n[BATCH 1](https://sudokupad.app/7ajji7ruwa)\n[BATCH 2](https://sudokupad.app/v89ibddw0s)\n[BATCH 3](https://sudokupad.app/1j6uols752)\n[BATCH 4](https://sudokupad.app/9njqruoy1y)\n[BATCH 5](https://sudokupad.app/bhm7c5sdhc)\n[BATCH 6](https://sudokupad.app/i5g8i00x77)\n[BATCH 7](https://sudokupad.app/bh1imdxp73)\n[BATCH 8](https://sudokupad.app/22mlnyl0x9)","solution":"175496823629138574834527169386271945542689731791345682457962318963814257218753496","fogLight":"R1C1,R1C9,R4C6,R4C4,R6C4,R6C6,R9C9,R9C1,R9C5,R5C1,R5C9,R1C5","constraints":["fog"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"7wf14f41d2","ctcId":2849,"ctcDifficulty":"HARD","title":"Red + Blue = Purple","author":"Kaktuslav","rules":"Normal Sudoku rules apply. Color each cell in the grid either red or blue, such that no 2×2 square is monochromatic and the cells of each color form a single orthogonally connected region. Every line that passes through at least one red cell is an alternating-parity line (i.e. each pair of consecutive digits along the line must include one even and one odd digit). Every line that passes through at least one blue cell is a region-sum line (i.e. box borders divide the line into segments with equal sums; these sums may vary between lines). Any line that passes through both red and blue cells is also a renban (i.e. it contains a set of consecutive, non-repeating digits in any order).","solution":"723165489981234756654789231348957612216843597597621348469312875132578964875496123","constraints":["custom","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Color each cell in the grid either red or blue, such that no 2×2 square is monochromatic and the cells of each color form a single orthogonally connected region. Every line that passes through at least one red cell is an alternating-parity line (i.e. each pair of consecutive digits along the line must include one even and one odd digit).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Every line that passes through at least one blue cell is a region-sum line (i.e. box borders divide the line into segments with equal sums; these sums may vary between lines).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Any line that passes through both red and blue cells is also a renban (i.e. it contains a set of consecutive, non-repeating digits in any order).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"n43qyhsj2p","ctcId":2850,"ctcDifficulty":"HARD","title":"Mind the Dot","author":"Kaktuslav","rules":"Normal Sudoku rules apply. Box borders divide each blue line into segments with equal sums (the sum may vary between different lines). The black dot connects two digits, one of which is double the other.","solution":"694158273213497856587362941425719368836524719971836425358271694749685132162943587","constraints":["kropki","region-sum-line"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jbliq30p6u","ctcId":2851,"ctcDifficulty":"HARD","title":"Roots in the Fog","author":"Kaktuslav","rules":"Normal Sudoku rules apply. Exactly nine cells in the grid are 'rooters'. The value of a rooter equals the square root of its digit (in all other cells, the value equals the digit). No two rooters share a row, column, box, or digit. A black dot connects two cells where one value is double the other (not all such dots are necessarily given). Values on thermometers strictly increase from bulb to tip. The sum of the values along an arrow equals the value in the attached circle.  Along green lines, neighboring values differ by at least 5. On each purple line, the set of values consists of consecutive integers in any order. All cages have the same product of values (digits or values may repeat within a cage if allowed by other rules). The grid is partially covered in fog. Entering correct digits may clear some fog (not necessarily beneath or around the entered digit). No guessing is required.","solution":"369541728817692345425378169271465893586239471943187256794853612158726934632914587","fogLight":"R1C1,R1C3,R3C1,R2C2,R3C2,R2C1,R1C2","constraints":["arrow","custom","fog","german-whispers","kropki","renban","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"The sum of the values along an arrow equals the value in the attached circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Exactly nine cells in the grid are 'rooters'. All cages have the same product of values (digits or values may repeat within a cage if allowed by other rules).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c10"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Along green lines, neighboring values differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"A black dot connects two cells where one value is double the other (not all such dots are necessarily given).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Values on thermometers strictly increase from bulb to tip.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]}]},{"id":"l310pkxn5d","ctcId":2852,"ctcDifficulty":"MEDIUM","title":"Fogtorization","author":"Kaktuslav","rules":"Normal Sudoku rules apply. All blue (“+”) cages have the same SUM; all yellow (“×”) cages have the same PRODUCT. Both constants are to be determined by the solver. Digits may repeat within a cage if allowed by Sudoku. The grid is partially covered in fog. Entering correct digits may clear fog somewhere in the grid. Usually a correct entry will clear its own cell, but not always — some fog is extra dense! No guessing is required.","solution":"651943872497682315382517964169238457273154698548769123724891536936425781815376249","fogLight":"R1C1,R2C1,R3C1,R3C2,R2C2,R1C2,R1C3,R2C3,R3C3,R7C7,R8C7,R9C7,R9C8,R8C8,R7C8,R7C9,R8C9,R9C9,R9C1,R8C1,R9C2","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All blue (“+”) cages have the same SUM; all yellow (“×”) cages have the same PRODUCT.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"vagzppve3v","ctcId":2855,"ctcDifficulty":"MEDIUM","title":"Connectivity","author":"Fenners","rules":"Normal sudoku rules apply.\n \nRegion Sum Lines: The 3x3 box borders divide a blue line into segments. Each segment along a line has the same sum. (This segment sum can be different for different lines). \n\nRenban: Digits on a pink line form a set of non-repeating consecutive digits – these digits can appear in any order.\n\nGerman Whispers: Adjacent digits on a green line must have a difference of at least 5. \n\nArrows: Digits along an arrow sum to the digit in that arrow’s circle.","solution":"356721489841693725927548136732915864594876213168432957483169572675284391219357648","constraints":["arrow","german-whispers","region-sum-line","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"tjl67sygqk","ctcId":2856,"ctcDifficulty":"MEDIUM","title":"Once And For All","author":"99%Sneaky","rules":"Normal sudoku rules apply. Each of the following constraint types may contain no repeated digits anywhere in the puzzle E.g., if an orange line cell contains a 5, then no other orange line cell in the puzzle may contain a 5. Constraint types: 1) A digit in a grey square is even; 2) A digit in a grey circle is odd; 3) For digits in cells separated by a white dot, one must be one greater than the other; 4) For digits in cells separated by a black dot, one must be double the other; 5) Adjacent digits along an orange line must differ by 4 or more.","rulesClarified":"Normal sudoku rules apply.\n\nFive constraint types, each checked on its own. Within one type, no digit may repeat anywhere in the puzzle: all of that type's cells hold different digits, however far apart they are. For example, if an orange-line cell contains a 5, no other orange-line cell in the puzzle may contain a 5.\n\nGrey squares: the digit in a grey square is even.\n\nGrey circles: the digit in a grey circle is odd.\n\nWhite dots: the two cells on either side of a white dot hold digits where one is exactly one greater than the other.\n\nBlack dots: the two cells on either side of a black dot hold digits where one is double the other.\n\nOrange lines: along an orange line, digits that are next to each other differ by 4 or more. A two-cell orange line compares its two cells.","solution":"934512678187936542625784391419367285376258419852149736543821967768495123291673854","constraints":["custom","dutch-whispers","even","kropki","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each of the following constraint types may contain no repeated digits anywhere in the puzzle E.g., if an orange line cell contains a 5, then no other orange line cell in the puzzle may contain a 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"ho057rtsy5","ctcId":2857,"ctcDifficulty":"HARD","title":"Quetzalcóatl","author":"aqjhs","rules":"Normal sudoku rules apply.\n\nCells one chess knight move apart may not contain the same digit.\n\nAny three consecutive cells along a green (modular) line must contain one digit of each residue class modulo 3: {147}, {258} and {369}.\n\nDigits joined by a black dot are in 1:2 ratio, digits joined by a white dot are consecutive, and digits joined by a green dot are both in the same residue class modulo 3. Not all possible dots are given.","rulesClarified":"Normal sudoku rules apply.\n\nCells one chess knight move apart may not contain the same digit.\n\nAny three consecutive cells along a green line must contain one digit from each residue class mod 3: {1, 4, 7}, {2, 5, 8} and {3, 6, 9}.\n\nA black dot between two neighbouring cells means their digits are in a 1:2 ratio, so one digit is double the other.\n\nA white dot between two neighbouring cells means their digits are consecutive.\n\nA green dot between two neighbouring cells means both digits are in the same residue class mod 3.\n\nNot all possible dots are drawn. Two neighbouring cells with no dot between them have no rule from the dots.","solution":"175398426823461795964725138697132584531684972482579361748253619319846257256917843","constraints":["antiknight","custom","kropki","modular-line"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits joined by a black dot are in 1:2 ratio, digits joined by a white dot are consecutive, and digits joined by a green dot are both in the same residue class modulo 3.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"llm83vvquh","ctcId":2858,"ctcDifficulty":"VERY HARD","title":"cento mani e cento occhi","author":"aqjhs","rules":"Normal sudoku rules apply.\n\nDigits along the slow thermometer line increase or stay the same starting from its only bulb end. The position of the single bulb end is to be determined and it is on one of the cells marked with circles.","solution":"723568149659314782814729563382495671965137824147682395596843217278951436431276958","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"kkny0tykl7","ctcId":2859,"ctcDifficulty":"VERY HARD","title":"sphinx of black quartz","author":"aqjhs","rules":"Normal sudoku rules apply.\n\nCells one chess knight's move apart may not contain the same digit.\n\nDigits joined by a white dot are consecutive. All possible dots are given.\n\nDigits joined by a V sum to 5. All such pairs are given.\n\nGrey line is a palindrome: its digits read the same in either direction.","rulesClarified":"Normal sudoku rules apply.\n\nAntiknight: two cells one chess knight's move apart may not contain the same digit.\n\nWhite dots: a white dot between two cells means their digits are consecutive, differing by exactly 1. The setter says all possible white dots are drawn, so two cells with no white dot between them are not consecutive.\n\nV: a V between two cells means their digits sum to 5. The setter says all such pairs are drawn.\n\nThe grey line is a palindrome: its digits read the same in either direction.","solution":"183624759926157483574839261748392615392516847615748392461973528839265174257481936","constraints":["XV","antiknight","kropki","palindrome"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"59fo21vx0w","ctcId":2860,"ctcDifficulty":"MEDIUM","title":"An Ill Omen","author":"aqjhs","rules":"Normal sudoku rules apply.\n\nCells separated by one move of a chess knight may not contain the same digit.\n\nFor each line, the digits in the two cells marked with dots are ‘look-and-say clues’ ie in at least one way of reading them, one digit indicates how many times the other digit appears on the line. (eg if the marked cells contain 78 it can mean the line has seven instances of 8, or eight instances of 7)\n\nAdjacent digits along an orange line must have a difference of at least 4.","solution":"629753814438126759571894623756941238982635147314287965247518396895362471163479582","constraints":["antiknight","custom","dutch-whispers"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For each line, the digits in the two cells marked with dots are ‘look-and-say clues’ ie in at least one way of reading them, one digit indicates how many times the other digit appears on the line. (eg if the marked cells contain 78 it can mean the line has seven instances of 8, or eight instances of 7)","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"7llvcaivec","ctcId":2861,"ctcDifficulty":"HARD","title":"can i pet that dog!?","author":"aqjhs","rules":"Normal sudoku rules apply.\n\nDoppel-Dög loop: Draw an orthogonal non-branching closed loop that doesn't cross or touch itself, not even diagonally.  The loop \"starts\" at the cell marked with the dog and is considered to be oriented in the direction indicated by the arrow (i.e. r6c6 and r6c7 are in the loop). A cell on the loop with a digit D will have a value equal to the cell D steps away along the loop in the orientation given by the arrow. Cells not on the loop will have a value equal to the digit in them.\n\nAdjacent digits (not values) along the loop must have a difference of at least 5.\n\nValues in a cage sum to the indicated total. \n\nCells marked with a circle are not part of the loop and have a digit that equal to the count of the, up to 8, neighboring loop cells. \n\nClues outside the grid show the value sum of loop cells in the indicated row/column.","solution":"517293846394865172862471539275618394946352781183947265438526917651739428729184653","constraints":["cage","custom","german-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Values in a cage sum to the indicated total.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The loop \"starts\" at the cell marked with the dog and is considered to be oriented in the direction indicated by the arrow (i.e. r6c6 and r6c7 are in the loop). Cells marked with a circle are not part of the loop and have a digit that equal to the count of the, up to 8, neighboring loop cells. Clues outside the grid show the value sum of loop cells in the indicated row/column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c8","c9"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"pzyl7pacx7","ctcId":2862,"ctcDifficulty":"HARD","title":"Harmonic Split","author":"gdc","rules":"Normal sudoku rules apply.\n\nDoubler Yin Yang: Shade each cell light or dark so that cells of the same color are orthogonally connected and each 2x2 contains both colors. Dark cells have double their digits as values. (Light cells are unaffected)\n\nEqual Split Lines: Dots split lines into segments with equal value-sums. Values may repeat on segments but digits may not.","solution":"215964378376281549849375162462519837938742651157836924683127495524698713791453286","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Dark cells have double their digits as values. Equal Split Lines: Dots split lines into segments with equal value-sums.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"sde0yq3oj3","ctcId":2863,"ctcDifficulty":"HARD","title":"8'","author":"ICHTUES & Florian Wortmann","rules":"Normal sudoku rules apply.\n\nDigits may not repeat along the marked diagonal.\n\nDigits an equal distance from the centre of a lavender line sum to the central digit of that line.","solution":"753649182291738564486125793925863417364217958817594326648351279579482631132976845","constraints":["diagonal","zipper-line"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"97wi902h8v","ctcId":2864,"ctcDifficulty":"HARD","title":"Get Your Crayons","author":"Eric Rathbun","rules":"Normal sudoku rules apply. \nClues outside the grid give the sum of the digits along the indicated diagonal. \nDigits separated by a white dot have a difference of one, while digits separated by a black dot are in a 1 to 2 ratio (ie one digit will be double the other). Not all possible dots are given. \nCells separated by a single knight's move (in chess) do not contain the same digit. \nCells separated by a single king's move (in chess) do not contain the same digit.","rulesClarified":"Normal sudoku rules apply.\n\nA clue outside the grid gives the total of the digits along the diagonal it points into. The diagonal starts at the cell next to the clue and runs to the edge of the grid.\n\nTwo digits separated by a white dot differ by exactly one.\n\nTwo digits separated by a black dot are in a 1 to 2 ratio: one digit is double the other.\n\nNot all possible dots are drawn. Where there is no dot between two cells, that pair gives no dot information.\n\nTwo cells a single knight's move apart (as in chess) do not contain the same digit.\n\nTwo cells a single king's move apart (as in chess) do not contain the same digit.","solution":"795681432681432795432795681956814327814327956327956814568143279143279568279568143","constraints":["antiking","antiknight","kropki","little-killer"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hvtrbv1n24","ctcId":2865,"ctcDifficulty":"MEDIUM","title":"Unique Under The Fog 6.0","author":"Visumation","rules":"Normal sudoku rules apply. \nThe grid is partially covered in fog; placing a correct digit may clear fog somewhere in the grid. \nEach of the following constraint types may contain no repeated digits anywhere in the puzzle. E.g., if a renban line contains a 5, then no other renban line cell in the puzzle  may contain a 5: \n1) Little Killer: Black numbers with an arrow outside the grid give the the sum of the digits on the indicated diagonal; \n2) X-Sums: Red numbers outside the grid indicate the sum of the first X digits in that row or column, where X is the first digit in that row or column; \n3)  Digits on a purple Renban (RB) line form a non-repeating set of consecutive digits NB All Renban lines are exactly three cells long; \n4) Neighbouring digits on a green German Whisper (GW) line must have a difference of at least 5; \n5) The 3x3 box borders divide blue Region Sum (RS) lines into segments. Each segment along a line has the same sum.","solution":"516827394729364158483195672931286745852743916674519283165938427248671539397452861","fogLight":"","constraints":["custom","fog","german-whispers","little-killer","region-sum-line","renban","x-sum"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each of the following constraint types may contain no repeated digits anywhere in the puzzle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"3esmd3dr55","ctcId":2866,"ctcDifficulty":"MEDIUM","title":"Packing Problem","author":"clover!","rules":"Normal sudoku rules apply. In each cage, there is one digit that equals the sum of the other three digits in that cage. Digits may repeat in cages if allowed by sudoku rules.","solution":"865793421743251869291486753674932518952618347318547692186324975537169284429875136","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"In each cage, there is one digit that equals the sum of the other three digits in that cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"ushr6uitov","ctcId":2867,"ctcDifficulty":"HARD","title":"Oh Bobbins","author":"apetersen","rules":"Normal Sudoku rules apply.\nIf a white dot separates digits, they are consecutive.\nIf a black dot separates digits, one is double the other.\nAdjacent digits along a green line have a difference of at least 5.\n(The dots in each of the 9 boxes are braille letters.)","solution":"637219845984765123125438796892543671576891234341672958463987512219356487758124369","constraints":["german-whispers","kropki"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"0lft1u2q32","ctcId":2868,"ctcDifficulty":"HARD","title":"Besties 2","author":"Jeet Sampat","rules":"Normal Sudoku rules apply. Any two cells separated by a single Chess knight's move must contain different digits. Digits within a cage (indicated by the dashed lines) must sum to the clue in its top-left corner. The clue outside the grid gives the sum of all digits along the indicated diagonal. Digits may repeat on this diagonal if allowed by the other rules.","solution":"241837956736529481895614372652148739378295614914376528563481297487952163129763845","constraints":["antiknight","cage","little-killer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"272yz2ohf1","ctcId":2869,"ctcDifficulty":"MEDIUM","title":"Ramify","author":"dumediat","rules":"- Normal sudoku rules apply; place the digits 1-9 in each row, column and box without repetition.\n- Killer: Digits in cages must sum to the number in the top left corner of the cage. Digits may not repeat within a cage.\n- Sandwich: The numbers outside the grid give the sum of the digits between the 1 and the 9 in that row or column.","solution":"796132548185467293342598167261879435957243681834615729473921856618354972529786314","constraints":["cage","sandwich"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"wixrf6c2bx","ctcId":2872,"ctcDifficulty":"HARD","title":"Addition By Subtraction","author":"Cane_Puzzles","rules":"Normal sudoku rules apply. Along thermometers, digits must increase from the bulb end. The purple line contains a set of consecutive digits in any order. Adjacent digits on a green line differ by at least 5.","solution":"813697524294518673657342189729453861461789235538261947982134756376925418145876392","constraints":["german-whispers","renban","thermometer"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"The purple line contains a set of consecutive digits in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"868i586sml","ctcId":2873,"ctcDifficulty":"MEDIUM","title":"Four At A Time","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Each grey line is a \"slow thermometer\" with an invisible bulb at one end. Digits on a slow thermometer either increase or stay the same, as they move away from the bulb, but they never decrease.","solution":"961437258485269173237851649842716395316594827759328416593642781628175934174983562","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Each grey line is a \"slow thermometer\" with an invisible bulb at one end.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"aadq3z8j80","ctcId":2874,"ctcDifficulty":"HARD","title":"Right Twice A Day","author":"Jeff Wajes","rules":"Normal sudoku rules apply. Adjacent digits along a green line must differ by at least 5. Each pink line contains a set of consecutive, non-repeating digits, which can appear in any order. Each grey line consists of one or more contiguous groups of cells, each of which sums to 10. These groups of cells cannot overlap; every cell is part of exactly one group. Lines may share endpoints, but otherwise don't overlap.","solution":"279316854831457926456289317648923175592174683713568492324791568985632741167845239","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each grey line consists of one or more contiguous groups of cells, each of which sums to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"5yg1tpwhow","ctcId":2876,"ctcDifficulty":"MEDIUM","title":"Scylla","author":"Phistomefel","rules":"Normal sudoku rules apply. In cages, digits must sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage.","solution":"531498267947265381286731495815629743694317852723584619469173528358942176172856934","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qz9m4zn7nf","ctcId":2877,"ctcDifficulty":"VERY HARD","title":"Blue Arrow","author":"Kaktuslav","rules":"Chaos construction: Divide the grid into 9 regions, each consisting of 9 orthogonally connected cells. Place the digits 1-9 exactly once in every row, column, and region. \n\nJumping arrow: The digits along the arrow sum to the three-digit number displayed in the attached pill. The arrow passes through the centers of all cells that are not part of the pill (note that consecutive arrow cells are not necessarily adjacent; for example, a portion of the arrow follows r7c1 → r7c3 → r8c1).\n\nRegion sum line: The arrow functions as a region sum line: along the arrow, every maximal sequence of digits within the same region has the same sum. I.e. when all non-pill cells are arranged in sequence according to the order in which the arrow visits their centers, this sequence will be composed of disjoint contiguous segments with equal sums. Two consecutive cells in this sequence belong to the same segment if and only if they are part of the same region.\n\nInequalities: The inequality sign points to the smaller digit.","solution":"387612954146298573958371426475186392263459187621735849739864215512943768894527631","constraints":["arrow","custom","inequality","region-sum-line"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Chaos construction: Divide the grid into 9 regions, each consisting of 9 orthogonally connected cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"w6uzuj1m0m","ctcId":2878,"ctcDifficulty":"HARD","title":"Befuddlement","author":"Oddlyeven","rules":"Rules: Normal Sudoku rules apply. Put the digits 1 to 9 once each into every row, column and box.\n\nDynamic Fog: The grid is covered in fog. Placing a correct digit will remove the fog from its cell and possibly other cells in the grid.\n\nDoublers: One cell in each row, column and box is a doubler. The value of a doubler cell is equal to twice its digit. Each of the digits from 1 to 9 appears in a doubler cell.\n\nUniqueness: On each of the constraints below, *values* do not repeat anywhere in the puzzle. For example, if there is a 2 on a parity line, 2 or double 1 can't appear anywhere else on a parity line, but double 2 could because it has a value of 4.\n\nWhispers: Adjacent values on a thin green line differ by at least 5.\n\nRenban: Values on a thick purple line form a set of consecutive numbers with no repeats.\n\nParity: Adjacent values on a hollow red line must alternate between odd and even.\n\nHigh: A value on an orange circle must be greater than 5.\n\nLow: A value on a blue square must be lower than 5.","rulesClarified":"Normal Sudoku rules apply: put the digits 1 to 9 once each into every row, column and box.\n\nDynamic fog: the grid is covered in fog. Placing a correct digit will remove the fog from its cell and possibly other cells in the grid.\n\nDoublers: one cell in each row, column and box is a doubler. The value of a doubler cell is twice its digit. Each of the digits from 1 to 9 appears in a doubler cell.\n\nA cell that is not a doubler has its digit as its value. The constraints below compare values, not digits.\n\nUniqueness: on each constraint below, values do not repeat anywhere in the puzzle. For example, if there is a 2 on a parity line, 2 or double 1 can't appear anywhere else on a parity line, but double 2 could because it has a value of 4.\n\nWhispers: adjacent values on a thin green line differ by at least 5.\n\nRenban: values on a thick purple line form a set of consecutive numbers with no repeats.\n\nParity: adjacent values on a hollow red line must alternate between odd and even.\n\nHigh: a value on an orange circle must be greater than 5.\n\nLow: a value on a blue square must be lower than 5.","solution":"486579231512836749937142865245713698178695324693284157754321986361958472829467513","fogLight":"R7C1,R9C1,R9C3,R9C5,R6C1,R5C2","constraints":["custom","fog","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Doublers: One cell in each row, column and box is a doubler. Uniqueness: On each of the constraints below, *values* do not repeat anywhere in the puzzle. Parity: Adjacent values on a hollow red line must alternate between odd and even. High: A value on an orange circle must be greater than 5. Low: A value on a blue square must be lower than 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c8","c12","c13","c14"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"Whispers: Adjacent values on a thin green line differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Renban: Values on a thick purple line form a set of consecutive numbers with no repeats.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c11"]}]},{"id":"wbwn6dl8xz","ctcId":2879,"ctcDifficulty":"VERY HARD","title":"Double the fun","author":"Lithium-Ion","rules":"Normal sudoku rules apply. Digits are not allowed to repeat on any positive diagonal (i.e. any diagonal going from the lower-left part of the grid to the upper-right part of the grid). A digit x in a black circle indicates exactly how many of the up to 8 neighboring cells (i.e. orthogonally and diagonally adjacent cells) contain a digit that is in a 1:2 ratio with x. All black circles are given. The sum of the digits in Phistomefel's ring (marked by the cage) is prime.","solution":"813625974749183256625749138564237819398561742271894563182456397437918625956372481","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits are not allowed to repeat on any positive diagonal (i.e. any diagonal going from the lower-left part of the grid to the upper-right part of the grid). A digit x in a black circle indicates exactly how many of the up to 8 neighboring cells (i.e. orthogonally and diagonally adjacent cells) contain a digit that is in a 1:2 ratio with x. The sum of the digits in Phistomefel's ring (marked by the cage) is prime.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5"]}]},{"id":"m408yajamc","ctcId":2880,"ctcDifficulty":"MEDIUM","title":"Under the Influence","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nINFLUENCER CELLS:\nThe grid contains nine 'influencer cells', each in a different row, column and box, and each containing a different digit.\n\nEvery cell in the grid has a value equal to its own digit plus the digits in any orthogonally adjacent influencer cells.\n\nEg: a cell containing a digit 2 would have a value of 10 if it neighbours an influencer 3 and an influencer 5, because 2 + 3 + 5 = 10.\n\nCAGES:\nThe small clue in the corner of a cage indicates the total value of the cells in that cage.\n\nREGION SUM LINES:\n3 x 3 box borders divide blue lines into segments. The values on each segment have the same sum, though this sum can be different for different lines.","solution":"793541826412836975658279413265918734984327651371465289849152367127693548536784192","constraints":["cage","custom","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The small clue in the corner of a cage indicates the total value of the cells in that cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The grid contains nine 'influencer cells', each in a different row, column and box, and each containing a different digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"The values on each segment have the same sum, though this sum can be different for different lines.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]}]},{"id":"jwyxh2qwad","ctcId":2881,"ctcDifficulty":"MEDIUM","title":"Threedoku","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along an orange line have a difference of at least four.\nEach cage has digits that sum to 3.\nThe central digit of the puzzle is even.","solution":"948273615372156849516984372624817953189365427753492186495738261261549738837621594","constraints":["cage","dutch-whispers","even"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"mhkw3cwjw3","ctcId":2882,"ctcDifficulty":"MEDIUM","title":"Royalty","author":"zetamath","rules":"Normal sudoku rules apply.\n\nRenban Lines: The purple lines in the grid are renban lines. Digits on a line form a set of non-repeating, consecutive digits in any order.","solution":"324956781596871432178324956861543297753219648942768513685197324439682175217435869","constraints":["renban"],"constraintFacts":[{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"j27rj7frco","ctcId":2883,"ctcDifficulty":"MEDIUM","title":"Half Circles","author":"Dorlir","rules":"Normal sudoku rules apply.\n\nA digit N placed inside a circle or semicircle indicates that exactly N full circles in the grid contain the digit N.\n\nTwo semicircles together count as one full circle. For example, if there are four semicircles containing the digit 5 and three full circles containing the digit 5, then the total count is 2+3=5 circles with the digit 5.","solution":"825714693936825714147936825582471369693582471714693582258147936369258147471369258","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit N placed inside a circle or semicircle indicates that exactly N full circles in the grid contain the digit N.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"cdifwlxo10","ctcId":2885,"ctcDifficulty":"VERY HARD","title":"Two Truths and a Different Truth","author":"Oddlyeven","rules":"Rules: Normal Sudoku rules apply. Put the digits 1 to 9 once each into every row, column and box.\nYin Yang: Shade some cells in the grid such that all shaded cells are orthoganally connected and all unshaded cells are orthogonally connected. No 2x2 may be all shaded or all unshaded.\nDoublers: A cell that is a doubler has value equal to twice its digit.\nTwo Truths and a Different Truth: For all the following constraints, if shaded cells are treated as doublers and unshaded cells are normal then two of the clues are correct and the third is incorrect. If unshaded cells are treated as doublers and shaded cells are normal then the same two clues are incorrect and the third is correct.\nRenban: Values on a pink line form a set of consecutive numbers with no repeats.\nArrows: Values on an arrow sum to the value in that arrow's circle.\nX: Values on an X sum to 10.\nDots: Values on a white dot are consecutive. Values on a black dot are in a 1:2 ratio.\nOdd and Even: A value on a grey circle is odd. A value on a grey square is even.","solution":"714298563923564817856371294231786945648159732579423681185932476397645128462817359","constraints":["XV","arrow","custom","even","kropki","odd","renban","yin-yang"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"X: Values on an X sum to 10.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Arrows: Values on an arrow sum to the value in that arrow's circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Doublers: A cell that is a doubler has value equal to twice its digit. Two Truths and a Different Truth: For all the following constraints, if shaded cells are treated as doublers and unshaded cells are normal then two of the clues are correct and the third is incorrect. If unshaded cells are treated as doublers and shaded cells are normal then the same two clues are incorrect and the third is correct.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c7"]},{"slug":"even","type":"even","variant":"modified","modifiers":[],"params":null,"note":"A value on a grey square is even.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c14"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Values on a black dot are in a 1:2 ratio.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c11","c12"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Renban: Values on a pink line form a set of consecutive numbers with no repeats.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"sw5a5iw9s2","ctcId":2886,"ctcDifficulty":"VERY HARD","title":"Purple Reign","author":"Math Pesto","rules":"Normal sudoku rules apply. Cells that are a knight's move apart in chess cannot contain the same digit. Digits on a line of any color form a set of non-repeating consecutive numbers (in any order).","solution":"813796524945823671726514983582371496691482357374659218138265749459137862267948135","constraints":["antiknight","renban"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"hrinu3frw3","ctcId":2887,"ctcDifficulty":"MEDIUM","title":"Blue or Yellow?","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nDraw a snake connecting the two green spots. The snake must be one cell wide, may only move orthogonally, and may not touch itself (not even diagonally.)\n\nAdjacent digits along the snake must have a difference of at least 5.\n\nA digit in a coloured circle indicates how many times that digit appears in a circle of that colour.\n\nAll circles of one colour are on the snake. All circles of the other colour are not on the snake.","solution":"563917284219485736784362591638271459971548362425693817192854673847136925356729148","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a snake connecting the two green spots. A digit in a coloured circle indicates how many times that digit appears in a circle of that colour.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"9jas258m1s","ctcId":2889,"ctcDifficulty":"MEDIUM","title":"Kritzeleien","author":"Myxo","rules":"Sudoku: Place the digits 1-9 exactly once in each row, column and box.\n\nRegion Sum Lines: Box borders divide blue lines into segments. The digits on each segment of the same line must sum to the same total.\n\nRenban: Digits on pink lines form a non-repeating, consecutive sequence in any order.","solution":"196837542824165973753294816472319685931658427568472139317946258249583761685721394","constraints":["region-sum-line","renban"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"0yr8dzgjd8","ctcId":2890,"ctcDifficulty":"HARD","title":"Caged Clones","author":"RockyRoer","rules":"Normal sudoku rules apply.\n\nEach cage must appear cloned somewhere in box nine, without rotations or reflections.  All cages marked with x must have the same total, to be deduced by the solver.\n\nCells separated by a gray dot must either be consecutive, or have a 2:1 ratio.","solution":"894257361237164598615398472721835649483976125569421783152649837376582914948713256","constraints":["cage","clone","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"zy1s9y2qi8","ctcId":2891,"ctcDifficulty":"HARD","title":"Threads of Silence","author":"Dorlir","rules":"Normal sudoku rules apply.\n\nEvery run of five digits on the yellow line contains a digit from {1,6}, a digit from {2,7}, a digit from {3,8}, a digit from {4,9}, and the digit 5.\n\nThe grey line consists of one or more contiguous groups of cells, each of which sums to 10. These groups of cells cannot overlap.\n\nDigits an equal distance from the center of the purple line must sum to the digit in the center of that purple line.\n\nAdjacent digits along the green line must differ by at least 5.\n\nDigits on the pink line form a set of consecutive integers in some order.","solution":"845639271739421658162758493258316749913247865476985312587162934391874526624593187","constraints":["custom","german-whispers","renban","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every run of five digits on the yellow line contains a digit from {1,6}, a digit from {2,7}, a digit from {3,8}, a digit from {4,9}, and the digit 5. The grey line consists of one or more contiguous groups of cells, each of which sums to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"2vyqqhy6ky","ctcId":2892,"ctcDifficulty":"VERY HARD","title":"Loopy Circles","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nDraw a 1 cell wide loop through the centers of some cells. The loop only moves orthogonally and cannot branch or touch itself, even diagonally.\n\nA digit in a circle on the loop indicates how many circles on the loop contain that digit. Similarly, a digit in a circle off the loop indicates how many circles off the loop contain that digit.\n\nBlack dots separate digits where one is double the other. Additionally, exactly one cell touching a black dot is on the loop, and the other is off the loop.\n\nWhite dots separate consecutive digits. Additionally, the two cells touching a white dot are either both on the loop, or both off the loop.\n\nNot all dots are necessarily given.","solution":"193765842562498137847123596925631478678954213431872659789516324316247985254389761","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a 1 cell wide loop through the centers of some cells. A digit in a circle on the loop indicates how many circles on the loop contain that digit. Similarly, a digit in a circle off the loop indicates how many circles off the loop contain that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c8"]}]},{"id":"luzxwziiq3","ctcId":2893,"ctcDifficulty":"HARD","title":"Entangled","author":"Phistomefel","rules":"Normal sudoku rules apply. Digits in cages must sum to the small clue in the top left corner of the cage. The two main diagonals each contain every number from 1 to 9 exactly once. The cells on a purple line contain a set of non-repeating consecutive digits, but not necessarily in order.","solution":"875632491396741258214859376923184567157963842468275139639428715581397624742516983","constraints":["cage","diagonal","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"sln1iupe4k","ctcId":2894,"ctcDifficulty":"MEDIUM","title":"v38","author":"Riffclown","rules":"• Normal Sudoku rules apply. Place the digits 1-9 in each row, column and box without repetition.\n• Killer: Digits in cages must sum to the number in the top left corner of the cage. Digits may not repeat within a cage.\n• V: Digits separated by an V sum to 5. No negative constraint","rulesClarified":"Normal Sudoku rules apply: each row, each column and each 3x3 box contains the digits 1 to 9 once each.\n\nKiller cages: the digits in a cage add up to the number shown in its top-left corner. No digit repeats within a cage.\n\nA V between two neighbouring cells means their two digits add up to 5.\n\nA pair of neighbouring cells with no V between them has no such constraint. Their digits may or may not add up to 5.","solution":"715249638293186574486753129547621983921438756638597241152364897864972315379815462","constraints":["XV","cage"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"pd589n0d3g","ctcId":2899,"ctcDifficulty":"HARD","title":"Quadrank Arrows","author":"Phil The Hat","rules":"Normal sudoku rules apply.\n\nQUADRANK ARROWS:\n• Each circle has a value equal to the four digits around the clue arranged in ascending order. Eg if the four digits were 4,3,6,4 then the value of the circle would be 3446. \n• Assign each circle a rank according to its value's position in a list of the all of the circles' values. The lowest rank would have rank 1, the next lowest would have rank 2 etc. Place each circle's rank into the cell at the tip of the arrow emerging from that circle. NB clues with the same value would have the same rank and would have the same digit in the tip of their circle's arrow.\n\nKILLER CAGES:\nDigits in a cage sum to the given total.","solution":"932475681571862934684193257418726593729531846365984712843657129256319478197248365","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Each circle has a value equal to the four digits around the clue arranged in ascending order. Eg if the four digits were 4,3,6,4 then the value of the circle would be 3446. • Assign each circle a rank according to its value's position in a list of the all of the circles' values. The lowest rank would have rank 1, the next lowest would have rank 2 etc. Place each circle's rank into the cell at the tip of the arrow emerging from that circle. NB clues with the same value would have the same rank and would have the same digit in the tip of their circle's arrow.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"xlt5uvwad5","ctcId":2900,"ctcDifficulty":"MEDIUM","title":"Luck ","author":"Chris Napolitano ","rules":"Normal sudoku rules apply. Digits on an arrow sum to the digit in that arrow’s circle. Within a cage, digits do not repeat and sum to the total given. All cages sum to 7 or 13.","solution":"216587943584139672397642815851793264762814359943256187478321596129465738635978421","constraints":["arrow","cage"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"pblc50fmga","ctcId":2901,"ctcDifficulty":"MEDIUM","title":"Mad 4 Diagonalz","author":"Chris Napolitano","rules":"Normal sudoku rules apply. Cells with squares in them contain even digits. In this grid, the digit '4' is the only even digit that is allowed to see itself diagonally.","solution":"283765914179834265654219387348651729512947638796328541837196452925483176461572893","constraints":["custom","even"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In this grid, the digit '4' is the only even digit that is allowed to see itself diagonally.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"8jf1461dp3","ctcId":2903,"ctcDifficulty":"MEDIUM","title":"Dippin' Dots","author":"Chris Napolitano","rules":"Normal sudoku rules apply. Oh no! I accidentally dropped all of my constraint types (flavors) into a bowl, took a whisk, and mashed them together. What a klutz; good thing I remember color theory! Digits connected by an olive dot must be from different parities (1 even/1 odd) and differ by at least 5. Digits connected by a lavender dot must be consecutive and from different entropic sets (123/456/789). Digits in killer cages do not repeat and must sum to the number in the top left of the cage.","solution":"613857294745962831289341657594276318128493765376518942432189576961725483857634129","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits connected by an olive dot must be from different parities (1 even/1 odd) and differ by at least 5. Digits connected by a lavender dot must be consecutive and from different entropic sets (123/456/789).","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"15v4c7jldc","ctcId":2904,"ctcDifficulty":"VERY HARD","title":"Sorry, could you repeat that?","author":"Chris Napolitano","rules":"Normal sudoku rules apply. Adjacent digits on green lines must differ by at least five and each line must contain exactly one repeat digit. Once a digit has appeared on a line as a 'repeat digit,' it may not do so again. Antiknight: Digits cannot be a knight's move (in chess) away from themselves. Digits in cages must not repeat and sum to the total in the top left corner.","solution":"126583479745629183389147625538914267967238514214765938851476392472391856693852741","constraints":["antiknight","cage","german-whispers"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qhx16aqc8i","ctcId":2905,"ctcDifficulty":"VERY HARD","title":"Lines Lines","author":"SSG","rules":"Normal sudoku rules apply.\n\nLines: Draw two non-branching lines in the grid - one green and one blue - that connect the centres of cells. The lines must only move orthogonally (i.e. not diagonally). Neither line may touch itself, even diagonally. The two lines may, however, touch or cross each other, but only at discrete points (i.e.if the two lines meet in the centre of one cell they cannot continue in the same direction into the centre of their next cell). The green line must form a closed loop; and, the ends of the blue line may not be on any intersections with the green line.\n\nProjected Sums: Clues outside the grid give the sum of digits on lines along the indicated direction. Coloured clues count only the line of that colour. Black clues count digits on both lines. If both lines pass through a cell, that cell's digit only counts once in the projected sum.\n\nGerman Whispers: Along the green line adjacent digits must differ by at least 5.\n\nModular Lines: Along the blue line, in every run of three cells, the three digits in those cells must each have a different remainder when divided by 3.\n\nClones: The two cages are exact clones of each other. They contain the same digits in the same positions and they contain the same lines (including colour) in the same positions. Digits may repeat within the clone if otherwise allowed.","solution":"137258694948613275265497183694581327572934861813726549781369452456172938329845716","constraints":["clone","custom","german-whispers","modular-line"],"constraintFacts":[{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Lines: Draw two non-branching lines in the grid - one green and one blue - that connect the centres of cells. Projected Sums: Clues outside the grid give the sum of digits on lines along the indicated direction.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]}]},{"id":"qhybrqkov4","ctcId":2906,"ctcDifficulty":"HARD","title":"The 23 Enigma","author":"sujoyku","rules":"- Normal sudoku rules apply, i.e. each row, column, and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- Killer cages: Digits in a cage do not repeat and must sum to 23.","solution":"715892643498736512326154798279648135183275964654913827547361289831529476962487351","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"s6pgqi6msp","ctcId":2907,"ctcDifficulty":"MEDIUM","title":"Happy Birthday Sujoyku","author":"sujoyku and friends (Ft: Calvinball, ChinStrap, gdc, mellowrobinson, MSDOS, Nordy, SamuPiano, and sujoyku)","rules":"Sudoku: Normal sudoku rules apply. Place the digits 1 to 9 once each in every row, column, and 3x3 box.\n\nKiller: Digits may not repeat in a cage and must sum to the number in the top left corner of the cage.\n\nDutch Whisper: Adjacent digits along a thicker orange line must differ by at least 4.\n\nRegion Sum Line: The 3x3 box borders divide the thinner blue line into segments, each of which has the same sum.\n\nOdd Lots: Digits in orange circles count the total number of odd digits along the line connected to the circle, including the circled cell.\n\nSplit Peas: Digits on a thin green line with circles at both ends sum to a two-digit number; the 'tens' digit of this sum is in one circle and the 'units' digit is in the other circle.","solution":"416987532382516479975234816641829357853761924729345681137698245264153798598472163","constraints":["cage","custom","dutch-whispers","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Odd Lots: Digits in orange circles count the total number of odd digits along the line connected to the circle, including the circled cell. Split Peas: Digits on a thin green line with circles at both ends sum to a two-digit number; the 'tens' digit of this sum is in one circle and the 'units' digit is in the other circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"2vnskp4zft","ctcId":2908,"ctcDifficulty":"MEDIUM","title":"Giza","author":"Kaktuslav","rules":"Normal sudoku rules apply. Every constraint in the puzzle is a straight line: every horizontal line is a renban, every vertical line is a German whisper, and every diagonal line is a region sum line. Different lines of the same type do not share cells. The grid is partially covered in fog. Entering correct digits may clear fog somewhere in the grid. No guessing is required.\n\nA renban line contains a set of consecutive, non-repeating digits in any order. Adjacent digits on a German whisper line must differ by at least 5. Box borders divide a region sum line into segments each of which must have the same total (different lines may have different totals).","solution":"197865243632741598548293671856934127321587964479612835914356782283179456765428319","fogLight":"R7C1,R8C1,R9C1,R9C2,R8C2,R7C2,R6C1,R8C3,R9C3,R9C4","constraints":["custom","fog","german-whispers","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Different lines of the same type do not share cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"3cm1bpm2jv","ctcId":2909,"ctcDifficulty":"HARD","title":"(+10)-Yang","author":"Kaktuslav","rules":"Normal sudoku rules apply.\nYin-Yang: Shade some cells in the grid so that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2×2 region is entirely shaded or entirely unshaded.\nA shaded cell containing digit x has value x+10; an unshaded cell has value equal to its digit.\nRegion sum lines: Blue lines are divided into segments by box borders. All segments along a single line must have the same sum of values (this sum may differ between lines).\nRatio kropki dots: Cells connected by a black dot have values, one of which is double the other. Not all dots are necessarily given.\nDynamic Fog of War: The grid is partially covered in fog. Placing correct digits reveals their own cell and may also lift fog elsewhere in the grid. No guessing is required.","solution":"924375168617894325835621974451986732792153486386247519149768253278539641563412897","fogLight":"R4C4,R5C4,R6C4,R6C5,R6C6,R5C6,R4C6,R4C5,R5C5","constraints":["fog","kropki","region-sum-line","yin-yang"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Ratio kropki dots: Cells connected by a black dot have values, one of which is double the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"Region sum lines: Blue lines are divided into segments by box borders.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"tkn1nytyis","ctcId":2910,"ctcDifficulty":"EASY","title":"Snackdoku Title Puzzle","author":"Panthera","rules":"Standard Sudoku rules apply.\nKropki Dots: Digits separated by a white dot are consecutive. Digits separated by a black dot have a 1:2 ratio.","solution":"315246987926783541847591236283654719691827354574319628158972463732468195469135872","constraints":["kropki"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"wcq666h4y2","ctcId":2913,"ctcDifficulty":"HARD","title":"Hamiltonian Killer Thermo","author":"Kaktuslav","rules":"Place the digits 1–9 exactly once in each row and each column of the grid. \nDraw a directed path that moves orthogonally between cell centers and visits every cell of the grid exactly once. Each of the 27 cages can be entered by the path at most once (i.e. the path must visit all cells of a cage in a single continuous run before leaving it).\nThe path acts as a thermometer with respect to cage totals: as the path moves away from its starting cell, the sums of the cages it visits must strictly increase.\nDigits may not repeat within a cage.","solution":"231469587123645879512378964346257198687934215795812436864193752958726341479581623","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a directed path that moves orthogonally between cell centers and visits every cell of the grid exactly once. Each of the 27 cages can be entered by the path at most once (i.e. the path must visit all cells of a cage in a single continuous run before leaving it). The path acts as a thermometer with respect to cage totals: as the path moves away from its starting cell, the sums of the cages it visits must strictly increase. Digits may not repeat within a cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]}]},{"id":"dkjeovl1up","ctcId":2914,"ctcDifficulty":"VERY HARD","title":"Th13teen","author":"IcyFruit","rules":"Place a digit from 1-7 in each cell. Each digit must appear exactly once in each row, column, and box, except for the digits 1 and 3, which may appear any positive number of times.\nEvery 1 and 3 must be part of at least one adjacent pair of cells which reads as '13' either from left to right or from top to bottom.\nDigits in a cage do not repeat (including 1 and 3) and sum to the total shown in the top left corner.","solution":"421571613713613245651342713137261354265413137134157126346315372132734561571326413","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every 1 and 3 must be part of at least one adjacent pair of cells which reads as '13' either from left to right or from top to bottom.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"sjk13nc1vf","ctcId":2915,"ctcDifficulty":"MEDIUM","title":"Golden Arrow","author":"James Kopp","rules":"Normal sudoku rules apply.\nNo digit can appear a chess knight's or a chess king's move away from itself.\nDigits along an arrow sum to the number in the oval which is a 2-digit number reading left-to-right.\nAdjacent digits along the arrow (including the oval) have a difference of at least four.","solution":"582941736736582941941736582658294173173658294294173658365829417417365829829417365","constraints":["antiking","antiknight","arrow","dutch-whispers"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"ue23keydhf","ctcId":2916,"ctcDifficulty":"VERY HARD","title":"That Boy Ain't Right","author":"Scott Williams","rules":"Apply normal Sudoku rules. Identical digits may not be a chess knight's move apart. Each pink line contains a set of consecutive digits in any order. Clues outside the grid give the sum of the digits between 1 and 9 in that row or column.","solution":"783196425642753819519842376278361954364579182195284637457618293826937541931425768","constraints":["antiknight","renban","sandwich"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"9cgfyvodo8","ctcId":2920,"ctcDifficulty":"HARD","title":"Coloured Groups","author":"Nahileon","rules":"Normal sudoku rules apply.\nColor each cell in one of two different colors, where cells containing the same digit must have the same color.\nIf an orthogonally connected group of cells of the same color has one or more circles in it, the circled cell(s) contain the size of that group.","solution":"394268751682175394157943862829657413765314289413829576546731928278496135931582647","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Color each cell in one of two different colors, where cells containing the same digit must have the same color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"foesxbaf60","ctcId":2922,"ctcDifficulty":"VERY HARD","title":"Let's Get Kraken","author":"James Kopp","rules":"Normal sudoku rules apply.\nReading from the bulb to the tips, digits along a thermometer must either increase or stay the same.\nAdjacent digits along the green line have a difference of at least five.\nAll digits along a blue line must sum to the same total in each 3x3 box that the line visits.\nEach cage has digits that sum to 8.","solution":"834275619972146538165938472723594186649821753581763294298617345316459827457382961","constraints":["cage","german-whispers","region-sum-line","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7udzz2bpg8","ctcId":2923,"ctcDifficulty":"MEDIUM","title":"Counting and whispering","author":"Lithium-Ion","rules":"Normal Sudoku rules apply. Digits along an arrow sum to the digit in its black circle. Digits may repeat along an arrow if allowed by other rules. A digit x in a circle (including black arrow circles and red circles) indicates exactly how many of the up to 8 neighboring cells (i.e. orthogonally or diagonally adjacent cells) contain a digit that differs by at least 5 from x.","solution":"965734182732158496418269753521386974384927561679541328147692835856473219293815647","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit x in a circle (including black arrow circles and red circles) indicates exactly how many of the up to 8 neighboring cells (i.e. orthogonally or diagonally adjacent cells) contain a digit that differs by at least 5 from x.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"2004fp6a0r","ctcId":2924,"ctcDifficulty":"VERY HARD","title":"Wanddeko","author":"Myxo","rules":"Normal sudoku rules apply. \nDigits separated by a white dot are consecutive. A black dot sits between two digits where one is double the other. Not all dots are necessarily given. \nInequality signs between two cells point towards the smaller digit.","rulesClarified":"Normal sudoku rules apply.\n\nWhite dot: the two digits either side of a white dot are consecutive, that is, they differ by one.\n\nBlack dot: the two digits either side of a black dot are in a 2 to 1 ratio: one is double the other.\n\nNot every dot is drawn. A pair of cells with no dot between them has no rule from this list.\n\nInequality signs: an inequality sign between two cells points towards the smaller digit.","solution":"417586923328914567596732148785641239264379851931258476842167395173495682659823714","constraints":["inequality","kropki"],"constraintFacts":[{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"s34y05j3cz","ctcId":2928,"ctcDifficulty":"MEDIUM","title":"Who's Afraid Of 13!","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. The sum of two orthogonal neighbours is at most 13 (ie no domino in the grid can sum to more than 13). The sum of two 'point symmetric' cells is always 10. (Point symmetric cells are pairs that are mirror images of each other across the exact center of the 9x9 grid (the middle of the central 3x3 box). ie Rotating the grid 180° around this central point maps a cell directly onto its symmetric partner). So, for example, r7c1's symmetric counterpart is r3c9.","solution":"843917625176285394925643817258439176761852943439176258392764581617528439584391762","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of two orthogonal neighbours is at most 13 (ie no domino in the grid can sum to more than 13). The sum of two 'point symmetric' cells is always 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"6hc3f9hbqu","ctcId":2929,"ctcDifficulty":"HARD","title":"Shanghai Skyline","author":"Black_Doom","rules":"Normal sudoku rules apply.\nYin-Yang: shade some cells such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected. No 2x2 area may be fully shaded or fully unshaded.\nKropki: digits separated by a black dot must have a ratio of 1:2. Additionaly, a black dot always separates a shaded and an unshaded cell. Not all dots are necessarily given.\nSkyscrapers: shaded digits in the grid represent skyscrapers of that height, with taller skyscrapers obscuring smaller ones. A clue outside the grid shows the number of all visible skyscrapers from the clue's direction. Unshaded digits do not affect the outside clues.","solution":"875912634126374958394568127732459861681237549459186372213795486567841293948623715","constraints":["kropki","skyscraper","yin-yang"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"skyscraper","type":"skyscraper","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5"]}]},{"id":"mm4b2w1a65","ctcId":2930,"ctcDifficulty":"HARD","title":"Ghosts In The Fog","author":"James Kopp","rules":"Normal sudoku rules apply. Placing a correct digit may clear fog somewhere in the grid. Adjacent cells cannot sum to 10. Grey lines are palindromes that read the same in both directions. If two digits are separated by a black dot one is double the other. Not all possible black dots are necessarily shown. A cell marked with a grey circle contains an odd digit. No guessing is required.","solution":"512639847976248135483175692149762583257983416638514279795421368861357924324896751","fogLight":"R3C6,R4C5,R4C3,R3C3,R2C3,R1C4,R1C6,R1C5,R2C4,R3C5,R2C5,R2C6,R3C4,R3C7,R2C7,R4C7,R1C7","constraints":["custom","fog","kropki","odd","palindrome"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent cells cannot sum to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"palindrome","type":"palindrome","variant":"modified","modifiers":[],"params":null,"note":"Grey lines are palindromes that read the same in both directions.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"g248qi5g6d","ctcId":2932,"ctcDifficulty":"VERY HARD","title":"Full Circle","author":"Qodec","rules":"Normal sudoku rules apply. Each row, column, and 3x3 box contains two 'indexer' cells: a 'row indexer' and a 'column indexer'. The digit in a row indexer gives the position of the column indexer in that row. The digit in a column indexer gives the position of the row indexer in that column. Positions are counted left-to-right in rows and top-to-bottom in columns . Digits in a cage sum to the small clue in the upper left corner, if given. Indexer cells cannot appear in cages.","rulesClarified":"Normal sudoku rules apply.\n\nEvery row, column and 3x3 box contains two indexer cells: one row indexer and one column indexer.\n\nA row indexer's digit gives the position of the column indexer in that same row. A column indexer's digit gives the position of the row indexer in that same column.\n\nPositions are counted from 1: left to right along a row, and top to bottom down a column.\n\nIndexer cells cannot appear in cages.\n\nA cage with a small number in its top left corner has digits that sum to that number. A cage with no number has no sum given.","solution":"125683479367954128984721356591432687872196543643875291736249815419568732258317964","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each row, column, and 3x3 box contains two 'indexer' cells: a 'row indexer' and a 'column indexer'. Indexer cells cannot appear in cages.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7"]}]},{"id":"ey3tqoay3j","ctcId":2933,"ctcDifficulty":"MEDIUM","title":"Creatures In The Dynamic Fog","author":"Br1312te","rules":"Normal sudoku rules apply, but once again strange things are afoot... \n\nFog has filled the land, thicker than ever before, and within it, lurk many Creatures of the night!\n\nYet fear not! If you can find them, friendly Wisps will aid you in navigating the fog. There is one Wisp in every row, column, and 3x3 box, marked by a pale blue dot. Cells containing a Wisp contain either their row, column or box number (read in normal reading order). No two Wisps can contain the same digit. Fog cleared by Wisps leaves an eerie blue light.\n\nThe Monsters!\n\nZombies: marked by a green dot, zombies have an infectious bite. Orthogonally adjacent cells are even when the zombie's number is even, or odd when the zombie's number is odd.\n\nVampires: marked by a red dot, vampires suck the power from their victims. Orthogonally adjacent cells sum up to the vampire's number.\n\nHeadless Horsemen: marked by an orange dot, horsemen have a knight's reach. Cells a chess-knight's move away from the horseman can't contain the same digit as the horseman's number.\n\nPoltergeists: marked by a grey dot, poltergeists throw everything into disarray. Orthogonally adjacent cells are either all higher than the poltergeist's number, or all lower.\n\nFog: the land is covered in dynamic fog. Putting in correct digits will clear the fog for that cell. Finding a Wisp will clear more fog. No guessing is required. The monster under your bed will know if you cheat!\n\nLove, Brigitte","solution":"368971425219548367754362819583619274627854931491723658945136782132487596876295143","fogLight":"R5C5","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells containing a Wisp contain either their row, column or box number (read in normal reading order). No two Wisps can contain the same digit. Orthogonally adjacent cells are even when the zombie's number is even, or odd when the zombie's number is odd. Orthogonally adjacent cells sum up to the vampire's number. Cells a chess-knight's move away from the horseman can't contain the same digit as the horseman's number. Orthogonally adjacent cells are either all higher than the poltergeist's number, or all lower.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7","c11","c13","c15","c17"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c18"]}]},{"id":"qx6r0v9p4f","ctcId":2934,"ctcDifficulty":"VERY HARD","title":"Picking Blackcurrants","author":"Kaktuslav","rules":"Normal sudoku rules apply. \n\nDraw a directed path through the centres of some cells in the grid, starting in one blue circle and ending in the other. The path may move only orthogonally north (↑), orthogonally east (→), or diagonally southwest (↙), and it may not visit any cell more than once. The path must function both as an entropic line and as a region sum line. Every black dot in the grid must be crossed by the path. A white dot joins two cells - neither of these cells may be visited by the path. \n\nAlong an Entropic line, every set of three consecutive cells along the line must contain one low digit (1,2,3), one middle digit (4,5,6), and one high digit (7,8,9). \n\nAlong a Region sum line. the 3x3 box borders divide the line into segments; and all such segments must have the same sum. \n\nA white dot between two digits means they must be consecutive. If two digits are separated by a black dot one is double the other. One of the dots contains an inequality sign pointing to the smaller digit.","solution":"143287659795634812682591473238149567519768324476352981367925148924816735851473296","constraints":["custom","entropic-line","inequality","kropki","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a directed path through the centres of some cells in the grid, starting in one blue circle and ending in the other.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9","c10"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"cn5h6c34mo","ctcId":2936,"ctcDifficulty":"VERY HARD","title":"Lighthouses","author":"IcyFruit","rules":"Normal sudoku rules apply. The grid is partly covered in fog. Placing correct digits may clear fog revealing other clues. No guessing is required. \n\nA digit in a square indicates the total number of digits smaller than itself that it 'sees' in all the four cardinal directions (North, East, South, West) along its row and column. In each direction, it 'sees' ALL digits smaller than itself until vision is blocked by a digit greater than itself or the edge of the grid. (For clarity it does not see itself). \n\nIf a black dot separates two digits, one of those digits is double the other.","solution":"852136479741928635936754281593412867627385194418697523289571346365249718174863952","fogLight":"R1C1,R1C2,R1C3,R3C2,R3C3","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a square indicates the total number of digits smaller than itself that it 'sees' in all the four cardinal directions (North, East, South, West) along its row and column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"pgLhjFH3bR","ctcId":2937,"ctcDifficulty":"MEDIUM","title":"Multiverse","author":"Jonesy","rules":"Normal sudoku rules apply. Draw a 1-cell wide loop that moves strictly orthogonally and doesn't branch or intersect itself. The loop doesn't touch itself, not even diagonally. Neighbouring digits on the loop must have a difference of at least 5. A digit in a circle indicates how many times that digit must appear in circles. The circled digits also indicate how many of the (up to 8) surrounding cells are on the loop. Circles are never on the loop.  Digits separated by a white dot are consecutive. Digits separated by a black dot have a 1:2 ratio.","rulesClarified":"Normal sudoku rules apply.\n\nDraw one closed loop, one cell wide, that moves strictly orthogonally. It may not branch or cross itself.\n\nThe loop may not touch itself, not even diagonally.\n\nTwo cells that are next to each other on the loop must have digits that differ by at least 5.\n\nCircles are never on the loop.\n\nA digit in a circle tells you how many times that digit must appear in circles across the whole grid. The circle that holds the digit counts as one of them.\n\nA circled digit also tells you exactly how many of its surrounding cells (up to eight: the orthogonal and diagonal neighbours) are on the loop.\n\nDigits separated by a white dot are consecutive: one is exactly one more than the other.\n\nDigits separated by a black dot have a 1:2 ratio: one is double the other.","solution":"659843721371925648824671935162754389937268514485139276716582493293416857548397162","constraints":["counting-circle","custom","german-whispers","kropki"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a 1-cell wide loop that moves strictly orthogonally and doesn't branch or intersect itself. The circled digits also indicate how many of the (up to 8) surrounding cells are on the loop.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8","c9"]}]},{"id":"egz2ug1ntj","ctcId":2938,"ctcDifficulty":"MEDIUM","title":"Four Finger Death Punch","author":"Jonesy","rules":"Hello\n\nNormal 9x9 sudoku rules apply.\n\nDraw a 1-cell wide loop that moves strictly orthogonally and doesn't branch or intersect itself. The loop doesn't touch itself, not even diagonally.\nThe loop acts as a german whispers line. Neighbouring digits on the loop must have a difference of at least 5.\n\nA digit in a circle indicates how many times that digit must appear in circles. \nThe circled digits also indicate how many of the up to 8 surrounding cells are on the loop.\nCircles are never on the loop.\n\nHave fun.","rulesClarified":"Normal 9x9 sudoku rules apply.\n\nDraw one loop through the grid. It is one cell wide, moves orthogonally from cell to cell, and does not branch or cross itself. Circled cells are never on the loop.\n\nThe loop may not touch itself, not even diagonally: two loop cells that are not next to each other along the loop may not share a side or a corner.\n\nThe loop acts as a German whispers line. Digits in cells that are neighbours along the loop must differ by at least 5.\n\nA circle's digit, say d, says how many times the digit d must appear in the circles of the grid. Exactly d circled cells contain the digit d. The circled cell itself counts.\n\nA circled digit also counts loop cells around it. A circled n means exactly n of the cells surrounding it (up to eight, in the 3x3 block around it) are on the loop.\n\nHave fun.","solution":"576493812123658794849271536395724681714836259682519473437165928958342167261987345","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a 1-cell wide loop that moves strictly orthogonally and doesn't branch or intersect itself. A digit in a circle indicates how many times that digit must appear in circles. The circled digits also indicate how many of the up to 8 surrounding cells are on the loop.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c7","c8"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"rh85pym4gj","ctcId":2939,"ctcDifficulty":"MEDIUM","title":"Keep 'em Separated","author":"Jonesy","rules":"Normal sudoku rules apply. (Place the digits 1-9, once each, into every row, column and 3x3 box.)\nCages within the same 3x3 box must sum to the same total. Any cage can only contain either all odd digits or all even digits.","solution":"375196842981274536246538197862941753453627981719853624534719268697382415128465379","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cages within the same 3x3 box must sum to the same total. Any cage can only contain either all odd digits or all even digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"4i0mviwdne","ctcId":2940,"ctcDifficulty":"HARD","title":"Sum assembly required.","author":"Jonesy","rules":"Hello!\n\n• Standard Sudoku rules apply: each row, column, and 3×3 box must contain the digits 1–9 exactly once.\n\n• Each cage has a two-digit total to be placed by the solver inside the cage. Place the tens digit in the leftmost cell of the topmost row of the cage, then write the total from left to right. If the cage shape doesn’t allow a left-to-right placement, write the digits from top to bottom instead.\n\n• If the total consists of two identical digits (e.g., 22, 33, 44), write only a single digit.\n\n• Digits may repeat within a cage, provided standard Sudoku rules are not broken.\n\n• Digits along an arrow sum to the digit in the attached circle.\n\nHave fun!","solution":"285136479174295836369784152598617243731842695642953781957421368413568927826379514","constraints":["arrow","cage"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"• Each cage has a two-digit total to be placed by the solver inside the cage. Place the tens digit in the leftmost cell of the topmost row of the cage, then write the total from left to right. If the cage shape doesn’t allow a left-to-right placement, write the digits from top to bottom instead.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"wut7orsq8b","ctcId":2941,"ctcDifficulty":"MEDIUM","title":"Bits and arrows","author":"Jonesy","rules":"Hello.\n\n\nNormal sudoku rules apply.\n\nA binary code is a sequence of bits that are either on or off.\nIn this puzzle, Odd digits represent bits that are 'OFF'(O) and Even digits represent bits that are 'ON'(E). \n\nThis gives us the following representation of the digits 1-9:\n\n1 → OOOE\n2 → OOEO\n3 → OOEE\n4 → OEOO\n5 → OEOE\n6 → OEEO\n7 → OEEE\n8 → EOOO\n9 → EOOE\n\nThe digit in an arrow cell dictates the parity (odd or even) of its four orthogonal neighbours.\nThese four neighbours must match the binary code of the digit with the small arrow.\nThe arrow points to the first bit of the binary code. (read from left to right.) The full code must wrap around the central cell clockwise.\n\nExample:\nIf a 6 is placed in an arrow cell, its code is OEEO.\nTherefore, its four neighbours (starting from the arrow direction, moving clockwise) must be Odd, Even, Even, Odd.\n\nHave fun.","rulesClarified":"Normal sudoku rules apply.\n\nEach digit has a 4-bit code, where odd digits are OFF (O) and even digits are ON (E):\n1 OOOE, 2 OOEO, 3 OOEE, 4 OEOO, 5 OEOE, 6 OEEO, 7 OEEE, 8 EOOO, 9 EOOE.\n\nEach arrow cell holds a digit, and the arrow drawn in it points to one of its four orthogonal neighbours. The digit in the arrow cell sets the parity of those neighbours: the four orthogonal neighbours must match the code of that digit.\n\nThe arrow points to the first bit of the code. Read the code from left to right: its first bit goes on the neighbour the arrow points to, and the remaining bits go on the next neighbours in clockwise order around the arrow cell.\n\nExample: a 6 in an arrow cell has code OEEO. If the arrow points to a neighbour, that neighbour is odd, the next neighbour clockwise is even, the next is even, and the last is odd.","solution":"473268159851947623269153874946521738127389546538476291684792315715834962392615487","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digit in an arrow cell dictates the parity (odd or even) of its four orthogonal neighbours.","evidence":"rules","lessonPolicy":"open","sectionIds":["c15"]}]},{"id":"27v1lv24c3","ctcId":2944,"ctcDifficulty":"VERY HARD","title":"Patient Zeroes","author":"gdc","rules":"Dr. Norma L. Dokes! A virus is spreading and causes people to eat each others brains! Please perform some measurements in the village and bring the results to the hospital. We need to see how severe the spread is. But be careful - It is highly contagious!\n\nNORMA L DOKES - Normal sudoku rules apply.\n\nINFECTIONS - The 3x3 boxes are numbered in normal reading order, 1 to 9. Each digit matching its own box number is a 'patient zero'. Each row and column contains a 'patient zero'. Patient zeroes are infected. Infected cells infect every orthogonally adjacent cell with a smaller digit. Infections keep spreading until no infected cell has a smaller uninfected orthogonal neighbour. (Every infected cell can be traced back to one or more patient zeroes.)\n\nPATH - Draw a 1-cell wide path from the doctor (👩‍⚕️) to the hospital (🏥). The path only moves orthogonally and may not touch itself, not even diagonally. The path may not contain infected cells.\n\nMICROSCOPES (🔬) are on the path and count the number of infected cells in the (up to 9) surrounding cells.\n\nKROPKI TABLETS (white dots) join consecutive uninfected digits.","solution":"467923518289451673351876294932184765145697382678532149813745926596218437724369851","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"INFECTIONS - The 3x3 boxes are numbered in normal reading order, 1 to 9. Each row and column contains a 'patient zero'. Patient zeroes are infected. PATH - Draw a 1-cell wide path from the doctor (👩‍⚕️) to the hospital (🏥). The path only moves orthogonally and may not touch itself, not even diagonally. The path may not contain infected cells. MICROSCOPES (🔬) are on the path and count the number of infected cells in the (up to 9) surrounding cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c9","c10","c14","c15","c16","c17"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c18"]}]},{"id":"wftydghvy6","ctcId":2945,"ctcDifficulty":"MEDIUM","title":"Candy Wrapper","author":"HalfBakedLunatic (aka David Workman)","rules":"• Normal Sudoku Rules Apply\n• Digits in cages must sum to the number in the corner of the cage\n• Digits in cells separated by a black dot must be in a 2:1 ratio, digits in cells separated by a white dot must be consecutive - not all dots are shown\n• Digits along a purple Renban line must be a set of consecutive digits in any order\n• Digits along a red palindrome must read the same forwards or backwards\n• Digits along the blue diagonal line must not repeat","solution":"562743981347198652198526473259374816834615729716289534973861245425937168681452397","constraints":["cage","diagonal","kropki","palindrome","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"urooueeutg","ctcId":2946,"ctcDifficulty":"MEDIUM","title":"Modular Zigzag","author":"Kaktuslav","rules":"Normal sudoku rules apply. Digits cannot repeat along the marked diagonal. Every 2×2 square of cells must contain all three possible remainders modulo 3 (i.e. at least one digit from each of the sets {1,4,7}, {2,5,8}, and {3,6,9}).\nDraw a path starting in the top-left corner cell and finishing in the bottom-right corner cell, visiting every 3×3 box at least once. In a single step, the path may move only east (→) or southwest (↙).\nAny three consecutive digits along the path must have three different remainders modulo 3. Box borders divide the path into segments; each segment is a renban, i.e. it must contain consecutive, non-repeating integers in any order.","solution":"564897231789123456312645978231564897456789123978312645897231564123456789645978312","constraints":["custom","diagonal"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every 2×2 square of cells must contain all three possible remainders modulo 3 (i.e. at least one digit from each of the sets {1,4,7}, {2,5,8}, and {3,6,9}). Draw a path starting in the top-left corner cell and finishing in the bottom-right corner cell, visiting every 3×3 box at least once. Any three consecutive digits along the path must have three different remainders modulo 3. Box borders divide the path into segments; each segment is a renban, i.e. it must contain consecutive, non-repeating integers in any order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c6","c7"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qndcjysi43","ctcId":2947,"ctcDifficulty":"HARD","title":"Squares And Primes Harmony","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. The cells in the grid are numbered from 1 to 81 in normal reading order ie 1 at the upper left, ..., 9 at the upper right until 81 at the bottom right. The digit in a square-numbered cell (eg 25, 49, etc) is itself a square (1,4,9) while the digit in a prime-numbered cell (eg 59, 61, etc) is a prime (2,3,5,7). In addition, any vertical or horizontal straight line of three cells never contains a consecutive set of digits.","solution":"137958264826314957594276138653792481248631795971485623785129346419563872362847519","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digit in a square-numbered cell (eg 25, 49, etc) is itself a square (1,4,9) while the digit in a prime-numbered cell (eg 59, 61, etc) is a prime (2,3,5,7). In addition, any vertical or horizontal straight line of three cells never contains a consecutive set of digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"br4k6gdpzz","ctcId":2948,"ctcDifficulty":"HARD","title":"The Snug Bug","author":"Allagem","rules":"Normal Sudoku rules apply.\nSnug Between Lines: Digits on a line between two circles must have values between the digits in those circles. Each circle digit must be consecutive with at least one digit on the line. For example, (2)-7-3-5-(8) is a valid fill for a Snug Between Line.","solution":"194852736532176489786493521978541263215639847643287915851764392367928154429315678","constraints":["between-line","custom"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"modified","modifiers":[],"params":null,"note":"Snug Between Lines: Digits on a line between two circles must have values between the digits in those circles.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each circle digit must be consecutive with at least one digit on the line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"mlt4l6zcak","ctcId":2949,"ctcDifficulty":"MEDIUM","title":"Colour Coordinated Differences","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nThe two digits on an arrow give the coordinates of a particular target cell somewhere in the grid. The digit on the arrow's shaft indicates the target cell's row, and the digit on the arrowhead indicates the target cell's column. The difference between the two digits should be placed into the target cell. No two arrows target the same cell.\n\nAlso:\n- A pink arrow contains two consecutive digits.\n- A green arrow contains two digits with a difference of at least 5.\n- On a black arrow, one digit is double the other.","solution":"219765438365248917847193256421857693786329541593614872652931784938472165174586329","constraints":["custom","german-whispers","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The two digits on an arrow give the coordinates of a particular target cell somewhere in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"- A green arrow contains two digits with a difference of at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c9"]}]},{"id":"9gk44l9w5x","ctcId":2950,"ctcDifficulty":"VERY HARD","title":"The Graveyard Of Emptiness","author":"fjam","rules":"- Normal Sudoku rules apply.\n- One cell in each row, column and 3x3 region is a nullifier cell. Nullifier cells have a value of zero.\n- In graves (cages), values must sum to the day, month or year of the date on the grave. Digits cannot repeat within graves.\n- Escape the graveyard by carefully plotting an orthogonally connected path between the green and red cells. The path may not cross the highest or lowest values in a grave.","solution":"948713625513962478276458391639174582785236149124589736357891264862345917491627853","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- One cell in each row, column and 3x3 region is a nullifier cell. Nullifier cells have a value of zero. - Escape the graveyard by carefully plotting an orthogonally connected path between the green and red cells. The path may not cross the highest or lowest values in a grave.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"vnxrlvh04f","ctcId":2951,"ctcDifficulty":"MEDIUM","title":"Anti-knight Singularis Alchemis","author":"Chip Sounder","rules":"Normal sudoku rules apply.\nCells separated by a knight's move (in chess) cannot contain the same digit.\nDigits on a thermometer must not decrease from the bulb end.\nConnected digits on a green line must differ by at least 5.\nDigits in a dotted cage sum to the total given in the top left corner of the cage.\nDigits on a purple line must form a set of consecutive digits in any order.\nDigits on an arrow sum to the digit in the connected circle.\nDigits separated by an X sum to 10.\nDigits separated by a V sum to 5.","solution":"698217534752346819143958627837591462926734185514682793381425976265179348479863251","constraints":["XV","antiknight","arrow","cage","german-whispers","renban","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8","c9"]},{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"mvqojfwq9a","ctcId":2952,"ctcDifficulty":"MEDIUM","title":"Parity Patrol 101","author":"Jonesy","rules":"Hello.\n\nNormal Sudoku rules apply.\n\nDigits in a cage sum to the number given in its corner. Digits may not repeat within a cage.\n\nIn any row or column, no more than two consecutive digits may have the same parity (i.e., be both odd or both even).\n\nExample:\nA sequence such as 2–4–5–7 is valid,\nbut 2–4–6–3 is not valid, since three even digits appear consecutively.\n\nHave fun.","solution":"893625147714398562526714893275463981631879254948152736187946325459231678362587419","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In any row or column, no more than two consecutive digits may have the same parity (i.e., be both odd or both even).","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"fmcdu9br5g","ctcId":2953,"ctcDifficulty":"MEDIUM","title":"From Albany to Buffalo","author":"Walking Writer","rules":"Blue mule Sal (with the short green tail) is pulling a packet boat across New York State along the original Erie Canal in 1825, traveling from Albany in the east to Buffalo in the west. While Sal takes a rest break during the journey, can you solve this Erie Canal Bicentennial Celebration themed sudoku puzzle? Here are the rules.\n\nNormal sudoku rules apply. Box borders divide the blue line into segments whose values have an equal sum N. Consecutive digits along the orange line have a difference of at least four. Consecutive digits along a green line have a difference of at least five. Cells connected by a black dot have a 2 to 1 ratio. Not all black dots are shown. Cells with a gray circle must contain an odd digit.\n\nHistorical tidbits about this puzzle. The original Erie Canal in New York State was completed on October 26, 1825, connecting the Hudson River near Albany in the east to Lake Erie near Buffalo in the west. This cut travel time across the state from weeks to days and opened the Midwest and beyond to more trade. Before it was modernized, the original Erie Canal was 363 miles long and contained 83 lift locks, basically water elevators to raise and lower boats along the canal when elevations changed. New York State is celebrating the 200th anniversary of the canal’s completion with many events throughout 2025.\n\nThe title of my puzzle and the mule’s name, Sal, come from the 1912 folk song “Low Bridge, Everybody Down” by Thomas S. Allen, though some of the song’s lyrics have varied over time.","solution":"279148653618253749345796281567384192123975468984612375891437526436529817752861934","constraints":["dutch-whispers","german-whispers","kropki","odd","region-sum-line"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"cum7kp045w","ctcId":2954,"ctcDifficulty":"HARD","title":"Big Latin Y²","author":"Kaktuslav","rules":"Latin square: Place the digits 1–9 exactly once in each row and each column.\n\nYin-yang: Shade some cells so that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2×2 area is entirely shaded or entirely unshaded.\n\nYY cages: Within each cage, the sum of the shaded digits equals the sum of the unshaded digits. Digits MAY repeat within a cage.\n\nClones: The corner cells with gray diamonds contain the same digit.","solution":"719538624197643582835214769574891236368472951652189347946325178281756493423967815","constraints":["clone","custom","yin-yang"],"constraintFacts":[{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"YY cages: Within each cage, the sum of the shaded digits equals the sum of the unshaded digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"f9wcvtflo1","ctcId":2955,"ctcDifficulty":"HARD","title":"Island Sum Lines","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nNurikabe:\n-- Shade some cells such that all shaded cells are orthogonally connected (water), but no 2x2 area is entirely shaded.\n-- Groups of orthogonally connected unshaded cells form islands.  An island may be of size 1.  Every cell with a circle clue is unshaded, and each island contains exactly one circle cell.  The digit in this circle cell gives the size of the island.  Note that an island may occupy a full 2x2 area (unlike water).\n\nDigits may not repeat within an island.\n\nEvery blue line must contain at least one shaded and at least one unshaded cell.  Switching between shaded and unshaded cells divides each line into segments with the same sum.  Different lines may have different sums.  Digits may repeat on a line if allowed by other rules.","solution":"571248369896351472324697158467915823183462795259783641635879214718524936942136587","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"-- Shade some cells such that all shaded cells are orthogonally connected (water), but no 2x2 area is entirely shaded. Every cell with a circle clue is unshaded, and each island contains exactly one circle cell. Switching between shaded and unshaded cells divides each line into segments with the same sum.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c6","c11"]}]},{"id":"5ut8ou1zu2","ctcId":2957,"ctcDifficulty":"VERY HARD","title":"Shambhala","author":"IcyFruit","rules":"Normal sudoku rules apply.\nCircle a digit in each row, column, and box. Each circled digit must be different. Shade some cells, such that within any row, column, or box, the number of shaded cells is equal to the circled digit.\nA digit in a diamond is not circled, and equals the sum of the circled digits in its row and column.\nShaded digits within a cage sum to the value given in the top left of the cage.","solution":"346891752951274836872536941423789615689415327715623489194357268538962174267148593","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Circle a digit in each row, column, and box. Each circled digit must be different. Shade some cells, such that within any row, column, or box, the number of shaded cells is equal to the circled digit. A digit in a diamond is not circled, and equals the sum of the circled digits in its row and column. Shaded digits within a cage sum to the value given in the top left of the cage.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6"]}]},{"id":"54q5oydbbj","ctcId":2958,"ctcDifficulty":"HARD","title":"Singles and Doubles","author":"James Kopp","rules":"Normal sudoku rules apply.\nThe grid is covered in fog. Placing correct digits reveals clues in the surrounding 3x3 area.\nThe digits 1 to 9 appear once each on both blue diagonals.\nThe digits along an arrow sum to either a single digit number in that arrow's circle or a two digit number (reading left-to-right) in that arrow's oval.","solution":"461758329952314687738269154549187263276935418183426795315872946824693571697541832","fogLight":"R4C6,R5C6,R5C4,R6C6,R4C4,R6C4","constraints":["arrow","diagonal","fog"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"kbv0s65hd7","ctcId":2959,"ctcDifficulty":"HARD","title":"This Puzzle Has Been SET","author":"Eric Rathbun","rules":"Normal sudoku rules apply. Digits in cages sum to the small total given in the top left corner of the cage. A clue outside the grid gives the sum of the digits along the indicated diagonal. Within the grid, digits along an arrow sum to the digit in that arrow's circle. Grey lines are palindromes which read the same forwards and backwards. Digits separated by a white dot have a difference of one. Not all possible dots are given.","solution":"145389672729546813863721459281637594956214738437958261392875146518463927674192385","constraints":["arrow","cage","kropki","little-killer","palindrome"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"lipt9yn6r4","ctcId":2960,"ctcDifficulty":"HARD","title":"Spooky Action at a Distance","author":"Michael Lefkowitz","rules":"- Normal Sudoku rules apply.\n- Some cells contain ghosts. Not all ghosts are visible!\n- Each ghost with the digit N is staring at another ghost with the digit N, exactly N diagonal steps away.\n- A headstone shows the sum of the ghosts in its column.","rulesClarified":"Normal Sudoku rules apply.\n\nSome cells contain ghosts. Not all ghosts are visible.\n\nEach ghost has a digit N. It stares at another ghost with the same digit N, exactly N diagonal steps away. That is a cell N rows up or down and N columns left or right, along a diagonal.\n\nA headstone shows the sum of the ghost digits in its column. Count every ghost in that column.","solution":"826397415539148672147652389315269847968734521472581963284975136651823794793416258","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Each ghost with the digit N is staring at another ghost with the digit N, exactly N diagonal steps away. - A headstone shows the sum of the ghosts in its column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"qqfj59akio","ctcId":2961,"ctcDifficulty":"HARD","title":"Under The Microscope","author":"gdc","rules":"Norma! You made it! While you were gone, we were able to isolate the pathogens. The way they reproduce is very unusual. It just started in culture 4. Look!\n\nNORMA L DOKES - Normal sudoku rules apply.\n\nINOCULATION SITES - The 3x3 boxes are numbered in normal reading order. Each digit matching its box number is an 'inoculation site'. Each row and column contains an inoculation site. They are infected. \n\nINFECTIONS - Infected cells infect every orthogonally adjacent cell with a smaller digit. Infections keep spreading until no infected cell has a smaller uninfected orthogonal neighbor. (Every infected cell can be traced back to one or more inoculation sites.)\n\nCAVE - All uninfected cells form one orthogonally connected area. Each orthogonally connected group of infected cells touches the grid's edge.\n\nDETECTOR CELLS - A digit in a blue circle is uninfected and counts the number of infected cells in its 8 surrounding cells.\n\nGERMY WHISPER lines connect 2 infected digits that differ by 5 or more. \n\nCOCCI DOTS join consecutive uninfected digits.","solution":"271386945354972186698145327935418762847623591126759438519864273783291654462537819","constraints":["custom","german-whispers","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each digit matching its box number is an 'inoculation site'. INFECTIONS - Infected cells infect every orthogonally adjacent cell with a smaller digit. CAVE - All uninfected cells form one orthogonally connected area. DETECTOR CELLS - A digit in a blue circle is uninfected and counts the number of infected cells in its 8 surrounding cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c9","c12","c15","c17"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c18"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c19"]}]},{"id":"cki7pvc7ts","ctcId":2962,"ctcDifficulty":"VERY HARD","title":"Thinking Inside The...","author":"Kennet's Dad","rules":"Normal sudoku rules apply. No domino in the grid can contain digits summing to 10. There is some fog in the grid; placing a correct digit might remove it. No guessing is required. Digits in a grey box cannot repeat. \n\nThere are lines in the grid that connect boxes; the digits in a box are summed to arrive at a value. That value applies to the following rules: \n1) Zipper: when box values equidistant from the centre box on a pink line are summed together, they are equal to the centre box's value on that line. The centre box is notated by a pink circle; \n2) Modular: every run of three boxes on a teal line must have a different remainder when divided by 3 (ie one value from each of 0 mod(3), 1 mod(3), and 2 mod(3)); \n3) Box values on a purple line make up at a set of consecutive, non-repeating values; \n4) The box values connected by a blue line must be the same; \n5) Box values joined by a white dot have a difference of 1.","solution":"254369781681257493793418526875124369169835274432796158926543817547981632318672945","fogLight":"R4C1,R4C2,R4C3,R4C4,R4C5,R4C6,R4C7,R4C8,R4C9,R5C1,R5C2,R5C4,R5C5,R5C6,R5C7,R5C8,R5C9,R5C3,R6C1,R6C2,R6C4,R6C5,R6C6,R6C7,R6C8,R6C9,R7C6,R8C6,R9C6,R7C4,R8C4,R9C4,R3C4,R3C5,R3C6,R2C4,R2C5,R2C6,R1C4,R1C5,R1C6,R9C5,R7C5,R8C5,R6C3","constraints":["custom","fog","kropki","modular-line","renban","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No domino in the grid can contain digits summing to 10. Digits in a grey box cannot repeat. 4) The box values connected by a blue line must be the same;","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c11"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"5) Box values joined by a white dot have a difference of 1.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"3) Box values on a purple line make up at a set of consecutive, non-repeating values;","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"e4i4jbq62m","ctcId":2963,"ctcDifficulty":"HARD","title":"Clapping On The 1 and 3","author":"Cris Moore","rules":"Each row, column, and box contains two 1s, two 3s, and one each of 2, 4, 5, 6, and 7. Cages sum to the totals shown. Digits MAY repeat in cages. Cells separated by a single knight's move (in chess) cannot contain the same digit.","solution":"362541713537312146114736352126453137753131264431267531243675311671313425315124673","constraints":["antiknight","cage","custom"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":["repeats-allowed"],"params":null,"note":"Digits may repeat inside a cage in this puzzle, so a cage total says nothing about which digits are distinct.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each row, column, and box contains two 1s, two 3s, and one each of 2, 4, 5, 6, and 7.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"m6sunffs9u","ctcId":2964,"ctcDifficulty":"MEDIUM","title":"Two-Tone Totals","author":"Marty Sears","rules":"Normal sudoku rules apply. \n\nColour each cell either yellow or blue. All cells of the same colour must be orthogonally connected, and no 2x2 area may be all one colour.\n\nA purple frame contains two cells of the same colour, and displays the total of the digits of that colour within that 3x3 box (reading left to right, or downwards.)\n\nIf two digits are joined by an X, they sum to 10.\n\nIf two digits are joined by a black dot, then one is double the other.","solution":"519378246743612895268495173897523461421867359635941782974236518182759634356184927","constraints":["XV","custom","kropki","yin-yang"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A purple frame contains two cells of the same colour, and displays the total of the digits of that colour within that 3x3 box (reading left to right, or downwards.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"bdiaxwjnxc","ctcId":2965,"ctcDifficulty":"MEDIUM","title":"Rupees","author":"Sotehr","rules":"German Whisper Line: Digits along a green line differ by at least 5.\nModulo Line: Every three digits along a cyan line alternate between the sets of {1,4,7}, {2,5,8}, and {3,6,9} in the same, continuous order.\nRenban Line: Digits along a magenta line contain a set of consecutive digits in any order, without repeats.\nDutch Whisper Line: Digits along an orange line differ by at least 4.\nThermometer Line: Digits along a gray thermometer strictly increase from the bulb.\nRegion Sum Line: Digits along a blue line are divided by box borders into sums of equal value.\nEntropic Line: Every three digits along a peach line alternate between the sets of {1,2,3}, {4,5,6}, and {7,8,9} in the same, continuous order.\nBlack Kropki Dots: Digits separated by a black dot have a ratio of 1:2.\nWhite Kropki Dots: Digits separated by a white dot are consecutive.","solution":"385491726269357184174826953943518267712963548658274391891635472536742819427189635","constraints":["dutch-whispers","entropic-line","german-whispers","kropki","modular-line","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8","c9"]},{"slug":"modular-line","type":"modular-line","variant":"modified","modifiers":[],"params":null,"note":"Modulo Line: Every three digits along a cyan line alternate between the sets of {1,4,7}, {2,5,8}, and {3,6,9} in the same, continuous order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"yuy1odkshr","ctcId":2967,"ctcDifficulty":"VERY HARD","title":"Fractured Flow","author":"Sotehr","rules":"Sudoku: Normal Sudoku rules apply; place the digits 1-9 once in every row, column, and 3x3 box.\n\nRegion Sum Line: Blue lines are divided by the 3x3 box borders into sums of equal value.\n\nRenban Line: Magenta lines contain a set of non-repeating consecutive values in any order.","solution":"326954718547128639891736452632849175758613924914275863463581297289367541175492386","constraints":["region-sum-line","renban"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"s9w5cterb4","ctcId":2969,"ctcDifficulty":"VERY HARD","title":"Hook or Crook","author":"Sotehr","rules":"Sudoku: Normal Sudoku rules apply; place the digits 1-9 once in every row, column, and 3x3 box.\n\nEntropic Line: Peach lines contain values that alternate in value between the sets of {1,2,3}, {4,5,6}, and {7,8,9} in the same, continuous order.\n\nModular Line: Teal lines contain values that alternate in value between the sets of {1,4,7}, {2,5,8}, and {3,6,9} in the same, continuous order.\n\nBlack Kropki: Cells separated by a black dot have values in a ratio of 1:2.\n\nAnti-Diagonal: Each main diagonal is constituted of a set of three digits.","solution":"348926157619547328257831649836152974125479863974683215582314796461798532793265481","constraints":["custom","entropic-line","kropki","modular-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Anti-Diagonal: Each main diagonal is constituted of a set of three digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"gcme2530d6","ctcId":2970,"ctcDifficulty":"MEDIUM","title":"Colour Coordinated Sums","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nThe two digits on an arrow give the coordinates of a particular target cell somewhere in the grid. The digit on the arrow's shaft indicates the target cell's row, and the digit on the arrowhead indicates the target cell's column. The sum of the two digits should be placed into the target cell. No two arrows target the same cell.\n\nAlso:\n- A pink arrow contains two consecutive digits.\n- A yellow arrow contains two non-consecutive digits.\n- A green arrow contains two digits with a difference of at least 5.\n- On a black arrow, one digit is double the other.","solution":"697542831382761945451839627568324179214976358739158462876213594123495786945687213","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The two digits on an arrow give the coordinates of a particular target cell somewhere in the grid. - A pink arrow contains two consecutive digits. - A yellow arrow contains two non-consecutive digits. - A green arrow contains two digits with a difference of at least 5. - On a black arrow, one digit is double the other.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7","c8","c9","c10"]}]},{"id":"7t1yva729p","ctcId":2971,"ctcDifficulty":"VERY HARD","title":"Overlooked","author":"IcyFruit","rules":"Normal sudoku rules apply.\nDigits along a purple line form a non-repeating set of consecutive digits in any order.\nA digit in a square indicates the number of cells it sees in its row and column that are smaller than itself, where digits larger than itself block vision.","solution":"586714932971238546234596781319825467625347819847169253762483195198652374453971628","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a square indicates the number of cells it sees in its row and column that are smaller than itself, where digits larger than itself block vision.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ew0fmz0exc","ctcId":2972,"ctcDifficulty":"MEDIUM","title":"Braided Sweetgrass","author":"Br1312te","rules":"Place the digits 1-9 in every row, column and each marked 9-cell region. Cells separated by a single knight's move (in chess) cannot contain the same digit. Every 2x2 square of cells must contain at least one digit from (1,4,7), at least one digit from (2,5,8), and at least one digit from (3,6,9). Cells that are orthogonally adjacent cannot contain consecutive digits. Clues outside the grid give the sum of the digits along the indicated diagonal. The cell with a circle must contain an odd digit.","solution":"384627951138462795513846279951384627795138462279513846627951384462795138846279513","constraints":["antiknight","custom","little-killer","non-consecutive","odd","region"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every 2x2 square of cells must contain at least one digit from (1,4,7), at least one digit from (2,5,8), and at least one digit from (3,6,9).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"d2kydms6ca","ctcId":2973,"ctcDifficulty":"HARD","title":"Balancing Regions","author":"Jonesy","rules":"Normal sudoku rules apply. Each row, column, and 9-cell region must contain the digits 1–9 exactly once.\nRegions consist of 9 orthogonally connected cells. Cages within the same region must have the same total (without repeating digits within a cage). Digits within a cage must be all odd or all even. A cage cannot cross region borders. Each region must contain at least two cages. Cages marked with X and Y have different totals. A white dot separates consecutive digits. A black dot indicates one digit is double the other. Not all possible dots are necessarily given.","solution":"467893251975136428123548679316289547548762913652917834831425796289374165794651382","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cages within the same region must have the same total (without repeating digits within a cage). Digits within a cage must be all odd or all even. Cages marked with X and Y have different totals.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9","c10"]}]},{"id":"dg8irdpkl3","ctcId":2974,"ctcDifficulty":"MEDIUM","title":"9 x 9 = 81","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. The digits along each line sum to 9.","solution":"489517623137628945652394187594163278726849531813275469971482356265731894348956712","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digits along each line sum to 9.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"329ytp25q2","ctcId":2975,"ctcDifficulty":"HARD","title":"Three Strikes and You’re Out","author":"James Kopp","rules":"Normal sudoku rules apply.\nCells separated by an X sum to ten and cells separated by a  V sum to five. Not all possible Xs and Vs are necessarily given.\nAny vertical or horizontal straight line of three cells never contains a consecutive set of digits.","solution":"693852471458173629271496385846215937517938264932764158764381592329547816185629743","constraints":["XV","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any vertical or horizontal straight line of three cells never contains a consecutive set of digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"ota96nsdfv","ctcId":2976,"ctcDifficulty":"MEDIUM","title":"Wicked","author":"arctan","rules":"Normal sudoku rules apply. Digits separated by a V sum to 5. Digits separated by an X sum to 10. Digits on a pink “renban” line contain a non-repeating set of consecutive digits – these digits can appear in any order. Adjacent digits on a green “German Whisper” line must have a difference of at least 5.","solution":"358916724672354819419827536246185973837469152195732648523678491961543287784291365","constraints":["XV","german-whispers","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"df7B2RJ4gB","ctcId":2978,"ctcDifficulty":"HARD","title":"Diamond mining","author":"Ratfinkz","rules":"Normal sudoku rules apply. A digit in a diamond means there are that many diamonds containing that digit in the grid. Cells a knight’s move apart cannot contain the same digit. Digits joined by a black dot must be in a 2:1 ratio. Digits along an arrow must add to the number in that arrow’s circle.","rulesClarified":"Normal sudoku rules apply.\n\nA digit in a diamond is a count. There are that many diamonds in the grid that contain that digit. The clue's own diamond counts as one of them, since it contains that digit.\n\nCells a knight's move apart cannot contain the same digit.\n\nDigits joined by a black dot must be in a 2:1 ratio.\n\nDigits along an arrow must add to the number in that arrow's circle.","solution":"913687425586924137247531689471356298369842751825719346752193864194268573638475912","constraints":["antiknight","arrow","custom","kropki"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a diamond means there are that many diamonds containing that digit in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"vgpr0pfsqm","ctcId":2979,"ctcDifficulty":"MEDIUM","title":"With friends like this...","author":"Ratfinkz ","rules":"Normal Sudoku rules apply.\n\nDigits in cages can not repeat and must sum to the total in the top left hand corner. Digits in cages may never share a border with a consecutive digit in the same cage.\n\nThere is 1 negator in every row, column and box. If negators appear in a cage they subtract their value from the sum of the other digits. Negators must be a set of the digits 1-9 with no repeats.\n\nEach diamond is a friendly square. Friendly cells are cells which match either their row number or their column number. Digits may never repeat in friendly cells, but not all digits need appear as a friendly cell.\n\nThe white Kropki dot marks two consecutive digits","solution":"531742986982615374647983512415396728723851469869427153198274635374568291256139847","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in cages can not repeat and must sum to the total in the top left hand corner.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in cages may never share a border with a consecutive digit in the same cage. There is 1 negator in every row, column and box. Each diamond is a friendly square.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"a8e1r5ewfy","ctcId":2981,"ctcDifficulty":"HARD","title":"Rat: Chinese Zodiac","author":"Ratfinkz","rules":"Normal sudoku rules apply.\n\nThe 9 blue circles must contain a set of the digits 1-9.\n\nLines are hit point lines. The blue circles show the total of the line's sum which is made up from digits in their correct position along the line. (Eg a line reading 14325 would have the total 9 as 1 is in the first position, 3 in the third and 5 in the 5th but 4&2 are not correct being in the second and 4th position respectively) \nDigits may not repeat along lines.\nSome lines have a square at the end. These squares mark the position of the first digit in the sequence. For lines without squares, the solver must determine in which direction they go, but they must always start at one end of the line and finish at the other.\n\nWhite dots mark consecutive digits, not all white dots are necessarily given. \n\nThe rat's nose contains an odd digit.","solution":"379528164512649387864371259628753491943186725751492836236917548497835612185264973","constraints":["custom","kropki","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The 9 blue circles must contain a set of the digits 1-9. Lines are hit point lines.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]}]},{"id":"x1cy1y9m7x","ctcId":2983,"ctcDifficulty":"EASY","title":"Fog Of War Rectangle","author":"Chip Sounder","rules":"Normal Sudoku rules apply. Place the digits 1-9 once each in every row, column and 3x3 box.\nThe grid is covered in fog, placing a correct digit will clear the cells surrounding that cell. No bifurcation is needed.\nDigits on a purple renban must form a set of consecutive digits in any order without repeating a digit.\nDigits in a dotted cage must sum to the sum given in the top left corner of the cage without repeat.\nAdjacent digits on a green german whisper line must differ by at least 5.\nClues outside the grid sum the digits between the 1 and 9 in their respective row/column.\nDigits separated by a black dot must have one digit double the other (1:2 ratio). \nNot all dots are given.","solution":"576329841348751926291684753867293415953146287124875369439518672612437598785962134","fogLight":"R8C1,R9C1,R9C2,R7C1,R7C2,R7C3,R8C3,R9C3","constraints":["cage","fog","german-whispers","kropki","renban","sandwich"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"i46kzqcugi","ctcId":2984,"ctcDifficulty":"HARD","title":"Ice Breaker","author":"IcyFruit","rules":"Normal sudoku rules apply.\nA digit cannot appear more than its own number of times across all lines in the grid. For example, there cannot be more than six 6s placed on lines.\nAdjacent digits on a green line differ by at least 5.\nDigits along a purple line form a non-repeating set of consecutive digits in any order.","solution":"384517296576982134921634587418273659652198743739456812893761425147325968265849371","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit cannot appear more than its own number of times across all lines in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"mgfzel558v","ctcId":2986,"ctcDifficulty":"MEDIUM","title":"Simple Miracle","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Cells separated by a single knight's move (in chess) cannot contain the same digit. In each positive diagonal (ie diagonal sloping from the South-West to the North-East), neighbouring digits differ by only 1 or 8.","solution":"837261594261594837594837261159483726483726159726159483372615948615948372948372615","constraints":["antiknight","custom"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In each positive diagonal (ie diagonal sloping from the South-West to the North-East), neighbouring digits differ by only 1 or 8.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"3QPdQd6Grn","ctcId":2988,"ctcDifficulty":"MEDIUM","title":"Rika's Endless Summer","author":"SUDOOOOOKUfan87","rules":"Normal sudoku rules apply. All cells are either island or water. Each shaded cell is an island cell; the number in it is the number of cells in that island. Each island must contain exactly one shaded cell, which contributes to a set of non-repeating digits that sum to the total in the shaded cell. Different islands may not touch orthogonally. The water cells are orthogonally connected and may not contain any 2×2 areas of water. Island totals are not necessarily in the top left most cell of an island.","solution":"931246587872519346456378219395864721147952638268137954714625893583791462629483175","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All cells are either island or water. Each shaded cell is an island cell; the number in it is the number of cells in that island. Each island must contain exactly one shaded cell, which contributes to a set of non-repeating digits that sum to the total in the shaded cell. Different islands may not touch orthogonally. The water cells are orthogonally connected and may not contain any 2×2 areas of water. Island totals are not necessarily in the top left most cell of an island.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c7"]}]},{"id":"hchxt4tcxs","ctcId":2989,"ctcDifficulty":"VERY HARD","title":"The Voice of the Masked Idol who has Got Talent","author":"SUDOOOOOKUfan87","rules":"Normal Sudoku rules apply.\n\nDigits along each main diagonal must not repeat. \n\nAdjacent digits on a green German Whispers line must have a difference of at least 5. \n\nAdjacent digits on a dark blue Factor line must have an integer quotient.\n\nA digit in a circle indicates how many times that digit appears in circles.","solution":"962784153548123796173956482436891275215467839789532641397618524624375918851249367","constraints":["custom","diagonal","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent digits on a dark blue Factor line must have an integer quotient. A digit in a circle indicates how many times that digit appears in circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"5y0k8sp8ev","ctcId":2990,"ctcDifficulty":"HARD","title":"Treasury Island","author":null,"rules":"Normal sudoku rules apply. All cells are either island or water. Each purple cell is an island cell. Each island must contain exactly one purple cell. Different islands may not touch orthogonally. The water cells are orthogonally connected and may not contain any 2×2 areas of water. Each island also contains a set of non-repeating digits that sums to the purple cell total if given. If no total is given, the sum is 6, 9 or 25. The number in the purple cell is the number of cells in the island. Totals are not necessarily in the top left most cell of an island. All islands are normal except one - Treasury Island, which has no given total. On this island, X's mark the spot - i.e. Treasury Island can be evenly divided into non-overlapping dominoes that each sum to 10. The purple cell's digit is inconsequential and digits may repeat.","solution":"537849261162357849894612537925486713478931652613725498246198375789563124351274986","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All cells are either island or water. Each purple cell is an island cell. Each island must contain exactly one purple cell. Different islands may not touch orthogonally. The water cells are orthogonally connected and may not contain any 2×2 areas of water. Each island also contains a set of non-repeating digits that sums to the purple cell total if given. If no total is given, the sum is 6, 9 or 25. The number in the purple cell is the number of cells in the island. Totals are not necessarily in the top left most cell of an island. All islands are normal except one - Treasury Island, which has no given total. On this island, X's mark the spot - i.e. Treasury Island can be evenly divided into non-overlapping dominoes that each sum to 10. The purple cell's digit is inconsequential and digits may repeat.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c7","c8","c9","c10","c11","c12","c13"]}]},{"id":"3w2n46bl22","ctcId":2991,"ctcDifficulty":"VERY HARD","title":"Two's Company, Three's a Crowd","author":"SUDOOOOOKUfan87","rules":"Normal Sudoku rules apply. \n\nArrow: Digits along an arrow sum to the digit in the attached circle. Digits on arrows may repeat if allowed by other rules. \n\nRenban: Digits on a purple Renban line must be consecutive and non-repeating, but can be in any order.","rulesClarified":"Normal Sudoku rules apply.\n\nArrow: each arrow starts at a circle. The digits along the arrow, not counting the circle, sum to the digit in that circle.\n\nDigits on arrows may repeat if allowed by other rules.\n\nRenban: the digits on each purple line are consecutive and non-repeating, and can be in any order.","solution":"576918342942573168831264597694735281358192674217846935429657813765381429183429756","constraints":["arrow","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"yh755nnm1j","ctcId":2993,"ctcDifficulty":"VERY HARD","title":"Distant Neighbors","author":"Knickolas","rules":"Normal sudoku rules apply. Cells separated by a white dot are consecutive. Draw a one-cell-wide loop that moves orthogonally through the centers of some cells. Adjacent digits along the loop are not consecutive. Numbers left of the grid indicate the number of cells on the loop in their row. Numbers above the grid indicate the sum of cells on the loop in their column. O, E, and P represent an odd, even, and prime number respectively.","rulesClarified":"Normal sudoku rules apply.\n\nTwo cells that share an edge with a white dot on it are consecutive: their digits differ by exactly 1.\n\nDraw one loop, one cell wide, through the centres of some cells. It moves orthogonally from one cell to the next and closes on itself.\n\nTwo digits that are next to each other along the loop are not consecutive.\n\nA number to the left of a row is the number of loop cells in that row.\n\nA number above a column is the sum of the digits in the loop cells of that column.\n\nO, E and P are letter clues: O means odd, E means even, P means prime. A letter to the left of a row says whether that row's loop-cell count is odd, even or prime. A letter above a column says whether that column's loop-digit sum is odd, even or prime.","solution":"162495873498637215573182469251378946934516782786249351317964528829751634645823197","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop that moves orthogonally through the centers of some cells. Numbers left of the grid indicate the number of cells on the loop in their row. Numbers above the grid indicate the sum of cells on the loop in their column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5","c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jjvussx9zq","ctcId":2995,"ctcDifficulty":"HARD","title":"Brink","author":"99%Sneaky","rules":"Normal sudoku rules apply. Digits along arrows sum to the digit in the attached circle. Digits along purple lines form a consecutive set. Digits in cages sum to the small number printed in the corner. Digits in cells separated by a chess King's move may not contain identical digits.","solution":"178932546546178923293456781785621439914783265632549178451367892867295314329814657","constraints":["antiking","arrow","cage","renban"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"d5s2c3o5j3","ctcId":2998,"ctcDifficulty":"VERY HARD","title":"Lost and Found","author":"Jeet Sampat, Myxo, dumediat, damasosos92, Agent, SSG, glum_hippo, Playmaker6174, tallcat, Malrog, mnasti2, Piatato, Christounet, MaizeGator, Shintaro Fushida-Hardy","rules":"Almost Sudoku: Fill the grid with digits 1-9 so that each row, column, and box contains exactly 8 unique digits.\n\nArrows: Digits along an arrow must sum to the digit in the attached bulb.\n\nSlow Thermometers: Digits along a thermometer must not decrease from the bulb end to the tip.\n\nGerman Whispers Line: Two cells connected by a green line must have a difference of at least 5.\n\nSkyscraper Clues: Clues outside the grid give the number of digits visible from the clue's position, given that each digit blocks the view of any digits behind it that aren't larger than it.\n\nRegion Sum Lines: Along a blue line, box borders divide the line into smaller segments with the same sum. Digits can repeat along a segment if allowed by other rules.","solution":"539218649471169283821743165913824758258391417867175932166952874395517264742438591","constraints":["arrow","custom","german-whispers","region-sum-line","skyscraper","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Almost Sudoku: Fill the grid with digits 1-9 so that each row, column, and box contains exactly 8 unique digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"skyscraper","type":"skyscraper","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"btl00ki232","ctcId":2999,"ctcDifficulty":"MEDIUM","title":"Satellite","author":"Kaktuslav","rules":"Normal sudoku rules apply.\n\nCounting by color constraints: Every digit on a line of color C counts how many times that digit appears on all lines of color C. For example, if there is a 3 on a green line, then there are exactly three 3s on all green lines combined.\n\nGerman whispers (decorated with squares): Adjacent digits along a green line differ by at least 5.\n\nParity lines (decorated with circles): Adjacent digits along a red line  have different parity (i.e., one of them is even and the other is odd).\n\nRegion sum lines (no decorations): Box borders divide each blue line  into segments of equal sum. The sum may be different for different lines.","solution":"861532974735149682942876351418395726659287413327461895573618249286954137194723568","constraints":["custom","german-whispers","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Counting by color constraints: Every digit on a line of color C counts how many times that digit appears on all lines of color C. For example, if there is a 3 on a green line, then there are exactly three 3s on all green lines combined. Parity lines (decorated with circles): Adjacent digits along a red line  have different parity (i.e., one of them is even and the other is odd).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"k4g3ubb8qe","ctcId":3002,"ctcDifficulty":"VERY HARD","title":"Yin-Yang-Yong","author":"Marty Sears","rules":"• Somedoku: Fill each cell with a digit from 1-9. For every row 'n' and column 'n' there are exactly 'n' unique digits. The remaining cells are filled with repeats.\n\n• Yin-Yang-Yong: Divide the grid into three regions. A region is an area of orthogonally connected cells. No 2x2 area may be entirely in one region. \n\n• Identical digits may not appear in different regions.\n\n• German Whisper (green): Adjacent digits on a green line have a difference of at least 5.\n\n• Nabner (yellow): No two digits anywhere on a yellow line may be consecutive (or the same.)\n\n• Entropic (orange): Any group of 3 adjacent cells on an orange line must contain one low digit (1, 2 or 3), one medium digit (4, 5 or 6) and one high digit (7, 8 or 9.)\n\n• Same Difference (turquoise): Adjacent digits on a turquoise line always have the same difference. This difference must be determined for each turquoise line.\n\n• X: Digits joined by an X sum to 10.\n\n• Blue Arrow: A digit on a blue arrow indicates how many region borders (separating two regions) are seen in the direction of the arrow. (Region edges at the outer perimeter of the grid don't count.)","solution":"888888888828228282821288121825292959825443443825945597825943515825941676821937564","constraints":["XV","custom","entropic-line","german-whispers","nabner-line","same-difference-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Somedoku: Fill each cell with a digit from 1-9. For every row 'n' and column 'n' there are exactly 'n' unique digits. The remaining cells are filled with repeats. • Yin-Yang-Yong: Divide the grid into three regions. A region is an area of orthogonally connected cells. No 2x2 area may be entirely in one region. • Identical digits may not appear in different regions. • Blue Arrow: A digit on a blue arrow indicates how many region borders (separating two regions) are seen in the direction of the arrow. (Region edges at the outer perimeter of the grid don't count.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c2","c3","c9"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"tdr0ywy332","ctcId":3004,"ctcDifficulty":"HARD","title":"Global Warming","author":"Br1312te","rules":"Normal sudoku rules apply. The 3x3 black box borders split grey thermometer lines into segments. Starting from the bulb, the sum of each segment must increase. Additionally, within each segment, starting from the original bulb, digits must also increase. Every 2x2 square of cells completely sitting within a red cage must contain a low digit (1,2,3), middle digit (4,5,6) and high digit (7,8,9). Digits connected by a white dot are consecutive. If a black dot sits between two digits, one is double the other.","rulesClarified":"Normal sudoku rules apply.\n\nThe black lines of the 3x3 boxes cut each grey thermometer into segments wherever it crosses a box border.\n\nEach grey thermometer starts at its bulb, the filled grey circle at one end. Working outward from the bulb:\n- the sum of each segment is larger than the sum of the segment before it;\n- within each segment, digits increase as you move away from the bulb.\n\nEvery 2x2 square of cells lying completely inside a red cage must contain a low digit (1, 2 or 3), a middle digit (4, 5 or 6) and a high digit (7, 8 or 9).\n\nDigits joined by a white dot are consecutive.\n\nIf a black dot sits between two digits, one of them is double the other.","solution":"578246193239581647641793825496327581385419276712865439853672914927154368164938752","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Starting from the bulb, the sum of each segment must increase. Additionally, within each segment, starting from the original bulb, digits must also increase. Every 2x2 square of cells completely sitting within a red cage must contain a low digit (1,2,3), middle digit (4,5,6) and high digit (7,8,9).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7"]}]},{"id":"c3qu3xglut","ctcId":3005,"ctcDifficulty":"HARD","title":"Heavy Is the Crown","author":"sujoyku","rules":"Happy Birthday, Calvinball!\n---\n- Normal sudoku rules apply, i.e. each row, column, and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- Tentropic Lines: Every set of four sequential digits on a hollow peach line must contain one each from {19}, {28}, {37}, and {46}. A 5 may not appear on a Tentropic Line. Digits on a line may repeat if allowed by other rules.\n\n- Region Sum Lines: Box borders divide the blue lines into segments with the same sum. (Different lines may have different sums.)\n\n- Killer Cages: Digits in a cage must sum to 20.","solution":"176549823982136547354782691743918265625374918819265734297453186538621479461897352","constraints":["cage","custom","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Tentropic Lines: Every set of four sequential digits on a hollow peach line must contain one each from {19}, {28}, {37}, and {46}. A 5 may not appear on a Tentropic Line. Digits on a line may repeat if allowed by other rules.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"ddgg4xrhlz","ctcId":3006,"ctcDifficulty":"HARD","title":"Horseshoes","author":"Kaktuslav","rules":"Normal sudoku rules apply.\n\nHorseshoes: Digits do not repeat along a line. The two digits at the ends of each line (marked with white circles) sum to the number displayed in the middle of that line.","solution":"634982157579631482218574963321849576746153829895726341187295634462318795953467218","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Horseshoes: Digits do not repeat along a line. The two digits at the ends of each line (marked with white circles) sum to the number displayed in the middle of that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"68spijnw4s","ctcId":3009,"ctcDifficulty":"MEDIUM","title":"Fallen Mast in a Storm","author":"Marty Sears","rules":"TRIPLE TROUBLE: Fill the grid with the digits 1-9, so that no digit repeats in any row or column. Each 3x3 box must be filled using only 3 distinct digits (with repeats being allowed.)\n\nSAME DIFFERENCE: Adjacent digits along a turquoise line always have the same difference. This difference must be determined for each turquoise line.\n\nREGION SUM: 3x3 box borders divide darker blue lines into segments, which each have the same sum. This sum must be determined for each darker blue line.","solution":"564321879456132987645213798798546213879654321987465132213879546321987654132798465","constraints":["region-sum-line","same-difference-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"wr8s0idhmw","ctcId":3010,"ctcDifficulty":"MEDIUM","title":"Shh-nooker (K)Nights","author":"olima","rules":"Normal Sudoku rules apply. Digits a knight's move (in chess) apart must be different. Adjacent digits on a green line differ by at least 5. The black dot indicates digits with one being double the other, the white dot indicates consecutive digits. Not all dots are necessarily given. Digits in circles appear at least once in the four surrounding cells.","solution":"358172964274639185916584732165748329783926541429315678647851293831297456592463817","constraints":["antiknight","german-whispers","kropki","quadruple"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"ut3m32qtmf","ctcId":3011,"ctcDifficulty":"HARD","title":"Crossroads on Another World","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nAdjacent digits along a green line must differ by at least 5.\n\nDigits along a pink line must form a non-repeating group of consecutive digits, but they may appear in any order along the line.\n\nEach gray line can be divided into segments of contiguous cells where the digits in each segment sum to 10. These segments cannot overlap, and every cell is part of exactly one segment. Digits may repeat freely on gray lines and within sums.","rulesClarified":"Normal sudoku rules apply.\n\nDigits along a pink line form a non-repeating set of consecutive digits. They may appear in any order along the line.\n\nAdjacent digits along a green line must differ by at least 5.\n\nEach gray line is cut into segments of contiguous cells. The digits in each segment add up to 10.\n\nThe segments on one gray line do not overlap, and every cell on a gray line belongs to exactly one segment. Cells that are not on a gray line are not part of any segment.\n\nDigits may repeat freely on gray lines and within sums.","solution":"846537291715492683932618547628941375473265918591873462189324756254786139367159824","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each gray line can be divided into segments of contiguous cells where the digits in each segment sum to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"oqn3ynpkm3","ctcId":3012,"ctcDifficulty":"HARD","title":"Ascending Starters Sudoku 10","author":"Akash Doulani","rules":"Classic Sudoku rules apply. \nClues outside the grid indicate the sum of the first set of all ascending digits starting from the first cell from the corresponding side. Sets may consist of only one digit.","rulesClarified":"Classic Sudoku rules apply.\n\nEach clue sits outside the grid, beside one row or column. It counts digits from the grid edge it points to, along that row or column.\n\nThe counted set is an ascending run of cells starting from the first cell on that side. It takes the first cell, then each following cell whose digit is larger than the digit before it, and stops at the first digit that is not larger. A run may be a single digit.\n\nThe clue is the sum of the digits in its run. For example, if a column reads 2, 5, 3 from the top, the run is 2 and 5, so a clue of 7 is correct there.","solution":"235189764864732195197654238578341629943526817621978543782413956419865372356297481","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Clues outside the grid indicate the sum of the first set of all ascending digits starting from the first cell from the corresponding side.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"cveeva5iz3","ctcId":3014,"ctcDifficulty":"MEDIUM","title":"For Daniël","author":"Jonesy","rules":"Normal sudoku rules apply. Digits in a cage sum to the total in the top left corner. Digits in box 5 (ie the central 3x3 box) must not see a digit of the same parity a knight’s move away. A “King's move constraint” is only applied to even digits: ie an even digit cannot repeat a king's move away from itself. Cells connected by an X sum to 10. ALL possible Xs are given. A white dot connects two consecutive digits. Not all possible dots are given.","solution":"629475318518923476347618925852749631961832547734561892183254769496187253275396184","constraints":["XV","cage","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in box 5 (ie the central 3x3 box) must not see a digit of the same parity a knight’s move away. A “King's move constraint” is only applied to even digits: ie an even digit cannot repeat a king's move away from itself.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"u5ej36c38t","ctcId":3015,"ctcDifficulty":"HARD","title":"The Two Wings of the Eagle Totem","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\nAdjacent digits along a green line must differ by at least 5.\nDigits along a pink line must form a non-repeating group of consecutive digits, but they may appear in any order along the line.\nEach gray line can be divided into segments of contiguous cells, where the digits in each segments sum to 10. These segments cannot overlap and every cell is part of exactly one segment. Digits may repeat freely on gray lines and within sums.","solution":"562719483789354612413826957935271846876543291241698735128937564397465128654182379","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each gray line can be divided into segments of contiguous cells, where the digits in each segments sum to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"cy362icfvw","ctcId":3016,"ctcDifficulty":"MEDIUM","title":"Par-King at the Garage","author":"olima","rules":"Normal Sudoku rules apply. Digits a King's move (in chess) apart must be different. Adjacent digits on a green line differ by at least 5. Box borders divide blue lines into segments with the same sum. Each of the digit in a circle appers at least once in the four cells touching the circle.","solution":"891563274324879156765214389517682943248397615639451827482736591953148762176925438","constraints":["antiking","german-whispers","quadruple","region-sum-line"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"mvjp2dw24q","ctcId":3018,"ctcDifficulty":"MEDIUM","title":"Killer cages dead end","author":"Patrick Junke","rules":"Normal Sudoku rules apply (place a set of digits [1-9] in each row, column, and 3x3 region).\nNormal Killer cages rules apply (digits don’t repeat in a cage and sum to the small total clue on top of the top left cell of the cage if indicated).\nAll instances of five of the nine digits, to be determined, constitute an area of orthogonnally connected cells, a \"labyrinth\". The other four digits are considered \"walls\".\nAn arrow appears in a \"dead end\" of the labyrinth pointing to the only way out, i.e. the only labyrinth cell to which it is connected. All arrows are given.\nA white dot between two digits indicates there are consecutives (not all white dots are given).","solution":"418593672529617483367428195184359267735286941296174358673842519941735826852961734","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"An arrow appears in a \"dead end\" of the labyrinth pointing to the only way out, i.e. the only labyrinth cell to which it is connected.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"hxw93rhz53","ctcId":3019,"ctcDifficulty":"HARD","title":"The buried clue walls","author":"Patrick Junke","rules":"Normal Sudoku rules apply.\n\nThe grid hides a labyrinth: a single continuous region of orthogonally connected cells. All remaining cells are walls. A 2×2 block may never consist entirely of labyrinth cells or entirely of wall cells.\n\nArrows mark ALL dead ends of the labyrinth, each pointing toward the only cell they connect to.\n\nWalls form isolated tetrominoes (4 orthogonally connected cells). Wall cells from different tetrominoes can't touch each other, even diagonally. Digits within a tetromino do not repeat and sum to 12.\n\nA white dot between two cells indicates that their digits are consecutive. (Not all white dots are given.)\n\nAn X between two cells indicates both that the cells are of different types (one labyrinth cell and one wall cell) and that their digits sum to 10. (Not all Xs are given.)","rulesClarified":"Normal Sudoku rules apply.\n\nThe grid hides a labyrinth: a single continuous region of orthogonally connected cells. The labyrinth is not drawn; you work it out. Every cell that is not part of the labyrinth is a wall.\n\nA 2×2 block may never consist entirely of labyrinth cells or entirely of wall cells.\n\nArrows mark all dead ends of the labyrinth. A dead end is a labyrinth cell with exactly one labyrinth neighbour. Each dead-end arrow points toward the only cell that dead end connects to.\n\nThe walls form isolated tetrominoes: each group of orthogonally connected wall cells is exactly one four-cell piece. Wall cells from different tetrominoes may not touch each other, not even diagonally.\n\nDigits within a tetromino do not repeat and sum to 12.\n\nA white dot between two orthogonally adjacent cells means their digits are consecutive. Not all white dots are drawn. A pair of cells with no dot has no such rule.\n\nAn X between two orthogonally adjacent cells means that one cell is a labyrinth cell and the other is a wall cell, and that their digits sum to 10. Not all Xs are drawn. A pair of cells with no X has no such rule.","solution":"795241863431658927826739415913827654547316289268495731189564372374182596652973148","constraints":["XV","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The grid hides a labyrinth: a single continuous region of orthogonally connected cells. Arrows mark ALL dead ends of the labyrinth, each pointing toward the only cell they connect to. Digits within a tetromino do not repeat and sum to 12.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"bos0gb2wea","ctcId":3020,"ctcDifficulty":"HARD","title":"Raining ten clues","author":"Patrick Junke","rules":"Normal sudoku rules apply.\n(Place the digits from 1 to 9 in every row, in every column, and in every 3x3 region.)\n\nStandard killer cages rules apply.\n(In dotted regions, digits don't repeat and sum to the indicated total - in this puzzle always 10).\n\nAn X between two digits indicates they sum to 10.\n\nAll Xs are given !","solution":"312975684675148923948236517236751498451389762789624135897462351564813279123597846","constraints":["XV","cage","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"ruz1c8uhcr","ctcId":3021,"ctcDifficulty":"MEDIUM","title":"The Fireflies' Pairing Dance!","author":"Patrick Junke","rules":"Normal sudoku rules apply ie Each row, column, and 3×3 box must contain the digits 1–9 exactly once.\n\nA golden dot between two cells indicates that their sum is divisible by 4. ALL possible golden dots are given.\nGolden dots take precedence over the black dots ie if two cells could have black dot and a golden dot, only the golden dot is shown. A black dot between two digits indicates that one is double the other. Not all possible black dots are given. A white dot between two digits indicates they are consecutive. Not all possible white dots are given. The sum of two adjacent cells separated by a 3x3 box border are even. Note that the sum of two adjacent cells not separated by a 3x3 box border may still be even.","rulesClarified":"Normal sudoku rules apply: each row, column and 3x3 box contains the digits 1 to 9 exactly once.\n\nEvery dot sits on the edge between two orthogonally adjacent cells.\n\nGolden dot: the two digits add up to a multiple of 4. All possible golden dots are drawn. So a pair of adjacent cells with no golden dot has a sum that is not a multiple of 4.\n\nIf a pair could carry both a golden dot and a black dot, only the golden dot is drawn.\n\nBlack dot: one digit is double the other. Not all possible black dots are drawn, so a pair with no black dot tells you nothing.\n\nWhite dot: the two digits are consecutive. Not all possible white dots are drawn, so a pair with no white dot tells you nothing.\n\nWhere two adjacent cells lie in different 3x3 boxes, their digits add up to an even number.\n\nAdjacent cells inside the same 3x3 box may or may not add up to an even number. Only the dots say more about them.","solution":"123745968459168237768239154382471596671592483594683721916827345247356819835914672","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A golden dot between two cells indicates that their sum is divisible by 4. The sum of two adjacent cells separated by a 3x3 box border are even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c7"]}]},{"id":"eu0r01u8nh","ctcId":3022,"ctcDifficulty":"MEDIUM","title":"HSSC Appetizer - Sudoku Mathrax","author":"Richard","rules":"Holiday Season Sudoku Contest - practise sudoku\n\nApply classic sudoku rules.\nSome intersections of the grid lines are marked by a number and an operator (+, -, x, /) in a circle.\nThe number is the result of the arithmetical operation, applied to both pairs of diagonally opposite cells. An \"E\" in the circle indicates that all four adjacent digits are even; an \"O\" indicates that all four adjacent digits are odd.","solution":"971236458532487916684915732893172564467359821215648379328764195146593287759821643","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The number is the result of the arithmetical operation, applied to both pairs of diagonally opposite cells. An \"E\" in the circle indicates that all four adjacent digits are even; an \"O\" indicates that all four adjacent digits are odd.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]}]},{"id":"ydam0gzn8q","ctcId":3023,"ctcDifficulty":"VERY HARD","title":"Friendly robots","author":"Jonesy","rules":"Hello.\n\nNormal 9x9 sudoku rules apply.\nDigits on an arrow sum to the digit in the attached circle. Cells that are visited twice by an arrow count twice for the total value.\n\nDigits separated by a white dot are consecutive.\n\nHave fun.","solution":"247958613185367294963214857729581346831496725654723189572139468396842571418675932","constraints":["arrow","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"jaw9z4nws6","ctcId":3024,"ctcDifficulty":"MEDIUM","title":"Web Design","author":"Marty Sears","rules":"• Normal sudoku rules apply.\n\nWEB: \n• Help Cecil the Spider to build a web using silky threads. \n• A single silky thread must start at a white spot and connect to another white spot that is either one or two cells away in a straight line (horizontally, vertically or diagonally.) Any further and the thread will break!\n• Two silky threads may not cross each other.\n• The digit on a white spot indicates how many silky threads attach to it.\n• The two white spots connected by a silky thread may not contain the same digit.\n\nINSECTS:\n• If a black insect sits between two digits, one is double the other.\n• If a stripy green insect sits between two digits, they have a difference of at least 5.\n• If a spotty red insect sits between two digits, one is odd and the other is even.\n\nCECIL:\n• The digit being thought about by Cecil the Spider indicates how many of the afore-mentioned insects have been caught on silky threads.","solution":"285749361617325984394186275728591643953462817461837592176258439549673128832914756","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• A single silky thread must start at a white spot and connect to another white spot that is either one or two cells away in a straight line (horizontally, vertically or diagonally.) Any further and the thread will break! • If a stripy green insect sits between two digits, they have a difference of at least 5. • If a spotty red insect sits between two digits, one is odd and the other is even. • The digit being thought about by Cecil the Spider indicates how many of the afore-mentioned insects have been caught on silky threads.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c10","c11","c13"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"jn8oxp9vmp","ctcId":3025,"ctcDifficulty":"HARD","title":"Battle Line","author":"DiMono","rules":"Normal Sudoku rules apply.\n\nBattlefield: Consider the first X cells and the last Y cells of each row and column, where X is the number in the first cell and Y is the number in the last cell. These groups of cells will either overlap or leave a gap. Clues outside the grid give the sum of the cells in the resulting gap or overlap.\n\nALL cells that are part of an overlap in BOTH their row and column are red. ALL cells that are part of a gap in BOTH their row and column are green.","solution":"195642387746583219832179645689327451527416893413895762358761924274958136961234578","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Clues outside the grid give the sum of the cells in the resulting gap or overlap. ALL cells that are part of an overlap in BOTH their row and column are red. ALL cells that are part of a gap in BOTH their row and column are green.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6"]}]},{"id":"3mjyxrx5og","ctcId":3026,"ctcDifficulty":"HARD","title":"Triple Trouble","author":"Marty Sears","rules":"Fill the grid with the digits 1-9, so that no digit repeats in any row or column. Each box may only contain three distinct digits.\n\nARROWS: Digits along a purple arrow sum to the digit in the attached circle.\n\nGERMAN WHISPERS: Adjacent digits on a green line have a difference of at least 5.\n\nSAME DIFFERENCE: Adjacent digits along a turquoise line always have the same difference. This difference must be determined for each turquoise line.\n\nNABNERS: No two digits on a yellow line may be the same or consecutive.\n\nBLACK DOTS: If two digits are separated by a black dot, then one is double the other.","solution":"831597462183975624318759246527146398275461983752614839649238715496382571964823157","constraints":["arrow","custom","german-whispers","kropki","nabner-line","same-difference-line"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each box may only contain three distinct digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"same-difference-line","type":"same-difference-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"fphttzusrk","ctcId":3027,"ctcDifficulty":"HARD","title":"Arrow Renban Sudoku","author":"Christounet","rules":"Normal sudoku rules apply. \n\nDigits along an arrow sum to the digit in that arrow's circle. \n\nDigits on a renban (purple lines) form a set of non-repeating consecutive digits in any order. \n\nIf two digits are separated by a black dot then one digit is double the other.","solution":"321867549798534261546129738914786352653492187872315694267958413185243976439671825","constraints":["arrow","kropki","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"4ecligavud","ctcId":3029,"ctcDifficulty":"HARD","title":"Star Of Bethlehem","author":"Aron Lidé (Aspartagcus)","rules":"Normal sudoku rules apply. The digits along an arrow sum to the digit in that arrow’s circle. Neighbouring digits on a curved line must differ by at least 4. Digits on the star-shaped line must form a set of consecutive digits.","solution":"742986135568123974193745682435619728817254369926837451384571296279468513651392847","constraints":["arrow","dutch-whispers","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"g4vx2p0ewp","ctcId":3030,"ctcDifficulty":"MEDIUM","title":"Xmas 2025","author":"James Kopp","rules":"Normal sudoku rules apply.\nClues outside the grid give the total of the digits placed between 1 and 9 in that column. \nAdjacent digits along a green line have a difference of at least five.\nDigits in a circle must be placed at least once in the four cells touching that circle.","solution":"168435792352978641794261358927143865516827934843596127481659273279314586635782419","constraints":["german-whispers","quadruple","sandwich"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"dxgxcqoyeg","ctcId":3031,"ctcDifficulty":"HARD","title":"Psst, I'm in the Loop","author":"Calvinball","rules":"Normal Sudoku rules apply.\n\nDraw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally.\n\nThe loop acts as a German Whisper line, all adjacent digits along the line must have a difference of at least 5.\n\nClues outside the grid are Loopwiches. Loopwiches indicate the sum of the digts between the first and last loop cell in their row or column. (Both loop and nonloop cells between the 2 crust cells are summed)","solution":"617285934385946172942371658154829763768534219293617485439768521871452396526193847","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally. Loopwiches indicate the sum of the digts between the first and last loop cell in their row or column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"syjv7l5c1o","ctcId":3032,"ctcDifficulty":"HARD","title":"The Score is Still Q to 12!","author":"Calvinball","rules":"Normal sudoku rules apply.\n\nDraw a snake in the grid. A snake is a one-cell-wide path of orthogonally connected cells which may not touch itself orthogonally or diagonally.\n\nArrow cells are always snake, and count the total amount of snake cells seen in all indicated directions (If R8C6 sees 4 cells up it’s column and 2 cells along the diagonal then it would be a 6).  Arrow cells do not count themselves.\n\nCircle cells are the head and tail of the snake, and count the total number of snake cells in their box.\n\nCages represent different zones which dictate how the snake functions through each zone. In the German Whisper Zone the snake functions as a German Whisper Line, along a German Whispers line, consecutive digits must differ by at least 5. In the Entropy Zone the snake functions as a Entropic Line, Along an entropic line, any three consecutive cells must contain a low digit {1,2,3}, a medium digit {4,5,6}, and a high digit {7,8,9}.\n\nWhere the snake crosses into different zones it doesn’t need to be either Entropic or German Whisper.\n\nCells separated by a white dot are always consecutive, not all dots are given.","solution":"271643598964158273385729164423867951596231487718495326659374812137582649842916735","constraints":["custom","entropic-line","german-whispers","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a snake in the grid. Arrow cells are always snake, and count the total amount of snake cells seen in all indicated directions (If R8C6 sees 4 cells up it’s column and 2 cells along the diagonal then it would be a 6). Circle cells are the head and tail of the snake, and count the total number of snake cells in their box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c6"]},{"slug":"entropic-line","type":"entropic-line","variant":"modified","modifiers":[],"params":null,"note":"In the Entropy Zone the snake functions as a Entropic Line, Along an entropic line, any three consecutive cells must contain a low digit {1,2,3}, a medium digit {4,5,6}, and a high digit {7,8,9}.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"In the German Whisper Zone the snake functions as a German Whisper Line, along a German Whispers line, consecutive digits must differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]}]},{"id":"6me9411h8m","ctcId":3034,"ctcDifficulty":"HARD","title":"Modular Masyu","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nMasyu: Draw a single non-intersecting loop through the centers of some cells that moves horizontally or vertically and passes through every circle clue. The loop must turn on black circles and pass straight through the cells on either side. The loop must go straight through white circles and turn in at least one of the cells on either side.\n\nThe loop acts as a modular line. Each set of three adjacent digits along the loop must be one each from the sets [147], [258], and [369].\n\nThe digit in each given circle clue counts the total number of loop cells in all straight loop segments coming off of the cell (counting the cells where the loop turns, and counting the clued cell itself once).","solution":"321657984759184236846239715695478321178326459234915678912563847483791562567842193","constraints":["custom","modular-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Masyu: Draw a single non-intersecting loop through the centers of some cells that moves horizontally or vertically and passes through every circle clue. The loop must turn on black circles and pass straight through the cells on either side. The loop must go straight through white circles and turn in at least one of the cells on either side. The digit in each given circle clue counts the total number of loop cells in all straight loop segments coming off of the cell (counting the cells where the loop turns, and counting the clued cell itself once).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c7"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"3l6bzhg2ji","ctcId":3035,"ctcDifficulty":"MEDIUM","title":"Tinsel and Baubles","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAdjacent digits on green tinsel have a difference of at least 5.\n\nThe digit on a gold bauble indicates exactly how many times that digit appears on green tinsel.","solution":"536497182849152376172683594715348629628915743493726815964571238387264951251839467","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digit on a gold bauble indicates exactly how many times that digit appears on green tinsel.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"q6rcz0d0og","ctcId":3036,"ctcDifficulty":"VERY HARD","title":"Happy Holiday Season","author":"Panthera","rules":"Normal sudoku rules apply. Antiknight rules apply. \nNormal Knapp Daneben Japanese sums rules apply. \n Colors used in this puzzle are blue (b), white (w) and red (unshaded). \n\nKnapp Daneben Japanese Sums rules: the squares outside the grid indicate the order of the runs of contiguous cells that must be shaded the color of the clue. The number in the square indicates the sum of the cells in the run OFF BY 1! There must be at least one unshaded cell between runs of the same color, but that is not required for runs of different colors.  All shaded runs are given. \n\nAntiknight rules: Digits a knights move away cannot be the same.","solution":"215936847637548192948721365594872631861395274372164589729613458186457923453289716","constraints":["antiknight","custom"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Knapp Daneben Japanese Sums rules: the squares outside the grid indicate the order of the runs of contiguous cells that must be shaded the color of the clue. The number in the square indicates the sum of the cells in the run OFF BY 1!","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"xag582l3t0","ctcId":3037,"ctcDifficulty":"HARD","title":"Bits And Nibbles!","author":"Jonesy","rules":"Normal sudoku rules apply.\nParity Counter Lines: the two digits at the ends of each line indicate the number of odd and even digits in that line, including the end digits themselves. One digit counts odd digits; the other counts even digits.\nBitClock: A BitClock is a group of five cells: a central arrow cell and its four orthogonally adjacent neighbours (up, right, down, left). The arrow shows where the pattern starts, and the pattern is then read clockwise around the four neighbours.  The digit in the central arrow cell tells you the odd/even pattern of those four neighbours, using a simple 4-bit code. In those neighbour cells, an even digit means the “bit” is ON; while an odd digit means the “bit” is OFF.  Each arrow cell digit has its own fixed 4-bit pattern (see table below). Eg If a 3 is placed in an arrow cell, its code is OOEE.
Starting from the direction of the arrow and reading clockwise, the four orthogonal neighbours must be Odd, Odd, Even, Even.\nDigit Codes: 1 → OOOE
2 → OOEO
3 → OOEE
4 → OEOO 5 → OEOE 6 → OEEO 7 → OEEE 8 → EOOO 9 → EOOE","solution":"641758329372619548589342176263491785958276431417583692794865213825137964136924857","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Parity Counter Lines: the two digits at the ends of each line indicate the number of odd and even digits in that line, including the end digits themselves. The digit in the central arrow cell tells you the odd/even pattern of those four neighbours, using a simple 4-bit code.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]}]},{"id":"gtbtt6llob","ctcId":3039,"ctcDifficulty":"VERY HARD","title":"Merry X/V-mas","author":"olima","rules":"Normal Sudoku rules apply. Adjacent digits on a green line differ by at least 5. No two cells sharing an edge sum to 5 or 10.","solution":"162795483897134256354862971429317568578926134613458792936271845781543629245689317","constraints":["XV","german-whispers"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"eo2tx5yh0c","ctcId":3040,"ctcDifficulty":"HARD","title":"Follow on Arrows","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow's circle. Digits cannot repeat along the blue diagonal line.","solution":"169527348825143796743986251317294865296758413584361927451839672978612534632475189","constraints":["arrow","diagonal"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"esjz6meusc","ctcId":3041,"ctcDifficulty":"VERY HARD","title":"Love Letter from Canada","author":"SUDOOOOOKUfan87","rules":"Normal Sudoku rules apply.\n\nHelp Rika Shimakura deliver a love letter from Canada to all her loved ones in Japan by drawing a path from r1c9 to r9c1. The path moves orthogonally and visits all 3x3 regions. Adjacent digits on the path must have a difference of at least 4. r1c9 and r9c1 are the only island cells on the path. \n\nAll cells are either island or water.\n\nEach lavender cell is an island cell; the number in it is the number of cells in that island.\n\nEach lavender island must consist of exactly one lavender cell, and a set of non-repeating digits that sum to the total in the lavender cell, if given. (r6c8's island total is a prime number). \n\nr1c9 (Canada) and r9c1 (Japan) are non-lavender island cells. Both islands' digits have the same product. The digits on the flags are inconsequential.  \n\nDifferent islands may not touch orthogonally.\n\nThe water cells are orthogonally connected and may not contain any 2×2 areas of water.\n\nKiller totals are not necessarily in the top left most cell of an island.","solution":"794126583836954712152738496978263145243815967561479238389542671415687329627391854","constraints":["cage","custom","dutch-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Each lavender island must consist of exactly one lavender cell, and a set of non-repeating digits that sum to the total in the lavender cell, if given. (r6c8's island total is a prime number).","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Help Rika Shimakura deliver a love letter from Canada to all her loved ones in Japan by drawing a path from r1c9 to r9c1. The path moves orthogonally and visits all 3x3 regions. Adjacent digits on the path must have a difference of at least 4. r1c9 and r9c1 are the only island cells on the path. All cells are either island or water. Each lavender cell is an island cell; the number in it is the number of cells in that island. r1c9 (Canada) and r9c1 (Japan) are non-lavender island cells. Both islands' digits have the same product. Different islands may not touch orthogonally. The water cells are orthogonally connected and may not contain any 2×2 areas of water.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c8","c9","c11","c12"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"r9fu3jqm1j","ctcId":3042,"ctcDifficulty":"HARD","title":"Venice","author":"Kaktuslav","rules":"Normal sudoku rules apply. Box borders divide each blue line into segments with the same sum (this sum may be different for different lines).","solution":"649238715237154896158769234975846123813572469462391578786423951324915687591687342","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"v1l5ri9ew3","ctcId":3043,"ctcDifficulty":"MEDIUM","title":"Double Counting","author":"Timotab","rules":"• Normal sudoku rules apply.\n• A circle's neighbourhood includes the cell containing the circle, and any cell touching it (on an edge or corner). The digit in the circle is the number of cells in its neighbourhood that have the same odd-even parity as the circled digit.\n• Digits in circles also indicate how many circles in the puzzle that contain that digit.","solution":"314598726967142853852763941479386215186425379235971684593217468748659132621834597","constraints":["counting-circle","custom"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• A circle's neighbourhood includes the cell containing the circle, and any cell touching it (on an edge or corner). The digit in the circle is the number of cells in its neighbourhood that have the same odd-even parity as the circled digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"de2dt3ohoq","ctcId":3044,"ctcDifficulty":"HARD","title":"Yin Yagn","author":"Timotab","rules":"• Normal sudoku rules apply: Place the digits 1-9 in every row, column, and box, without repetition.\n• Yin Yang: Shade some cells such that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2x2 area is fully shaded or fully unshaded. \n• A clue that is in cells that are all shaded or all unshaded is RIGHT. A clue that has at least one cell shaded and at least one cell unshaded is very, very WROGN. See below for exact definitions of WROGN clues. \n• RIGHT Cages: Digits in cages must sum to the value in the top left corner of the cage.\n• RIGHT Kropki: Where digits are separated by a black dot, one must be double the other. Not all dots are necessarily given.\n• RIGHT Renban: Digits on a purple line form a set of non-repeating, consecutive digits in any order. \n• RIGHT Nabner: No two digits on a gold line can be consecutive, regardless of their position on the line. Digits may not repeat on lines.\n• RIGHT Quadruples: Digits in a Quadruple circle must be placed at least once in the four cells touching that circle.\n• WROGN Cages: Digits in cages must not sum to the value in the top left corner of the cage.\n• WROGN Kropki: Where digits are separated by a black dot, neither is allowed to be double the other. \n• WROGN Renban: No two digits on a purple line can be consecutive, regardless of their position on the line. Digits may not repeat on lines.(ie, WROGN renban lines are RIGHT nabner lines).\n• WROGN Nabner: Digits on a gold line form a set of non-repeating, consecutive digits in any order. (ie, WROGN nabner lines are RIGHT renban lines)\n• WROGN Quadruples: Digits in a Quadruple circle must not be placed at all in the four cells touching that circle.","solution":"798165432354928671621437895839216547465379218217584369182743956546891723973652184","constraints":["cage","custom","kropki","nabner-line","quadruple","renban","yin-yang"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"• RIGHT Cages: Digits in cages must sum to the value in the top left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• A clue that is in cells that are all shaded or all unshaded is RIGHT. A clue that has at least one cell shaded and at least one cell unshaded is very, very WROGN. See below for exact definitions of WROGN clues. • WROGN Cages: Digits in cages must not sum to the value in the top left corner of the cage. • WROGN Kropki: Where digits are separated by a black dot, neither is allowed to be double the other. • WROGN Quadruples: Digits in a Quadruple circle must not be placed at all in the four cells touching that circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c9","c10","c13"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c11"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c12"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"n8sgls1q8a","ctcId":3045,"ctcDifficulty":"MEDIUM","title":"Medieval World War","author":"FastSandals and Timotab","rules":"• Normal Sudoku rules apply. Place the digits 1-9 once each in every row, column, and box.\n• Fortress: Cells shaded gray must be larger then their orthogonal non-fortress neighbors. \n• Arrows: Digits on an arrow must sum to the digit in the attached circle.","solution":"147639582856142379329785641538974216462351798791826435284513967615497823973268154","constraints":["arrow","maximum"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"maximum","type":"maximum","variant":"modified","modifiers":[],"params":null,"note":"• Fortress: Cells shaded gray must be larger then their orthogonal non-fortress neighbors.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"6og3rrs1zc","ctcId":3047,"ctcDifficulty":"MEDIUM","title":"Sting in the Tail","author":"Timotab","rules":"• Normal sudoku rules apply: Place the digits 1-9 in every row, column, and box, without repetition.\n• Adjacent digits along a green German Whispers line must differ by at least 5.\n• Digits separated by IX must sum to 9. Digits separated by XI must sum to 11.","solution":"276391845839542716145678293951726384384159627627483951718234569493865172562917438","constraints":["XV","german-whispers"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"0vbqutu0cp","ctcId":3048,"ctcDifficulty":"HARD","title":"Echolocation","author":"Erin Toler","rules":"Normal Sudoku rules apply.\n\nEcho Lines: Indigo lines are filled with a repeating sequence of different digits. The sequence must appear at least twice along the line and must always appear in its entirety. Different lines may contain different sequences.\n\nXV: Digits separated by an X sum to 10. Digits separated by a V sum to 5.\n\nKropki Dots: Digits separated by a black dot must have a ratio of 2:1 (i.e. one must be double the other).","solution":"842957613135486972679231458418793526327645891596128734764319285281574369953862147","constraints":["XV","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Echo Lines: Indigo lines are filled with a repeating sequence of different digits. The sequence must appear at least twice along the line and must always appear in its entirety.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"6xsugxgm9r","ctcId":3054,"ctcDifficulty":"HARD","title":"Through the Comets Eye","author":"Secret Santa","rules":"Normal Sudoku rules apply.\n\nStar Battle: Each row, column, and box contains exactly two stars. Stars may not touch orthogonally or diagonally.\nStars also contain digits and behave as normal Sudoku cells.\n\nHabitable Zone: Any digit orthogonally adjacent to a star must differ from the star’s digit by at least 3.\n\nComets: Little-killer clues give the sum of star digits along the indicated diagonal (only star cells count).\n\nResonance: Identical digits may not be a knight’s move apart.","rulesClarified":"Normal Sudoku rules apply.\n\nStar Battle: each row, column and region contains exactly two stars. Stars also hold digits and follow the normal Sudoku rules.\n\nStars may not touch, orthogonally or diagonally.\n\nHabitable Zone: any digit orthogonally next to a star must differ from that star's digit by at least 3.\n\nComets: each comet clue is a number at the edge of the grid, at the start of an arrow. It gives the sum of the star digits along the indicated diagonal. Only star cells count; other cells on that diagonal add nothing.\n\nResonance: two identical digits may not be a knight's move apart.","solution":"384951627627384951951627384495162738738495162162738495516273849849516273273849516","constraints":["antiknight","custom","little-killer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Star Battle: Each row, column, and box contains exactly two stars. Stars may not touch orthogonally or diagonally. Habitable Zone: Any digit orthogonally adjacent to a star must differ from the star’s digit by at least 3.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"svjdl9l4ck","ctcId":3055,"ctcDifficulty":"MEDIUM","title":"Heavy!","author":"tallcat and zetamath","rules":"Normal sudoku rules apply.  Each purple line contains a non-repeating set of consecutive digits in any order.  In this puzzle, the largest digit on each line must be at one of the line’s ends.","solution":"873156429694287531521349768318562947946738152257914683469821375185473296732695814","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In this puzzle, the largest digit on each line must be at one of the line’s ends.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ah1c5p6zcr","ctcId":3057,"ctcDifficulty":"VERY HARD","title":"Ten Ring Circus","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nEach gray line can be divided into segments of contiguous cells, where the digits in each segments sum to 10. These segments cannot overlap and every cell is part of exactly one segment.\n\nUsing red, green, and blue, color in all circles such that:\n-Orthogonally adjacent circles are different colors.\n-The digit inside a circle appears that many times in circles of that color.","solution":"671528493438967215259143687827314569963852741145796328786439152592671834314285976","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each gray line can be divided into segments of contiguous cells, where the digits in each segments sum to 10. -Orthogonally adjacent circles are different colors. -The digit inside a circle appears that many times in circles of that color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c6"]}]},{"id":"nd0191ecm9","ctcId":3058,"ctcDifficulty":"MEDIUM","title":"The Witching Hour","author":"Chefofdeath","rules":"Normal Sudoku rules apply.\n\nDifference: Digits separated by a white dot have a difference of 3.\n\nRenban: Digits along a line form a set of non-repeating consecutive digits in any order.\n\nX-Sums: Clues outside the grid indicate the sum of the first X numbers where X is the first digit seen.","solution":"967841325145923867328657941276195483593478612814362579651234798789516234432789156","constraints":["kropki","renban","x-sum"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"uojuxaw1qw","ctcId":3059,"ctcDifficulty":"MEDIUM","title":"Space Invaders","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply.\n\nINVADERS - Each invader sums to 10 with a digit in some orthogonally adjacent cell.\n\nDIFFERENCE BOMBS - Digits connected by a 𐌔 always have the same difference.\n\nTURRETS - Strategically place 3 turrets into cells in the bottom row. Each turret has as many missiles as the digit in its cell, and can pivot to fire them upwards or diagonally. A turret can destroy an Invader on a digit N by shooting it N times. Each invader is only shot by one of the turrets.\n\nAll Invaders must be destroyed!","rulesClarified":"Normal Sudoku rules apply.\n\nINVADERS: each invader sums to 10 with a digit in some orthogonally adjacent cell.\n\nDIFFERENCE BOMBS: digits connected by a bomb symbol (𐌔) always have the same difference.\n\nTURRETS: place three turrets into cells in the bottom row. Each turret has as many missiles as the digit in its cell, and can pivot to fire them upwards or diagonally.\n\nA turret can destroy an invader on a digit N by shooting it N times. Each invader is shot by only one of the turrets. All invaders must be destroyed.","solution":"693417582824935167571826943347258691918764325265391874489173256736582419152649738","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"INVADERS - Each invader sums to 10 with a digit in some orthogonally adjacent cell. DIFFERENCE BOMBS - Digits connected by a 𐌔 always have the same difference. TURRETS - Strategically place 3 turrets into cells in the bottom row. Each turret has as many missiles as the digit in its cell, and can pivot to fire them upwards or diagonally. A turret can destroy an Invader on a digit N by shooting it N times. Each invader is only shot by one of the turrets. All Invaders must be destroyed!","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c7","c8"]}]},{"id":"7oe1c7nwpc","ctcId":3061,"ctcDifficulty":"MEDIUM","title":"What an Odd Sight","author":"damo_89","rules":"Normal sudoku rules apply: Place the digits 1 to 9 once each in every row, column and 3x3 box\n\nA digit in a circle is odd and counts the number of odd digits that can be seen in all orthogonal directions combined, including itself. Even digits block the view.\n\nA digit in a square is even and counts the number of even digits that can be seen in all orthogonal directions combined, including itself. Odd digits block the view.\n\nALL circles and squares are given","rulesClarified":"Normal sudoku rules apply: place the digits 1 to 9 once each in every row, column and 3x3 box.\n\nAll circles and squares are given.\n\nA circle holds an odd digit. The number in a circle counts the odd digits the circle can see, in the four orthogonal directions combined, including its own digit. Looking out from the circle, even digits block its view.\n\nA square holds an even digit. The number in a square counts the even digits the square can see, in the four orthogonal directions combined, including its own digit. Looking out from the square, odd digits block its view.","solution":"728619453639574821451832796372958164915346278846127539164795382297483615583261947","constraints":["custom","even","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle is odd and counts the number of odd digits that can be seen in all orthogonal directions combined, including itself. A digit in a square is even and counts the number of even digits that can be seen in all orthogonal directions combined, including itself. ALL circles and squares are given","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c6"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"lldn0vubxi","ctcId":3062,"ctcDifficulty":"MEDIUM","title":"Iteration","author":"damo_89","rules":"Normal sudoku rules apply: Place the digits 1 to 9 once each in every row, column, and 3x3 box\n\nCoordinate Arrows: Digits on an arrow spell out the coordinates for the digit that is their sum. The row number is written on the start of the arrow, the column number is written on the arrow tip. For example, read from shaft to tip, if an arrow contained the digit 14 then there must be a 5 in r1c4. All the arrows must correspond to different coordinates. Digits may repeat on an arrow if allowed by other rules","solution":"796532841182674953453819276564197328271368594839425617615243789948756132327981465","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Coordinate Arrows: Digits on an arrow spell out the coordinates for the digit that is their sum. All the arrows must correspond to different coordinates.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5"]}]},{"id":"c1nrs6w6wq","ctcId":3063,"ctcDifficulty":"VERY HARD","title":"Mineswee-Pea-Er","author":"damo_89","rules":"Normal sudoku rules apply: Place the digits 1 to 9 once each in every row, column, and 3x3 box\n\nYin Yang: Shade the grid such that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2x2 area is entirely shaded or unshaded\n\nMinesweeper: Circles are unshaded, and count the number of shaded cells in the (up to 8) neighbouring cells\n\nSplit Pill Arrows (Split Peas): Digits along a green line sum to a concatenation of the two digits in the connected circles. For example 3_436_1 would be a valid fill as 436 sums to 13 which can be made from the connected 3 and 1.","solution":"185347962246985731739216458573168294824793516961524873657832149398471625412659387","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Minesweeper: Circles are unshaded, and count the number of shaded cells in the (up to 8) neighbouring cells Split Pill Arrows (Split Peas): Digits along a green line sum to a concatenation of the two digits in the connected circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"by6i2h7toi","ctcId":3064,"ctcDifficulty":"HARD","title":"Coordinate Coordinate Arrows Arrows","author":"damo_89","rules":"Normal sudoku rules apply: Place the digits 1 to 9 once each in every row, column, and 3x3 box\n\nDoublers: 9 cells in the grid are doublers, one in every row, column, and 3x3 box, each containing a different digit. The value of a doubler cell is double the digit in that cell\n\nCoordinate Arrows: Values on an arrow spell the coordinates for the value that is their sum. The row value is on the start of the arrow and the column value on the tip. For example if an arrow contained the values 15, then a 6 (or a doubled 3) is placed in R1C5. Each arrow indicates a different cell","solution":"216483795497651382853729164164978523379542618582136479725864931948317256631295847","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Doublers: 9 cells in the grid are doublers, one in every row, column, and 3x3 box, each containing a different digit. The value of a doubler cell is double the digit in that cell Coordinate Arrows: Values on an arrow spell the coordinates for the value that is their sum. The row value is on the start of the arrow and the column value on the tip. Each arrow indicates a different cell","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7"]}]},{"id":"zvfum6weab","ctcId":3065,"ctcDifficulty":"MEDIUM","title":"Twenty Six","author":"James Kopp","rules":"Normal sudoku rules apply.\nDigits inside the grid represent the heights of skyscrapers, and clues outside the grid indicate the number of skyscrapers visible in that row or column, looking in that direction.\nThe cell with a gray circle contains an odd digit.","solution":"172635849863914257954827631517342968498156723236789514681593472729461385345278196","constraints":["odd","skyscraper"],"constraintFacts":[{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"skyscraper","type":"skyscraper","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"yp4js8z1ck","ctcId":3066,"ctcDifficulty":"VERY HARD","title":"Budowa","author":"Alaric Taqi A. (Crusader175)","rules":"• Chaos Construction: Divide the grid into regions, each consisting of 9 orthogonally connected cells, such that every cell is part of exactly one region. Place the digits 1-9 exactly once in each row, column and region.\n• Kreska: Adjacent digits along a line must either be consecutive and belong to a different region or have a 1:2 ratio and belong to the same region. (Digits have a 1:2 ratio if one is double the other.) If 1 and 2 are adjacent along a line, they can satisfy either condition.","solution":"563842791845976312624317859351468927419285673937621584298754136786139245172593468","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Chaos Construction: Divide the grid into regions, each consisting of 9 orthogonally connected cells, such that every cell is part of exactly one region. Place the digits 1-9 exactly once in each row, column and region. • Kreska: Adjacent digits along a line must either be consecutive and belong to a different region or have a 1:2 ratio and belong to the same region. (Digits have a 1:2 ratio if one is double the other.) If 1 and 2 are adjacent along a line, they can satisfy either condition.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c2"]}]},{"id":"97b5wl5ii6","ctcId":3067,"ctcDifficulty":"MEDIUM","title":"Increasing Sum Line","author":"Florian Wortmann","rules":"Normal sudoku rules apply. \n\nThe 3x3 box borders divide the blue line into segments. Each segment’s total is found by summing the digits on that segment. The segment totals must increase from one end of the line to the other.","rulesClarified":"Normal sudoku rules apply.\n\nThe blue line is one path through the grid, from one end to the other.\n\nThe 3x3 box borders cut the blue line into segments. A segment is a run of consecutive line cells that lie in the same 3x3 box. When the line leaves a box and later enters it again, that is a new segment.\n\nEach segment's total is the sum of the digits on its cells.\n\nThe segment totals increase from one end of the line to the other. Each segment's total is larger than the total of the segment before it along the line.","solution":"724395168839612475561784392178256934246938751953471826382549617495167283617823549","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The segment totals must increase from one end of the line to the other.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"o6x08u2omv","ctcId":3068,"ctcDifficulty":"MEDIUM","title":"Bidirectional","author":"Kaktuslav","rules":"Normal sudoku rules apply. Digits along an arrow sum to the number in the attached bulb (the two-digit number is read left to right). Digits separated by the dot are not consecutive.","solution":"856732941739541826421968357682419573917325468543876219364297185278153694195684732","constraints":["arrow","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"kszsitwn8p","ctcId":3069,"ctcDifficulty":"MEDIUM","title":"Simon's Sigil","author":"Riffclown","rules":"• Normal Sudoku rules apply.\n• Thermo: Digits on grey thermos must increase from the bulb to the tip.\n• Modular Lines: Any set of three sequential cells along a line must contain a digit that is 1 mod 3 (147), and a digit that is 2 mod 3 (258). and a digit that is 0 mod 3 (369). Vertical columns on a keypad are a good reference.\n• All lines in this puzzle conform to both rulesets. In the case where thermos share a bulb the entire line is considered for the modular logic.","solution":"246751893173298456895463217961384572528917634437625189314576928659832741782149365","constraints":["modular-line","thermometer"],"constraintFacts":[{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"u10p16g8n5","ctcId":3070,"ctcDifficulty":"VERY HARD","title":"Build Your Own Hitlines","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nFrom each square, draw a valid hitline moving through the centres of cells. Each hitline must occupy at least two cells. Hitlines may travel orthogonally and diagonally between cells, but may not branch, share cells, or cross themselves or each other.\n\nDigits may not repeat on a hitline.\n\nThe small white clue on a square indicates the total sum of all the digits along that hitline that match their position number, with the square itself being position 1.\n\nEg: if a hitline reads 82195 then its square would have a 7 clue, as this is the sum of 2 and 5 which are the only two digits on the line which match their position number (they are in the 2nd position and 5th position.)","solution":"389267154624351897571489326912734568746518239853692741437126985195843672268975413","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"From each square, draw a valid hitline moving through the centres of cells. Each hitline must occupy at least two cells. Hitlines may travel orthogonally and diagonally between cells, but may not branch, share cells, or cross themselves or each other. Digits may not repeat on a hitline. The small white clue on a square indicates the total sum of all the digits along that hitline that match their position number, with the square itself being position 1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6"]}]},{"id":"swe3t7imco","ctcId":3071,"ctcDifficulty":"HARD","title":"Happy MMXXVI","author":"olima","rules":"Normal Sudoku rules apply. Purple lines contain a set of distinct consecutive digits in any order. Adjacent digits on a green line differ by at least 5. The gray line is a palindrome. No two cells sharing an edge contain digits summing to 5 or 10.","solution":"651297438892634517347518926184726359263159874579843162426381795718965243935472681","constraints":["custom","german-whispers","palindrome","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No two cells sharing an edge contain digits summing to 5 or 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ml7764ol17","ctcId":3072,"ctcDifficulty":"HARD","title":"Quality Street","author":"Jay Dyer","rules":"Normal sudoku rules apply. On either main diagonal (marked with a thin blue line), digits may not repeat. The 3x3 box borders divide thick blue lines into segments; each segment on a line has the same sum. Different lines may have different sums.","solution":"879634521561289734423715698634178952792453186158962347987526413346891275215347869","constraints":["diagonal","region-sum-line"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"2ofk8u9afe","ctcId":3073,"ctcDifficulty":"MEDIUM","title":"SVS #454 - Little Thermometers","author":"Richard","rules":"Apply classic sudoku rules.\nClues outside the grid indicate the presence of a thermometer that is fully placed in the direction of the arrow where all the digits on the thermometer add to the number of the clue and the bulb is always the closest to the clue. Digits on a thermometer are all different and strictly increasing from the bulb to the tip. Thermometers are mimimal three cells long and they include all possible digits. I.e.: the first digit behind the thermometer may not be larger than the last digit on the thermometer, and the last digit before a thermometer may not be smaller than the digit in the bulb.\nThermometers may overlap other thermometers.","solution":"835214697671398245924567813586472139792631584413859762359786421267143958148925376","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Clues outside the grid indicate the presence of a thermometer that is fully placed in the direction of the arrow where all the digits on the thermometer add to the number of the clue and the bulb is always the closest to the clue. Thermometers are mimimal three cells long and they include all possible digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"cbbvbid2vt","ctcId":3074,"ctcDifficulty":"VERY HARD","title":"Entropic Detour","author":"Myxo","rules":"Sudoku: Place the digits 1-9 exactly once in each row, column and box.\n\nDifference Pairs: Digits separated by a small white dot must be consecutive.\n\nLoop: Draw a closed loop into the grid that travels orthogonally between cells and doesn't visit the same cell more than once. The loop must not visit any big circles.\n\nEntropic Line: The loop acts as an entropic line, i.e. three adjacent digits along the loop must contain one digit from {1,2,3}, one digit from {4,5,6} and one digit from {7,8,9}.\n\nDetour: The number of loop turns is different in each box. A digit in a big circle indicates the number of times the loop turns in that box.","solution":"817953426965124873243678195378519642421786359659432718192367584786245931534891267","constraints":["custom","entropic-line","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Loop: Draw a closed loop into the grid that travels orthogonally between cells and doesn't visit the same cell more than once. The loop must not visit any big circles. Detour: The number of loop turns is different in each box. A digit in a big circle indicates the number of times the loop turns in that box.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c6","c7"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"bbcodg1b5w","ctcId":3075,"ctcDifficulty":"HARD","title":"RAT RUN 21: Friendly","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths may not share cells except for where they meet at the cupcake cell.\n\nAs well as moving orthogonally, Finkz and Phinx may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBLACKCURRANTS: If two digits are joined by a blackcurrant, one is double the other.\n\nGRAPES: If two digits are joined by a grape, they have a difference of at least 5.\n\nFORBIDDEN DOORS: If two digits are joined by a red X, they sum to 10. Finkz and Phinx may not pass directly through a red X.\n\nTEST CONSTRAINT: In this experiment, a cell may only be visited by Finkz or Phinx if its digit matches its row number, column number or box number. (Boxes are numbered 1-9 in normal reading order from top left to bottom right.)","solution":"129385647873416295465927318536879421718243569294561783647158932382794156951632874","constraints":["XV","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths may not share cells except for where they meet at the cupcake cell. As well as moving orthogonally, Finkz and Phinx may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. GRAPES: If two digits are joined by a grape, they have a difference of at least 5. Finkz and Phinx may not pass directly through a red X. TEST CONSTRAINT: In this experiment, a cell may only be visited by Finkz or Phinx if its digit matches its row number, column number or box number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7","c9","c10"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"ef10mw7nxl","ctcId":3076,"ctcDifficulty":"HARD","title":"Tuning the Thermostat","author":"FullDeck and Missing a Few Cards","rules":"**Sudoku, Thermometers, Skyscrapers**\n\n- Standard sudoku rules apply: The digits 1 through 9 appear in every row, column, and box.\n- Thermometers: Digits on thermometers are strictly increasing from bulb to tip.\n- Skyscrapers: Each cell represents a ‘skyscraper’ whose height is the digit in that cell. Taller skyscrapers obscure the view of smaller ones. Clues outside the grid tell how many skyscrapers are visible looking across the row or column from the direction of the clue.\n\nSubscribe to our mailing list to receive a weekly email with all of our puzzles from the past week: https://missingdeck.net/mailing.html","solution":"378419265659382147124567938416753892537928614892146573941875326283694751765231489","constraints":["skyscraper","thermometer"],"constraintFacts":[{"slug":"skyscraper","type":"skyscraper","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9ecadg11io","ctcId":3078,"ctcDifficulty":"MEDIUM","title":"Nala's Toy Battle","author":"Panthera","rules":"Wait? It seems like Nala gets to choose between  2 different toys today that are hidden in the fog of not 1, but 2 sudoku! Can you help her find them? And which one will she end up picking to play with? \n\nNormal sudoku rules apply. There is a red cage from r3-r9 and c3-c9 in which the Japanese sums colorings will take place. The clues are given in c1-2 and r1-2. Clues are colored pink, and if there is a cage there, the sum is known to be the small digit in the corner * 10 +  the value in the cage. So if a cage had a little 1 and a 4 was placed in it, the JSS clue would be 14. If there is no cage, you know there's a run of coloring, but not what it sums to. \n\nJapanese sums rules apply.\n\nThe clues inside the grid (r1-2 and c1-2) indicate the sums of the contiguous runs found in that row or column that must be shaded. There must be an unshaded cell between runs of the same color. If a row or column is unclued (no pink cells at all), there is no shading in that row or column.\n\nCells attached with a V sum to 5. Not all V's are given.\n\nIn addition the following ambiguity rules apply.\n\nThere are 4 colored dots in the grid: Green, Red, Blue and Yellow. They are ratio dots and may represent any ratio from 1:2, 1:3, 1:4, 1:5, 1:6, 1:7, 1:8, or 1:9. It's up to the solver to determine which dot is which type. \n\nThere are several pink lines in the picture. Those are either Renban OR they are German Whisper. Each line must be determined individually.\n\nCircle = Odd.\nAnd there is FOG","solution":"368425971974138265512697384123569847489371652756842139895713426631254798247986513","fogLight":"R2C5","constraints":["XV","custom","german-whispers","odd","renban","fog"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c15"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There is a red cage from r3-r9 and c3-c9 in which the Japanese sums colorings will take place. Clues are colored pink, and if there is a cage there, the sum is known to be the small digit in the corner * 10 +  the value in the cage. If there is no cage, you know there's a run of coloring, but not what it sums to. The clues inside the grid (r1-2 and c1-2) indicate the sums of the contiguous runs found in that row or column that must be shaded. There must be an unshaded cell between runs of the same color. If a row or column is unclued (no pink cells at all), there is no shading in that row or column. They are ratio dots and may represent any ratio from 1:2, 1:3, 1:4, 1:5, 1:6, 1:7, 1:8, or 1:9. Each line must be determined individually.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c8","c10","c12","c13","c14","c19","c23"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c22"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c24"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c22"]}]},{"id":"9ra2ew24s8","ctcId":3079,"ctcDifficulty":"MEDIUM","title":"2026 Killer","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nDigits may not repeat on the marked diagonal.\n\nDigits in a cage may not repeat and sum to the small number in the top left corner of the cage.","solution":"327951864195684372846723915659472138471538296283169547738216459962345781514897623","constraints":["cage","diagonal"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"t9hgy6k213","ctcId":3080,"ctcDifficulty":"MEDIUM","title":"Windmill","author":"Kaktuslav","rules":"Normal sudoku rules apply. The 3x3 box borders divide each of the 8 blue lines into segments with the same sum (this sum may be different for different lines).","solution":"647582319829731645351946287135629874982457163476318952263875491718294536594163728","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"lhid2td2zu","ctcId":3081,"ctcDifficulty":"VERY HARD","title":"Grid Racer","author":"Jonesy","rules":"Hello.\n\nStandard Sudoku rules apply.\n\nThe Racetrack (Loop):\nDraw a single closed loop representing the car’s path, viewed from above.\n\nThe car drives clockwise around the grid through cell centers and moves strictly orthogonally.\n\nThe path may touch itself orthogonally but must not cross or branch. Cages are obstacles which the car can never enter.\n\nDriving Inputs:\nThe digit in any cell the loop passes through determines the car’s movement:\n\nOdd digits (1,3,5,7,9): go straight.\n\nEven digits (2,4,6,8): turn, using absolute numpad directions: \n\n2 → Up \n4 → Left\n6 → Right\n8 → Down\n\nBox Balance:\nIn each 3×3 box, the sum of the odd digits on the loop equals the sum of the digits inside the cage(s) in that box. (multiple visits of the loop contribute to the same total.)\n\nThe loop must visit each region at least once !\nA region without a cage indicates the sum of odd digits  for that region is zero.\n\n\nHave fun.","solution":"942567813863921574715834926327415689458796132691283457586379241174652398239148765","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single closed loop representing the car’s path, viewed from above. The car drives clockwise around the grid through cell centers and moves strictly orthogonally. The path may touch itself orthogonally but must not cross or branch. Cages are obstacles which the car can never enter. Odd digits (1,3,5,7,9): go straight. Even digits (2,4,6,8): turn, using absolute numpad directions: In each 3×3 box, the sum of the odd digits on the loop equals the sum of the digits inside the cage(s) in that box. (multiple visits of the loop contribute to the same total.) The loop must visit each region at least once !","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6","c7","c10","c11","c17","c18"]}]},{"id":"m9qm0m5qj0","ctcId":3083,"ctcDifficulty":"VERY HARD","title":"RAT RUN 22: Copyrat","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, share cells, or pass through any thick maze walls. \n\nAs well as moving orthogonally, Finkz and Phinx may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nCOPYCAT CELLS: Find nine copycat cells in the maze; one in each row, column and 3x3 box, and each containing a different digit. The value of a copycat cell equals the digit in the cell that is 180° rotationally opposite it in the grid. Eg: if r1c3 is a 6 and r9c7 is a copycat cell, then r9c7 will have a value of 6, regardless of what digit it contains.\n\nBLACKCURRANTS: If two cells are joined by a blackcurrant then the value of one is double the value of the other.\n\nREDCURRANTS: If two cells are joined by a redcurrant then one has an even value and the other has an odd value.\n\nGRAPES: If two cells are joined by a grape then their values have a difference of at least 5.\n\nTEST CONSTRAINT: In this experiment, in any 3x3 box, the total value of the cells visited by Finkz is the same as the total value of the cells visited by Phinx. (This total must be determined for each box.)","solution":"961547283472983516538261794283415679197836425654729138849672351326158947715394862","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, share cells, or pass through any thick maze walls. As well as moving orthogonally, Finkz and Phinx may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. COPYCAT CELLS: Find nine copycat cells in the maze; one in each row, column and 3x3 box, and each containing a different digit. The value of a copycat cell equals the digit in the cell that is 180° rotationally opposite it in the grid. REDCURRANTS: If two cells are joined by a redcurrant then one has an even value and the other has an odd value. GRAPES: If two cells are joined by a grape then their values have a difference of at least 5. TEST CONSTRAINT: In this experiment, in any 3x3 box, the total value of the cells visited by Finkz is the same as the total value of the cells visited by Phinx.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c9","c10","c11"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"BLACKCURRANTS: If two cells are joined by a blackcurrant then the value of one is double the value of the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]}]},{"id":"v2ey7c3lac","ctcId":3084,"ctcDifficulty":"MEDIUM","title":"Gray circles in gray fog","author":"Lithium-Ion","rules":"Normal Sudoku rules apply. Placing correct digits may reveal fog somewhere in the grid. Cells that are a knight's move (in chess) apart, are not allowed to contain identical digits. Cells connected with a gray circle have to contain digits that are consecutive or in a 1:2 ratio (or both). Box borders divide blue lines into segments with the same sum. Different blue lines can have different sums.","rulesClarified":"Normal Sudoku rules apply.\n\nAny two cells that are a knight's move apart (as in chess) may not contain the same digit.\n\nA grey circle sits between two cells. The two digits in those cells must be consecutive (differ by 1), or one must be exactly double the other, or both. For example, 1 and 2 are both consecutive and in a 1:2 ratio.\n\nThe 3x3 box borders cut each blue line into segments. The digits in each segment of one blue line add up to the same sum. Different blue lines may have different sums.\n\nPlacing correct digits may reveal fog somewhere in the grid.","solution":"659821743348957126721643895576132984984576231132498657463219578897365412215784369","fogLight":"R2C2","constraints":["antiknight","fog","kropki","region-sum-line"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Cells connected with a gray circle have to contain digits that are consecutive or in a 1:2 ratio (or both).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"h2sdbmic8x","ctcId":3085,"ctcDifficulty":"HARD","title":"Mosaic","author":"zetamath and friends","rules":"Normal sudoku rules apply.  \n\nGW: Adjacent digits along a German Whispers line must differ by at least five.\n\nEnt: Any set of three adjacent cells along an Entropic line must contain a low digit (123), a middle digit (456), and a high digit (789).\n\nBlack Dot: If two digits are separated by a black dot then one digit is double the other. Not all Black dots are necessarily given.\n\nWhite Dot: Digits separated by a white dot are consecutive.  Not all White dots are necessarily given.\n\nTen Lines: Digits along grey lines must be broken into one or more contiguous groups of cells that add to ten. Such groups cannot overlap. Digits may repeat within such sums if allowed by other rules. For example, 513173 is a valid fill for a length 6 line, because it can be broken into 5131 and 73, each of which sum to 10.\n\nDW: Adjacent digits along a Dutch Whispers line must differ by at least four.\n\nPar: Digits along a Parity line alternate odd/even.\n\nNab: No two digits along a Nabner line can be consecutive, regardless of their position on the line.","solution":"617349285438725619925618743193257468754896132286431957862574391349182576571963824","constraints":["custom","dutch-whispers","entropic-line","german-whispers","kropki","nabner-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Ten Lines: Digits along grey lines must be broken into one or more contiguous groups of cells that add to ten. Par: Digits along a Parity line alternate odd/even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c8","c13"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"GW: Adjacent digits along a German Whispers line must differ by at least five.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c6"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]}]},{"id":"2hn8xg3p9b","ctcId":3086,"ctcDifficulty":"MEDIUM","title":"Carnival","author":"Math Pesto","rules":"Normal sudoku rules apply. Digits in a cage cannot repeat and must sum to the given total.","solution":"279346185635817924814925736347158269581692473926734518158269347793481652462573891","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qpd5keiva9","ctcId":3087,"ctcDifficulty":"HARD","title":"Equipoise","author":"James Kopp","rules":"Normal sudoku rules apply.\nDigits strictly increase along each thermometer starting from the bulb end. Additionally, the digits on each thermometer of the same colour sum to the same total. Green thermometers and blue thermometers may sum to different totals.","solution":"517492638829637451643815972786349125135268794492751863271586349358974216964123587","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Additionally, the digits on each thermometer of the same colour sum to the same total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"14uqnkivwz","ctcId":3088,"ctcDifficulty":"MEDIUM","title":"10 Million Views","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Along a main diagonal (marked in blue), digits may not repeat. Digits along an arrow sum to the digit in that arrow's circle. The green central 3x3 box forms a \"magic square\": each row, column and 3-cell main diagonal of this box must sum to the same total.","solution":"175428693694513278832796415319672854486159732257834961721985346563247189948361527","constraints":["arrow","custom","diagonal"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The green central 3x3 box forms a \"magic square\": each row, column and 3-cell main diagonal of this box must sum to the same total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"dd1oxg0w6b","ctcId":3092,"ctcDifficulty":"HARD","title":"Stretching","author":"Kaktuslav","rules":"Divide the grid into nine regions, each consisting of 9 orthogonally-connected cells. Regions cannot overlap. Place the digits 1–9 once each in every row, column, and region. In cells with arrows, the digit equals the number of cells in its own region (including itself) visible in the arrow directions; sight is blocked by region borders or the edge of the grid.","rulesClarified":"Divide the grid into nine regions, each made of nine orthogonally connected cells. Regions cannot overlap.\n\nPlace the digits 1 to 9 once each in every row, column and region.\n\nArrow cells: in a cell with arrows, the digit equals the number of cells in its own region that can be seen along the arrow directions, plus the cell itself.\n\nLook along each arrow from its cell. Sight stops at the grid edge and at a region border. A cell beyond a region border is not counted, and neither is any cell beyond a stop. Cells of other regions are never counted.\n\nWhen a cell has arrows in more than one direction, add the cells seen along each direction. The rays from one cell in different directions share no cells, so nothing is counted twice.","solution":"624135789139726854245879361961384572357418296872641935713592648486957123598263417","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into nine regions, each consisting of 9 orthogonally-connected cells. In cells with arrows, the digit equals the number of cells in its own region (including itself) visible in the arrow directions; sight is blocked by region borders or the edge of the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c4"]}]},{"id":"k18i652bjj","ctcId":3093,"ctcDifficulty":"HARD","title":"Within and without","author":"Merdock","rules":"Normal Sudoku Rules: The digits 1-9 appear in every row, column, and box\n\nBetween Lines: Digits on a thin grey line must be between the digits in the circles\n\nLocked-out Lines: Digits on a thick blue line must NOT be between the digits in the diamonds. Digits in the diamonds must differ by at least 4.\n\nDisjoint Groups: Cells with the same position in the boxes contains number from 1 to 9 i.e no number can repeat in the same position in the boxes.\n\nBlack Kropki Dots: black dots sitting between two digits indicate that the two digits have a ratio of 2:1\n\nWhite Kropki Dots: White Dots sitting between two digits indicate that the two digits are consecutive \n\nNot all dots are given","solution":"278694153413257698596813427387425916162379845945168372831542769724936581659781234","constraints":["between-line","disjoint-groups","kropki","lockout-line"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7"]},{"slug":"lockout-line","type":"lockout-line","variant":"modified","modifiers":[],"params":null,"note":"Locked-out Lines: Digits on a thick blue line must NOT be between the digits in the diamonds. Digits in the diamonds must differ by at least 4.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3","c4"]}]},{"id":"9sxe7q81rb","ctcId":3094,"ctcDifficulty":"HARD","title":"Factoring in the Difference","author":"Merdock","rules":"Normal Sudoku Rules: Place the numbers 1-9 in every row column, and box\n\nPositive & Negative Diagonal Lines: Place the digits 1-9 on both the main positive and negative Diagonals (The thin red lines that go from r1c1 to r9c9 and r9c1 to r1c9). Digits can not repeat on their respective diagonals. \n\nRegion Sum Line: Box borders divide each blue line into segments with the same sum. \n\nWhite Kropki Dots: White dots placed between two cells indicate the digits in those cells are consecutive (no negative constraint\n\nKiller cages: Digits in cages must sum to the number in the upper left corner of the cage. No guessing is required to determine the value of x (x can not be a negative number as that would require the ability to insert negative digits, which you can not)\n\nSome of the killer cage numbers are difficult to read, so below is a key you can reference that shows the killer cages number as well as the row and column numbers:\n\nr1c5: x+3\nr1c6: 5x\nr4c1: 3x\nr5c1: x²-3\nr5c5: x\nr5c8: 2x-1\nr6c7: x²+6\nr7c4: x+5\nr7c5: x²+x","solution":"587413629432569718169872534291756843673948152845321967958634271326197485714285396","constraints":["cage","diagonal","kropki","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"l9mam4ijsg","ctcId":3095,"ctcDifficulty":"VERY HARD","title":"Artemis ","author":"Merdock","rules":"Normal Sudoku Rules\nPlace the digits 1-9 in every row, column, and box. \n\nRegion Sum Line: \nBox borders divide each thin blue line into segments with the same sum.\n\nRenban Line: \nDigits placed on the thick magenta Renban Line must be a set of consecutive, non-repeating digits, in any order.\n\nAnti-Knight: \nDigits cannot repeat a (chess) knights’s move away from each other\n\nBlack Kropki Dots:\nBlack dots separate pairs of digits that have a ratio of 2:1. \n\nNot all dots are given","solution":"724369581583127964961584732612958473379412856458673219246835197837291645195746328","constraints":["antiknight","kropki","region-sum-line","renban"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"r3n9cwda1t","ctcId":3096,"ctcDifficulty":"MEDIUM","title":"Rip City","author":"Merdock","rules":"Normal Sudoku Rules: The digits 1-9 appear once each in each column, row, and box\n\nParity Line: Adjacent digits on the red line alternate between even and odd digits\n\nWhite Kropki Dots: White dots separate consecutive digits that are adjacent to each other along the red line. All dots are given. If two cells both have a red line, but the cells are not adjacent along the path of the line, no dot will be given even if the digits are consecutive. For example, r2c6 and r2c7 both have a red line passing through them, but because the line does not travel immediately from r2c6 to r2c7, the lack of a dot does not mean anything.\n\nKiller Cages: There are four single cell cages at the corner of the grid. These individual cages act as a single combined cage. The 4 digits must sum to 16\n\nNegative Diagonal: digits can not repeat on the marked digital diagonal","solution":"413296587972385416586174329651943278749852163238761954127639845894527631365418792","constraints":["cage","custom","diagonal","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The four single-cell cages in the corners count as one cage: their four digits together sum to 16.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Parity Line: Adjacent digits on the red line alternate between even and odd digits","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"All dots are given.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3","c4"]}]},{"id":"753umuwjuz","ctcId":3097,"ctcDifficulty":"VERY HARD","title":"Method to the Madness","author":"Merdock","rules":"Normal Sudoku Rules:\nPlace the digits 1 through 9 in every row, column, and box.\n\nXV:\nDigits separated by an X sum to 10, digits separated by a V sum to 5. Not all X's and V's given\n\nHowling Mad Lines: Purple Lines indicate a sequence of digits where no other standard* line type could go\n\nFor this puzzle, Howling Mad lines are always three cells long and are always either strictly vertical or strictly horizontal. Additionally lines cannot overlap each other. No sets of digits appear on more than one line. For example, if one line contains 1, 2, and 4, no other line can contain all three of those digits.\n\nGiven those rules, all lines are given. If a set of digits appear like they would form a line, but don't they violate an expressed rule. They are longer than three cells, they are not strictly vertical or horizontal, the set of digits already appear on another line, placing a line over the digits would cause them to overlap, or the digits are ordered in a way that prevents a line.\n\nDynamic fog: fog clears when specific cells are populated by correct digits. \n\n*The following are types of line that cannot replace a Howling Mad Line are relevant to this puzzle\n\nRenban: Consecutive non-repeating digits\n\nNabner: Non-consecutive non-repeating digits\n\nParity: Alternating even/odd\n\nEntropy: Every 3 digits has a [1,2,3], [4,5,6], and [7,8,9] digit\n\nModular: Every 3 digits has a [1,4,7], [2,5,8], and [3,6,9] digit\n\nDutch Whisper: Adjacent digits differ by at least 4\n\nRegion Sum: Box borders divide lines into segments with the same sum.","solution":"425671893189253764376894215951726348864315972237948651598162437643587129712439586","fogLight":"R7C7,R8C7,R9C7,R9C8,R9C9,R8C9,R7C9,R7C8,R8C8","constraints":["XV","custom","dutch-whispers","entropic-line","fog","modular-line","nabner-line","region-sum-line","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Howling Mad Lines: Purple Lines indicate a sequence of digits where no other standard* line type could go For this puzzle, Howling Mad lines are always three cells long and are always either strictly vertical or strictly horizontal. Additionally lines cannot overlap each other. No sets of digits appear on more than one line. Given those rules, all lines are given. Parity: Alternating even/odd","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7","c8","c9","c11","c18"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c21"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c19"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c20"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c17"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c22"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c16"]}]},{"id":"3pev731294","ctcId":3099,"ctcDifficulty":"VERY HARD","title":"RAT RUN 23: Notable Differences","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT:\nFinkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths may not share cells except where they meet at the cupcake cell.\n\nAs well as moving orthogonally, Finkz and Phinx may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBLACKCURRANTS: If two digits are joined by a blackcurrant then one is double the other.\n\nREDCURRANTS: If two digits are joined by a redcurrant then one is even and the other is odd.\n\nGRAPES: If two digits are joined by a grape then they have a difference of at least 5.\n\nTEST CONSTRAINT:\nIn this experiment, Finkz and Phinx both visit the same number of cells. Before reaching the cupcake, the Nth digit visited by Finkz and the Nth digit visited by Phinx always have the same difference (to be deduced.) This difference equals the digit on the cupcake cell.\n\nEg: if the 3rd digit visited by Finkz is 5 and the 3rd digit visited by Phinx is 9, the cupcake cell would contain a 4.","solution":"317294586682537149549618723825143967961782354734965218193856472258479631476321895","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths may not share cells except where they meet at the cupcake cell. As well as moving orthogonally, Finkz and Phinx may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. REDCURRANTS: If two digits are joined by a redcurrant then one is even and the other is odd. GRAPES: If two digits are joined by a grape then they have a difference of at least 5. In this experiment, Finkz and Phinx both visit the same number of cells. Before reaching the cupcake, the Nth digit visited by Finkz and the Nth digit visited by Phinx always have the same difference (to be deduced.) This difference equals the digit on the cupcake cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c6","c8","c9","c11","c12","c13"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"akgkajm6cv","ctcId":3100,"ctcDifficulty":"VERY HARD","title":"Cornered in the 9’s","author":"Panthera","rules":"Normal Sudoku rules apply. Digits in killer cages do not repeat and sum to the digit in the top left corner","solution":"216498735359761842784523691631984527842357169975216384498135276167842953523679418","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9lceh4k7v3","ctcId":3101,"ctcDifficulty":"HARD","title":"quadcopter","author":"arctan","rules":"normal sudoku rules apply.\n\ndigits may not repeat along either diagonal.\n\ndigits along an arrow sum up to the digit in the arrow's circle.\n\nif two digits are adjacent on a black line, then one digit is double the other.\n\nif two digits are adjacent on a magenta line, then they are consecutive. \n\nthe grid is covered in fog; placing correct digits will clear the fog in that cell, and may also clear fog in other cells. no guessing is necessary to solve the puzzle.","solution":"615283749792541368843976125437158692186729453259364871924837516371695284568412937","fogLight":"R3C2,R3C3,R2C3,R2C7,R3C7,R3C8,R7C2,R7C3,R8C3,R5C5,R8C7,R7C7,R7C8","constraints":["arrow","custom","diagonal","fog"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"if two digits are adjacent on a black line, then one digit is double the other. if two digits are adjacent on a magenta line, then they are consecutive.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"1qkwdlzd2p","ctcId":3102,"ctcDifficulty":"MEDIUM","title":"Broken Windmill","author":"Aron Lidé (Aspartagcus)","rules":"Sudoku: Fill each row, column and region with the digits 1-9.\nArrows: Digits on an arrow sum to the digit in the circle of that arrow.\nDouble arrows: Digits on a line sum to the sum of the two circles at the end of the line.\nAll double arrow lines are straight.","rulesClarified":"Normal sudoku rules apply: the digits 1 to 9 appear once each in every row, column and region.\n\nArrows: each arrow starts at a circle. Digits on an arrow sum to the digit in the circle of that arrow.\n\nDouble arrows: a double arrow is a line with a circle at each end. Digits on a line sum to the sum of the two circles at the end of the line.\n\nAll double arrow lines are straight.","solution":"159764832286193475743825169815372946492516387637948521961437258574281693328659714","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Double arrows: Digits on a line sum to the sum of the two circles at the end of the line. All double arrow lines are straight.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"yeb6vd8pem","ctcId":3103,"ctcDifficulty":"HARD","title":"Sunblock","author":"Kaktuslav","rules":"Chaos Construction: Divide the grid into nine regions, each consisting of nine orthogonally connected cells. Regions do not overlap. Place the digits 1–9 once each in every row, column, and region. Suns: The digit in a sun counts how many of the up to nine cells in the 3×3 square centered on that sun belong to the same region as the sun (including the sun cell itself). Example: If R4C1 = 3, then exactly three of the cells R3C1, R3C2, R4C1, R4C2, R5C1, and R5C2 belong to the same region as R4C1.","solution":"679214358458726913936458721581673294124897536345982167267135849792341685813569472","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Chaos Construction: Divide the grid into nine regions, each consisting of nine orthogonally connected cells. Suns: The digit in a sun counts how many of the up to nine cells in the 3×3 square centered on that sun belong to the same region as the sun (including the sun cell itself).","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c4"]}]},{"id":"xclqgh5tsm","ctcId":3107,"ctcDifficulty":"MEDIUM","title":"X-ist","author":"Riffclown","rules":"• Normal Sudoku rules apply. Place the digits 1-9 in each row, column and box without repetition.\n• Digits may not repeat along the marked diagonals.\n• German Whispers: Adjacent digits on a line must have a difference of at least 5.\n• Nabner: No two digits on a line can be consecutive, regardless of their position on the line. Digits may not repeat ona line.\n• All lines are both German Whisper and Nabner","solution":"294817536163954278587236149346172985825693714971548362758369421639421857412785693","constraints":["diagonal","german-whispers","nabner-line"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"1b3iaeit8s","ctcId":3108,"ctcDifficulty":"HARD","title":"RAT RUN 24: Between You and Me","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths must only converge at the cupcake cell.\n\nAs well as moving orthogonally, Finkz and Phinx may move diagonally if there's a 2x2 space in which to do so, but they may never pass diagonally through a round wall-spot on the corner of a cell.\n\nCAGES: Digits may not repeat within a cage. All cages have the same total, to be deduced. An electricity symbol indicates the cage's shock value. Cages with a shock value of 5 or higher may not be entered. Cages with a shock value lower than 5 are safe to enter.\n\nFORBIDDEN DOORS: If a red X sits between two digits, they sum to 10.\n\nTEST CONSTRAINT: In this experiment, both paths must be a valid 'between line', ie: the highest and lowest digits on a path can be found at its ends (on the rat and the cupcake cell, in some order) and not anywhere else along that path.","solution":"612453897957812436483976512576138249348269751129745683294681375831527964765394128","constraints":["XV","between-line","cage","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths must only converge at the cupcake cell. As well as moving orthogonally, Finkz and Phinx may move diagonally if there's a 2x2 space in which to do so, but they may never pass diagonally through a round wall-spot on the corner of a cell. All cages have the same total, to be deduced. An electricity symbol indicates the cage's shock value. Cages with a shock value of 5 or higher may not be entered. Cages with a shock value lower than 5 are safe to enter.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7","c8","c9","c10"]}]},{"id":"420s9bg0dc","ctcId":3109,"ctcDifficulty":"HARD","title":"Numbered Rooms Sudoku","author":"JonaS2010","rules":"Normal sudoku rules apply. A clue's digit must appear in the Nth position looking into the grid in the row/column, where N is the digit in the first position.","solution":"754216983193478562826395174312564897645789231987132645261947358438651729579823416","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A clue's digit must appear in the Nth position looking into the grid in the row/column, where N is the digit in the first position.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"e8vw82a7x0","ctcId":3110,"ctcDifficulty":"HARD","title":"Whispers In The Shadows","author":"Scruffamudda","rules":"Normal sudoku rules apply.\nYin-Yang: Shade some cells such that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected and no 2x2 square is completely shaded or unshaded. Every dot must touch a shaded cell.\nGerman Whispers: Adjacent digits within the shaded region must differ by at least 5.\nKropki Pairs: Digits joined by a black dot are in a 2:1 ratio. Digits joined by a white dot are consecutive.","solution":"249381576573496182618275934356748291927153648481629753734562819192837465865914327","constraints":["custom","german-whispers","kropki","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every dot must touch a shaded cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"sotpbtg8o1","ctcId":3111,"ctcDifficulty":"HARD","title":"Cookie Crime Part 1: Hide And Sneak","author":"Sandra & Nala","rules":"The bag of treats is empty and Nala has put on her guilty face. The bag had way too many of her chicken flavoured bones left for her to have eaten them all, so chances are that she left some for later. But where? There seem to be some clues that might be useful for re-creating Nala’s creative backyard mapping and narrowing down the regions where she might have attempted to hide things. It’s worth a try! \n\nDynamic fog: The grid is partially covered in fog. Placing correct digits might clear some fog from its surrounding cells, possibly revealing more clues. Sometimes extra cells can be revealed as well.\n\nChaos Construction: Each row, column, and region contains the digits 1-9 exactly once each. A region is an orthogonally connected collection of cells. The shape and position of the regions have to be determined with the help of the following clues:\n\nCircles: There are 9 blue circles (with thicker outline) in the grid. Each blue circle belongs to a different region. \nAdditionally there are black circles (with thinner outline). These can be in any region and a region can have more than 1 black circle.\n\nThe digit in a circle (blue as well as black) counts the number of cells that the circle sees from its own region in the row and column up to the first border including itself. \n\nSmall magenta arrows count the number of region borders seen in the direction of the small arrow. If a cell has more than arrow, they see the same amount of borders in all pointed directions (not the sum of borders). The outer edges of the grid do not count as borders.\n\nDigits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. Not all possible dots are given. (There is no negative constraint.)","solution":"325467891248531967416792538653814279961378425897125346789246153172953684534689712","fogLight":"R1C3,R1C2,R1C1,R4C1","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Chaos Construction: Each row, column, and region contains the digits 1-9 exactly once each. Each blue circle belongs to a different region. The digit in a circle (blue as well as black) counts the number of cells that the circle sees from its own region in the row and column up to the first border including itself. Small magenta arrows count the number of region borders seen in the direction of the small arrow.","evidence":"rules","lessonPolicy":"open","sectionIds":["c9","c13","c16","c17"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c20","c21"]}]},{"id":"mjek1gdfcg","ctcId":3112,"ctcDifficulty":"MEDIUM","title":"Field of View","author":"Matt Tressel","rules":"Normal sudoku rules apply.\n\nMagnets: A digit in a magnet cell (M) is the sum of all digits seen in the indicated direction up to the first cell seen that contains a digit larger than M.","solution":"453276189681349752279815643934182576815697324726453918568921437192734865347568291","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Magnets: A digit in a magnet cell (M) is the sum of all digits seen in the indicated direction up to the first cell seen that contains a digit larger than M.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"8ui7lv2d7j","ctcId":3113,"ctcDifficulty":"MEDIUM","title":"The Greatest Line","author":"Dorlir","rules":"Normal sudoku rules apply. On each line, there is exactly one cell whose value is greater than the sum of any other two cells on that line.","solution":"943216758256748913187539264418392576325687149769451382574823691631974825892165437","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On each line, there is exactly one cell whose value is greater than the sum of any other two cells on that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"0g7nns4iny","ctcId":3114,"ctcDifficulty":"HARD","title":"Skewed Boxes","author":"Aad van de Wetering","rules":"Place the digits 1 to 9, once each in every row, column and region. Note that isolated cells (like r1c1) are part of the region of the same colour on the other side of the grid). Digits cannot repeat within a bold outlined region. Cells separated in the grid by a single knight's move (in chess) cannot contain the same digit. No domino in the grid can contain consecutive digits.","solution":"648271539963824157716392485271539648824157963392485716539648271157963824485716392","constraints":["antiknight","non-consecutive","region"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"jcdh680q0f","ctcId":3115,"ctcDifficulty":"MEDIUM","title":"Forcing","author":"Kaktuslav","rules":"Divide the grid into nine non-overlapping regions, each consisting of nine orthogonally connected cells. Place the digits 1–9 once each in every row, column, and region. In each region, place a circle in the leftmost cell of its topmost row. Every circled digit counts how many cells of its own region (including itself) are visible in its column (region borders block the view). The nine circled cells together form an extra region, i.e. they are orthogonally connected and contain the digits 1–9 once each.","rulesClarified":"Divide the grid into nine non-overlapping regions, each made of nine orthogonally connected cells.\n\nPlace the digits 1 to 9 once each in every row, column and region.\n\nIn each region, the leftmost cell of its topmost row has a circle.\n\nA circled digit counts the cells of its own region that it can see in its column, including its own cell. Look down the column from the circle. The view stops at a region border, so only cells of the circle's region reached before the first border are counted. Cells above the circle are never in its region, so only the cells below matter.\n\nThe nine circled cells together form an extra region. They are orthogonally connected to each other and hold the digits 1 to 9 once each.","solution":"918765432187654329876543291765432918654329187543291876432918765329187654291876543","constraints":["custom","region"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into nine non-overlapping regions, each consisting of nine orthogonally connected cells. In each region, place a circle in the leftmost cell of its topmost row. Every circled digit counts how many cells of its own region (including itself) are visible in its column (region borders block the view).","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c3","c4"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"daypits38m","ctcId":3116,"ctcDifficulty":"VERY HARD","title":"Ça fait la rue Michel","author":"Patrick Junke","rules":"Normal Sudoku rules apply.\n\nThe grid hides a labyrinth: a single continuous region of orthogonally connected cells.\nA 2×2 block may never consist entirely of labyrinth cells.\nThere are no dead ends in the labyrinth (every labyrinth cell is connected to at least two other labyrinth cells).\n\nAll remaining cells are walls.\nWalls form isolated groups of exactly four orthogonally connected cells. “Isolated” means that wall cells from different groups cannot touch each other, not even diagonally. Digits within a group of walls do not repeat and sum to 14.\n\nAn X between two cells indicates that their digits sum to 10. ALL Xs ARE GIVEN.\n\nAn X is always framed when it lies between two cells of the same type: either labyrinth cells or wall cells.","solution":"534987216219634875876125439941856723753249168628713954362491587485372691197568342","constraints":["XV","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c9","c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The grid hides a labyrinth: a single continuous region of orthogonally connected cells. A 2×2 block may never consist entirely of labyrinth cells. There are no dead ends in the labyrinth (every labyrinth cell is connected to at least two other labyrinth cells). Walls form isolated groups of exactly four orthogonally connected cells. Digits within a group of walls do not repeat and sum to 14. An X is always framed when it lies between two cells of the same type: either labyrinth cells or wall cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c6","c8","c11"]}]},{"id":"69x5obq89n","ctcId":3117,"ctcDifficulty":"MEDIUM","title":"Big Zs","author":"James Kopp","rules":"Normal sudoku rules apply.\nPlacing a correct digit may clear fog somewhere in the grid.\nThe digits along an arrow sum to a two digit number (reading left-to-right) in that arrow's oval.\nCells separated by an X sum to ten and cells separated by a V sum to five. Not all possible Xs and Vs are necessarily given.","solution":"289751346176394582534628197967532814451987623328146759695413278843275961712869435","fogLight":"R3C8,R4C8,R5C8,R5C9,R4C9,R3C9,R5C7,R4C7,R3C7","constraints":["XV","arrow","fog"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"z3tyv4nda6","ctcId":3118,"ctcDifficulty":"HARD","title":"RAT RUN 25: Mod Cons","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, share cells, cross themselves or each other, or pass through any thick maze walls. \n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBLACKCURRANTS: If a blackcurrant sits between two digits then one is double the other.\n\nONE-WAY DOORS: Finkz and Phinx may only pass directly through a purple arrow if moving in the direction the arrow is pointing. An arrow always points to the smaller of the two digits it sits between.\n\nMOTION SENSORS: The digit on a pink motion sensor indicates the number of cells that are visited within the (up to 9) cells immediately surrounding the sensor. The sensor itself is counted, if visited.\n\nVIDEO CAMERAS: The digit on a grey camera indicates the total SUM of the digits in any visited cells that the camera's lens points towards (before a wall is reached, which blocks vision.)\n\nTEST CONSTRAINT: In this experiment, both paths are valid 'modular lines'. Any set of 3 successive cells along a path contain one digit from each of the groups [1,4,7], [2,5,8] and [3,6,9].","solution":"487563129659712834213849756136425987795681243824937615372194568561378492948256371","constraints":["custom","inequality","kropki","modular-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, share cells, cross themselves or each other, or pass through any thick maze walls. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. ONE-WAY DOORS: Finkz and Phinx may only pass directly through a purple arrow if moving in the direction the arrow is pointing. MOTION SENSORS: The digit on a pink motion sensor indicates the number of cells that are visited within the (up to 9) cells immediately surrounding the sensor. VIDEO CAMERAS: The digit on a grey camera indicates the total SUM of the digits in any visited cells that the camera's lens points towards (before a wall is reached, which blocks vision.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c6","c8","c10"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]}]},{"id":"xl1dhvvzjt","ctcId":3119,"ctcDifficulty":"MEDIUM","title":"2026","author":"Lizzy01","rules":"Normal sudoku rules apply.\nRed (circled) clues are sandwiches, i.e. they indicate the sum of the digits between the 1 and the 9 in the corresponding row or column.\nBlue clues are X-sums, i.e. they indicate the sum of the first X digits in the corresponding row or column, where X is the digit in the first cell.","solution":"913247856852163479764598213579481632138726945246359781397614528485932167621875394","constraints":["sandwich","x-sum"],"constraintFacts":[{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"czl46gmq8l","ctcId":3121,"ctcDifficulty":"MEDIUM","title":"Episode 16- whisper- The lonely X","author":"Chip Sounder","rules":"Normal sudoku rules apply. Place the digits 1-9 once each in every row, column and 3x3 box.\nAdjacent digits along a green line must differ by at least 5.\nCells separated by an X sum to 10. \nNot all Xs are given.","solution":"452681973961743258738259614687314529124597836593826147245978361876135492319462785","constraints":["XV","german-whispers"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"pbe8o0wy1e","ctcId":3122,"ctcDifficulty":"HARD","title":"Split Ends","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nEach horizontal blonde line sums to a 2 digit number. These two digits are at the start and end of its row, in some order.\n\nEach vertical brunette line also sums to a 2 digit number. These two digits are at the top and bottom of its column, in some order.","solution":"973246158681593742452781693845639271169872435327415986718364529536927814294158367","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each horizontal blonde line sums to a 2 digit number. These two digits are at the start and end of its row, in some order. Each vertical brunette line also sums to a 2 digit number. These two digits are at the top and bottom of its column, in some order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]}]},{"id":"c5jnbcdxf1","ctcId":3123,"ctcDifficulty":"MEDIUM","title":"Hearts and Flowers","author":"James Kopp","rules":"Normal sudoku rules apply.\nOrthogonally adjacent cells do not sum to 5 or 10.\nAdjacent digits along a green line have a difference of at least five.\nCells separated by a flower sum to 13. Not all possible flowers are necessarily given.","solution":"813529476625347981749681253178935624394862715562174839936718542481256397257493168","constraints":["XV","german-whispers"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"Cells separated by a flower sum to 13.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2","c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"f75ku3v4p7","ctcId":3124,"ctcDifficulty":"HARD","title":"Caves can hide secrets","author":"cornishjohn","rules":"Normal sudoku and arrow rules apply.\n\nSudoku: Fill the grid with the digits 1-9 with no repeats in rows, columns and boxes.\nArrows: Digits in a circle sum to the value of the digits on the attached arrow.\n\nCave: Shade some cells in the grid such that they form an orthogonally connected area. All unshaded cells must be part of an orthogonally connected group that contains all the digits 1 to N exactly once, where N is the size of that group. All groups must be connected to the outside of the grid. All circles (including arrow bulbs) are unshaded.","solution":"431876952697253184852941673543182769716539248928764315169428537374695821285317496","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cave: Shade some cells in the grid such that they form an orthogonally connected area. All unshaded cells must be part of an orthogonally connected group that contains all the digits 1 to N exactly once, where N is the size of that group. All groups must be connected to the outside of the grid. All circles (including arrow bulbs) are unshaded.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6","c7"]}]},{"id":"za3z46tyiu","ctcId":3125,"ctcDifficulty":"MEDIUM","title":"More Powerful Than Hate","author":"FullDeck and Missing a Few Cards","rules":"**Sudoku, Entropic Line, Renban, Parity Line, Consecutive Pairs**\n\n- Standard sudoku rules apply: The digits 1 through 9 appear in every row, column, and box.\n- Entropic Line: Any set of three adjacent cells along an entropic line must contain a low digit (123), a middle digit (456), and a high digit (789). The outer heart in this puzzle is an Entropic Line.\n- Renban line: Digits along a Renban line must form a set of non-repeating consecutive digits in some order. The middle heart in this puzzle is made up of two Renban lines.\n- Parity line: Digits along a parity line alternate odd/even. The inner heart in this puzzle is a parity line.\n- Consecutive Pairs: Digits in cells separated by a white dot are consecutive.\n\nFor more of our puzzles, please visit https://missingdeck.net or join our mailing list to get a weekly digest of puzzles: missingdeck.net/mailing","solution":"281493567375682491496175283147268359938754612652319748513826974764931825829547136","constraints":["custom","entropic-line","kropki","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Parity line: Digits along a parity line alternate odd/even. The inner heart in this puzzle is a parity line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"if8eo8da5h","ctcId":3126,"ctcDifficulty":"HARD","title":"Guided Sums","author":"Dorlir","rules":"Normal sudoku rules apply. A digit N on a cell with an arrow indicates that there is a straight line N cells long starting from the cell the arrow clue is on and extending in the direction of that arrow. This line acts as a region sum line: box borders divide the line into segments with the same sum. Each line must cross at least one box border.","solution":"193258764875164239426937815219746583584312697637895142741583926358629471962471358","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit N on a cell with an arrow indicates that there is a straight line N cells long starting from the cell the arrow clue is on and extending in the direction of that arrow. Each line must cross at least one box border.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"bg5cxr23it","ctcId":3127,"ctcDifficulty":"MEDIUM","title":"Cookie Crime Part 2: Connecting Clues","author":"Sandra & Nala","rules":"Nala tries to find a connection between the clues left by the cookie thief. She takes careful steps around what she believes are important clues. Whenever she finds something, she tries to connect it and get closer to solving the mystery. This is very important because she does not want any more of her treasured foods to disappear!\n\nNormal Sudoku rules apply: Place the digits 1-9 in every row, column and box exactly once each. \n\nAdditionally the grid is partially covered in fog. Placing correct digits will clear at least some of the fog from surrounding cells, possibly revealing more clues. Some dynamic fog elements might prevent all (up to) 8 cells from being revealed at once.\n\nAll given lines in this puzzle are German whisper lines. Digits along a line must have a difference of at least 5. Each line has its own color. Elements of the same color are connected.\n\nAdditionally you have to build your own between lines by matching clues (footprints to footprints, cookie crumbles to cookie crumbles etc). The clues act as the circled endpoints of a between line. All such lines must be connected by choosing the shortest possible orthogonally connected path that does not share any cells with any other line, including the German whisper lines. Digits along a between line must be between the digits on the circled ends of the line.\n\nDigits in a dashed cage must sum to the value in the top left corner of the cage. Digits may not repeat within their own cage. \n\nDigits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. Not all possible dots are given. (There is no negative constraint.)","solution":"251948376483726195679135842318457629542693718967812534125384967896271453734569281","fogLight":"R1C8,R2C8,R1C5,R1C4,R4C8,R4C9","constraints":["between-line","cage","custom","fog","german-whispers","kropki"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c16"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c17"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Additionally you have to build your own between lines by matching clues (footprints to footprints, cookie crumbles to cookie crumbles etc). All such lines must be connected by choosing the shortest possible orthogonally connected path that does not share any cells with any other line, including the German whisper lines.","evidence":"rules","lessonPolicy":"open","sectionIds":["c13","c15"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c19","c20"]}]},{"id":"k4zgmts5h9","ctcId":3128,"ctcDifficulty":"HARD","title":"RAT RUN: Hit and Miss","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths may not share cells except where they meet at the cupcake cell.\n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBLACKCURRANTS: If two digits are separated by a blackcurrant, one is double the other.\n\nGRAPES: If two digits are separated by a grape, they have a difference of at least 5.\n\nTEST CONSTRAINT: In this experiment, 3x3 box borders divide both rats' paths up into segments.\n\nNot all blue hexagonal platforms need to be visited, but any blue platform that does gets stepped on becomes a 'hit counter'; its digit will indicate exactly how many digits along its path segment match their position number (the first cell visited along a segment is 'position 1'.)\n\nEg: If Finkz visits the digits 97325 (in that order) along a segment, then the 2 would be on its blue hit counter, because two digits match their position number; 3 is visited 3rd and 5 is visited 5th.","solution":"769852143243791685158643297914386572526974831387215469831567924492138756675429318","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths may not share cells except where they meet at the cupcake cell. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. GRAPES: If two digits are separated by a grape, they have a difference of at least 5. TEST CONSTRAINT: In this experiment, 3x3 box borders divide both rats' paths up into segments. Not all blue hexagonal platforms need to be visited, but any blue platform that does gets stepped on becomes a 'hit counter'; its digit will indicate exactly how many digits along its path segment match their position number (the first cell visited along a segment is 'position 1'.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7","c8","c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"1jiqahq6q7","ctcId":3129,"ctcDifficulty":"HARD","title":"G4G16","author":"olima","rules":"Normal sudoku rules apply: Place the digits 1 to 9 once each in every row, column and box.\nGerman Whisper: Adjacent digits on a green line differ by at least 5.\nRenban: Digits on a purple line are a set of distinct consecutive digits in any order.\nRatio dots: A black dot indicates a domino of cells with one digit being double the other. Not all dots are necessarily shown.","solution":"276345198183976542594281763327164859861592374459738216742653981635819427918427635","constraints":["german-whispers","kropki","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"329yqbkq53","ctcId":3130,"ctcDifficulty":"MEDIUM","title":"Schubladen","author":"Myxo","rules":"Sudoku: Place the digits 1-9 exactly once in each row, column and box.\n\nDiagonals: Digits must not repeat along either of the main diagonals.\n\nThermometer: Along a grey thermometer, digits strictly increase, reading from the bulb end.","solution":"134276859792538614685194732869415327573962148241387596918643275326759481457821963","constraints":["diagonal","thermometer"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"m2nrLqqt6m","ctcId":3132,"ctcDifficulty":"HARD","title":"Drawers and Pearls","author":"Mile Lemaic","rules":"Normal sudoku rules apply. Digits do not repeat on a marked diagonal. Along a thermometer, digits must increase from the bulb.","solution":"896452317234167895715389246451928673672513984389674521123846759947235168568791432","constraints":["diagonal","thermometer"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"ays2k7hm6t","ctcId":3133,"ctcDifficulty":"VERY HARD","title":"Mexican Standoff","author":"Mile Lemaić","rules":"Normal sudoku rules apply. Cells separated by a knight’s move (in chess) cannot contain the same digit. The digits along an arrow must sum up to the digit in that arrow’s circle. Digits on thermometers must increase from the bulb end.","solution":"673489512925163784481527369317248695256791843894635127132854976568972431749316258","constraints":["antiknight","arrow","thermometer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"The digits along an arrow must sum up to the digit in that arrow’s circle.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"75vvw5rjbb","ctcId":3134,"ctcDifficulty":"VERY HARD","title":"Facing the Void","author":null,"rules":"Normal sudoku rules apply. Identical digits cannot be separated by a knight's move. Digits along an arrow sum to the number in the attached circle.","solution":"178594362395862471462731598781945623953126847624378159819457236536219784247683915","constraints":["antiknight","arrow"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"vnc80d8n88","ctcId":3135,"ctcDifficulty":"VERY HARD","title":"Was It A Cat I Saw?","author":"Mile Lemaić","rules":"Normal sudoku rules apply. Cells separated by a knight's move (in chess) cannot contain the same digit. The grey line is a palindrome: its digits read the same in either direction. Clues outside the grid give the sum of the indicated diagonals.","solution":"589471263726953841341628795835147629972536184164892537613789452257364918498215376","constraints":["antiknight","little-killer","palindrome"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"r834e3uouc","ctcId":3136,"ctcDifficulty":"HARD","title":"Bonds","author":"Playmaker6174","rules":"Normal Sudoku rules apply.\n\nWithin a cage, digits don't repeat and they must sum to the small number written at the top left of that cage.\n\nDigits along an arrow must sum to the digit in the circle cell attached to that arrow.","solution":"426791583785263194913854726894617352531982647267435819179546238658329471342178965","constraints":["arrow","cage"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"d9fq0ll77a","ctcId":3137,"ctcDifficulty":"MEDIUM","title":"Hariyama","author":"Justalilguy & Chefofdeath","rules":"Normal Sudoku rules apply.\n\nRegion Sum: Box borders divide lines into segments with equal sums. Different lines may have different sums.\n\nKiller: Digits in a cage do not repeat and sum to the given total. Cages marked with an “A” sum to the same total.","solution":"641982753397465281258137649823546197975218364164793528739624815486351972512879436","constraints":["cage","custom","region-sum-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cages marked with an “A” sum to the same total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"wobk83t65m","ctcId":3138,"ctcDifficulty":"HARD","title":"Quadratics","author":"Dorlir","rules":"Normal sudoku rules apply.\n\nQuads: Each circle contains four invisible digits (not necessarily distinct and to be deduced). These must each appear in the surrounding four cells.\n\nQuadratics: Of the four digits on a circle, two of them are the two solutions of X^2 - aX + b = 0, where a & b are the other two digits on that circle. If the equation has only one solution, that digit is repeated twice.","solution":"269435178481726539537891264876942351195368742342517986724659813618273495953184627","constraints":["custom","quadruple"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Quadratics: Of the four digits on a circle, two of them are the two solutions of X^2 - aX + b = 0, where a & b are the other two digits on that circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"n5avmxmtyt","ctcId":3140,"ctcDifficulty":"VERY HARD","title":"Sources","author":"Kaktuslav","rules":"Normal sudoku rules apply. If a cell with an arrow contains the digit N, then the straight line starting in that cell and extending N cells in the arrow’s direction (including the arrow cell) is a valid region sum line: it must cross at least one 3×3 box border, and box borders divide it into segments with equal digit sums. E.g. if r1c1 = 5, then r1c1+r1c2+r1c3 = r1c4+r1c5.","solution":"831246759942357168675819234517493826298761345364582971126974583483125697759638412","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If a cell with an arrow contains the digit N, then the straight line starting in that cell and extending N cells in the arrow’s direction (including the arrow cell) is a valid region sum line: it must cross at least one 3×3 box border, and box borders divide it into segments with equal digit sums.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"tnoai9qlvv","ctcId":3141,"ctcDifficulty":"MEDIUM","title":"XII","author":"Aad van de Wetering","rules":"Place the digits 1 to 9, once each, into every row and column. No digit shares an edge with a consecutive digit. Each straight line is a palindrome. (So eg r3c1=r4c2 so that that straight line would read the same from either direction.)","solution":"973641528496375182251839647528163974742586391185924736819257463637492815364718259","constraints":["non-consecutive","palindrome"],"constraintFacts":[{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"d6pi3xs4wu","ctcId":3142,"ctcDifficulty":"VERY HARD","title":"Quivers","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along an orange line have a difference of at least four.\nDigits on an arrow sum to the digit in the circle of that arrow.","solution":"917285643452637198836149572381564927765928431249371856624893715178452369593716284","constraints":["arrow","dutch-whispers"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"syu6xcezzm","ctcId":3143,"ctcDifficulty":"VERY HARD","title":"RAT RUN 27: Productivity","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. \n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nGOLDENBERRIES: If two digits are joined by a goldenberry, they are NOT consecutive.\n\nTEST CONSTRAINT: In this experiment, both paths are divided into segments by 3x3 box borders. Along a path, the digits on each segment have the same product (the result of multiplying the digits on the segment together.) This product may be different for Finkz and Phinx. Note: if a segment contains only one cell, that digit is considered to be the product.","solution":"593762148784139265621854793345298617917546382862317459158423976439675821276981534","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. GOLDENBERRIES: If two digits are joined by a goldenberry, they are NOT consecutive. Along a path, the digits on each segment have the same product (the result of multiplying the digits on the segment together.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7"]}]},{"id":"7sf4felfun","ctcId":3144,"ctcDifficulty":"MEDIUM","title":"Sums Plus","author":"Cane_Puzzles","rules":"- Classic Sudoku rules apply.\n - The gray region must contain each digit 1-9 once.\n - The digits on each arrow must sum to the digit in the attached circle.","solution":"812754936396182754754963128189326547673415892245879613437598261528641379961237485","constraints":["arrow","region"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"73oh4m8m8m","ctcId":3145,"ctcDifficulty":"HARD","title":"Region Sum Circus","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nThe 3x3 box borders divide the blue lines into segments with the same sum, but the sum may be different for different lines.\n\nUsing red, green, and blue, color all circles such that:\n-Orthogonally adjacent circles are different colors.\n-The digit inside a circle appears that many times in circles of that color.","rulesClarified":"Normal Sudoku rules apply.\n\nThe blue lines are region sum lines. The 3x3 box borders cut each blue line into segments. All segments of the same blue line have the same sum. The sums are not given, and different blue lines may have different sums.\n\nColour every circle red, green or blue.\n\nOrthogonally adjacent circles must be different colours.\n\nThe digit inside a circle appears that many times in circles of that color.","solution":"594826317762431859138957642913765428476283591825194736247518963689342175351679284","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"-Orthogonally adjacent circles are different colors. -The digit inside a circle appears that many times in circles of that color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"fyn51hk3yu","ctcId":3146,"ctcDifficulty":"MEDIUM","title":"Counting to 7","author":"zetamath","rules":"Normal sudoku rules apply.\n\nRenban Line: Digits along a renban line must form a set of non-repeating consecutive digits in some order.\n\nNumbered Rooms: A clue outside the grid indicates the digit which has to be placed in the Nth cell in the corresponding direction, where N is the digit placed in the first cell in that direction.","solution":"654923718312876954798514362937168245826495137145732896289651473461387529573249681","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Numbered Rooms: A clue outside the grid indicates the digit which has to be placed in the Nth cell in the corresponding direction, where N is the digit placed in the first cell in that direction.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ydgn4bxilt","ctcId":3147,"ctcDifficulty":"HARD","title":"RAT RUN 28: Hypothesis","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls.\n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nTELEPORTS: Entering a teleport will cause a rat to be instantly transported to the matching coloured teleport. Matching teleports always have identical digits, but teleports that don't match always have different digits.\n\nONE-WAY DOORS: A purple arrow may only be passed through in the direction the arrow is pointing. An arrow always points to the smaller of the two digits it sits between.\n\nGRAPES: A green grape sits between two digits with a difference of at least 5.\n\nTEST CONSTRAINT: In this experiment, Finkz may only visit even digits, and Phinx may only visit odd digits. You must determine which rat is which.","solution":"842695173351742869967318542179256438428937615635481927284563791716829354593174286","constraints":["custom","inequality"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. TELEPORTS: Entering a teleport will cause a rat to be instantly transported to the matching coloured teleport. Matching teleports always have identical digits, but teleports that don't match always have different digits. ONE-WAY DOORS: A purple arrow may only be passed through in the direction the arrow is pointing. GRAPES: A green grape sits between two digits with a difference of at least 5. TEST CONSTRAINT: In this experiment, Finkz may only visit even digits, and Phinx may only visit odd digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c7","c9","c10"]},{"slug":"inequality","type":"inequality","variant":"modified","modifiers":[],"params":null,"note":"An arrow always points to the smaller of the two digits it sits between.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]}]},{"id":"1pdzuv445k","ctcId":3149,"ctcDifficulty":"HARD","title":"Zombie Drome","author":"R. Mullinix","rules":"Normal Sudoku Rules Apply:   Place the numbers 1-9 in every row, column, and 3x3 region.\n\nZombie Cells: There is one zombie cell in every row, column, and box. There are no duplicate numbers in the zombie cells.  The value of a zombie cell is the number in the cell plus 1.  The value of non-zombie cells is the number in the cell.\n\nPalindrome: \nThe sequence of values along the marked grey lines reads the same forwards and backwards.\n\nKiller Cages: \nThe cell values in a cage must add up to the small total given in the top-left corner of the cage.  \n\nX Clues:\nCell values separated by an X sum to 10.\n\nWhite Kropki Dots:\nCell values separated by white dot are consecutive.\n\nBlack Kropki Dots:\nCell values separated by black dot are in a 1/2 ratio.","solution":"326591478598674321174283965687932154213845796459167283931756842762418539845329617","constraints":["XV","cage","custom","kropki","palindrome"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"Cell values separated by an X sum to 10.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c11"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The cell values in a cage must add up to the small total given in the top-left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Zombie Cells: There is one zombie cell in every row, column, and box. There are no duplicate numbers in the zombie cells. The value of a zombie cell is the number in the cell plus 1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Cell values separated by white dot are consecutive. Cell values separated by black dot are in a 1/2 ratio.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c13","c15"]},{"slug":"palindrome","type":"palindrome","variant":"modified","modifiers":[],"params":null,"note":"The sequence of values along the marked grey lines reads the same forwards and backwards.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]}]},{"id":"uwqqgafi9m","ctcId":3150,"ctcDifficulty":"MEDIUM","title":"Zebra Knights","author":"R. Mullinix","rules":"Normal sudoku rules apply.\n\nCells separated by a single knight's move (in chess) cannot contain the same digit. \n\nFor all rules below:  Do not duplicate any digit within a ruleset.  For example, if 1 appears on Renban line, it must not appear on any other Renban line.\n\nRenban (purple line): Digits along a purple line form a set of consecutive digits in any order.\n\nThermometer: (thicker grey line) Digits along a thermometer increase from bulb to tip.\n\nKropki dots: Digits in cells joined by a white dot are consecutive.\n\nKiller: Digits in a cage may not repeat.","solution":"675189324891423675234675891123798546987546132546231789362917458719854263458362917","constraints":["antiknight","cage","custom","kropki","renban","thermometer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"For all rules below:  Do not duplicate any digit within a ruleset.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"c8shq67xrf","ctcId":3151,"ctcDifficulty":"HARD","title":"Fog Eraser","author":"R. Mullinix","rules":"Normal Sudoku Rules Apply:   Place the digits 1-9 in every row, column, and 3x3 region.\n\nDynamic Fog: The grid is covered in fog.  Entering correct digits may clear fog.\n\nEraser Cells: There is one eraser cell in every row, column, and box. The nine eraser cells all contain different digits. The value of an eraser cell is always 0.  The value of non-eraser cells is the digit in the cell.\n\nThermometers: Values along a thermometer increase from bulb to tip.\n\nV Clues: Values in cells joined by a V sum to 5.\n\nKiller: Values in a cage may not repeat and sum to the small clue total given in the cage's top left cell.  Digits MAY repeat in a cage.\n\nGerman Whispers: If two cells are joined by a green line the values in those cells must have a difference of at least 5.","solution":"594678213783129456612453978276945831348712695951836724837261549465397182129584367","fogLight":"R2C2,R3C2,R3C3,R2C3,R1C3,R1C4,R1C5,R1C6,R2C6,R7C3,R8C3","constraints":["XV","cage","custom","fog","german-whispers","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"V Clues: Values in cells joined by a V sum to 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Killer: Values in a cage may not repeat and sum to the small clue total given in the cage's top left cell. Digits MAY repeat in a cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c10","c11"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Eraser Cells: There is one eraser cell in every row, column, and box. The nine eraser cells all contain different digits. The value of an eraser cell is always 0.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"German Whispers: If two cells are joined by a green line the values in those cells must have a difference of at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Thermometers: Values along a thermometer increase from bulb to tip.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]}]},{"id":"18arjzoqpi","ctcId":3152,"ctcDifficulty":"MEDIUM","title":"Seventeen Fives","author":"R. Mullinix","rules":"Normal sudoku rules apply. \nPlace the digits 1–9 exactly once in every row, column, and 3×3 box.\n\nMiddlers: Find nine Middler cells in the grid, one in each row, column, and 3×3 box, each containing a different digit. The value of a Middler cell is 5, regardless of the digit in the cell.\n\nGerman Whispers: If two cells are joined by a green line, the values of those cells must have a difference of at least 5.\n\nV Clues: Cells joined by a V have values that sum to 5.\n\nX Clues: Cells joined by an X have values that sum to 10.\n\nKropki: Cells separated by a white dot contain consecutive values.\n\nPalindrome: The values along the gray line read the same forwards and backwards.","solution":"652718394397254816814396725945681237123475689768923451239167548571842963486539172","constraints":["XV","custom","german-whispers","kropki","palindrome"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"X Clues: Cells joined by an X have values that sum to 10.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6","c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Middlers: Find nine Middler cells in the grid, one in each row, column, and 3×3 box, each containing a different digit. The value of a Middler cell is 5, regardless of the digit in the cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"palindrome","type":"palindrome","variant":"modified","modifiers":[],"params":null,"note":"Palindrome: The values along the gray line read the same forwards and backwards.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]}]},{"id":"j5947yd09n","ctcId":3153,"ctcDifficulty":"VERY HARD","title":"Uniqueness, with a Nudge","author":"R. Mullinix","rules":"Normal Sudoku Rules apply: place the digits 1–9 exactly once in each row, column, and 3×3 box.\n\nFind nine Nudge cells in the grid, one in each row, column, and 3×3 box, each containing a different digit. The value of a nudge cell equals the digit in the cell plus 1.\n\nNatural Cells. A natural (non-nudge) cell has a value equal to its written digit.\n\nFor all clue types below: No value may appear more than once on each clue type.  Eg if a cage contains the value 4, no other cage contains the value 4. \n\nGerman Whispers: If two cells are joined by a green line, the values must differ by at least 5.\n\nWhite dots: Cell values separated by white dot are consecutive.\n\nBlack dots: Cell values separated by black dot are in a 1/2 ratio.\n\nCages: No value may repeat in a cage.\n\nBlue Diagonal: Values along the marked diagonal must not repeat.\n\nNote: In the settings, turn conflict checker to off or classic sudoku.","rulesClarified":"Normal Sudoku rules apply: place the digits 1 to 9 exactly once in each row, column and 3x3 box.\n\nNudge cells. Find nine nudge cells in the grid, one in each row, column and 3x3 box, each containing a different digit. The nudge cells are not drawn; you find them.\n\nThe value of a nudge cell is the digit in it plus 1.\n\nNatural cells. Any cell that is not a nudge cell is a natural cell. The value of a natural cell is the digit written in it.\n\nThe clues below compare values, not written digits.\n- Uniqueness: for each clue type below, no value may appear more than once across that clue type's clues. For example, if one cage contains the value 4, no other cage contains the value 4.\n- Cages: no value may repeat within a single cage.\n- Green lines (German whispers): two cells joined by a green line have values that differ by at least 5.\n- White dots: a white dot sits between two cells, and their values are consecutive, meaning they differ by exactly 1.\n- Black dots: a black dot sits between two cells, and one value is half the other.\n- Blue diagonal: no value may repeat along the marked blue diagonal.\n\nNote: in the settings, turn the conflict checker off or set it to classic sudoku.","solution":"491852637783469152256173498879516324514327869632948715965781243148235976327694581","constraints":["cage","custom","diagonal","german-whispers","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":["no-sum","repeats-allowed"],"params":null,"note":"A cage holds each value once, not each digit: a nudge cell counts as its digit plus 1, and the cages carry no totals.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c11"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Find nine Nudge cells in the grid, one in each row, column, and 3×3 box, each containing a different digit. The value of a nudge cell equals the digit in the cell plus 1. For all clue types below: No value may appear more than once on each clue type.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c6"]},{"slug":"diagonal","type":"diagonal","variant":"modified","modifiers":[],"params":null,"note":"Blue Diagonal: Values along the marked diagonal must not repeat.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]},{"slug":"german-whispers","type":"german-whispers","variant":"modified","modifiers":[],"params":null,"note":"German Whispers: If two cells are joined by a green line, the values must differ by at least 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Black dots: Cell values separated by black dot are in a 1/2 ratio.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9","c10"]}]},{"id":"tn30l4epty","ctcId":3155,"ctcDifficulty":"MEDIUM","title":"Kropki Drops","author":"Michael Lefkowitz","rules":"- Normal Sudoku rules apply.\n- A white drop indicates how many digits in the indicated direction differ from it by 1.\n- A black drop indicates how many digits in the indicated direction are double or half its value.","solution":"574623981138459276296871543723985614845216739961734825317598462452167398689342157","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- A white drop indicates how many digits in the indicated direction differ from it by 1. - A black drop indicates how many digits in the indicated direction are double or half its value.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"91jlsoujs1","ctcId":3156,"ctcDifficulty":"MEDIUM","title":"Σ","author":"Kaktuslav","rules":"Normal sudoku rules apply. Each pink line is a renban: it contains a set of consecutive digits (in any order). No two pink lines have the same digit sum.","solution":"231897564876524391954316728693245187518973246427681935765439812342158679189762453","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No two pink lines have the same digit sum.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"8HQfQ4tD9q","ctcId":3157,"ctcDifficulty":"MEDIUM","title":"Difference Of Squares","author":"MathGuy_12","rules":"Normal sudoku rules apply. Digits in cages sum to the expression or value in the top left corner. X and Y are positive integers such that X > Y. Digits may repeat within cages if allowed by other rules. Digits along an arrow sum to the digit in that arrow’s circle. Purple lines are “renban” lines. A renban line is a collection of consecutive non-repeating digits arranged in any order.","solution":"572946381634851297981732564768429153459318672213567948825194736197683425346275819","constraints":["arrow","cage","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in cages sum to the expression or value in the top left corner.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"20prr0i65d","ctcId":3158,"ctcDifficulty":"MEDIUM","title":"Golden Palindromes","author":"MathGuy_12","rules":"Normal sudoku rules apply.\n\nClues outside the grid provide the sum of the indicated diagonal. Digits may repeat along a diagonal if allowed by other rules.\n\nDigits in cages sum to the value in the top left corner.\n\nDigits along a golden palindrome line are read the same from either direction. In addition, the central digit on the line marked by a golden circle is the same as the digit on the ends of the line.","rulesClarified":"Normal sudoku rules apply.\n\nKiller cages: the digits in each labelled cage sum to the number in its top-left corner. Digits may repeat along a diagonal if other rules allow.\n\nOutside clues: a clue outside the grid gives the sum of the digits along the diagonal it points into.\n\nGolden palindromes: each golden line, read from either end, gives the same digits. Each golden line is a palindrome.\n\nGolden circles: a golden circle marks the middle cell of a line. For that line, the middle digit equals the digits at its two ends.","solution":"841527396736981452259634871615293784492718563378465219187349625523176948964852137","constraints":["cage","custom","little-killer","palindrome"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In addition, the central digit on the line marked by a golden circle is the same as the digit on the ends of the line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"nqdf4egrll","ctcId":3159,"ctcDifficulty":"MEDIUM","title":"Double Dippin' Dots","author":"MathGuy_12","rules":"Normal sudoku rules apply.\n\nCells with same colour circle contain the same digit.\n\nCells touched by a 'Sum Dot' add to the indicated value. Digits may repeat within a dot if allowed by other rules.","solution":"345829716296174538187563294852417369619358472473692185934281657761945823528736941","constraints":["clone","custom"],"constraintFacts":[{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells touched by a 'Sum Dot' add to the indicated value.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9qw21nnjuy","ctcId":3161,"ctcDifficulty":"HARD","title":"Xerox","author":"MathGuy_12","rules":"Normal sudoku rules apply. \n\nAll the 2x2 areas of the grid, when read in normal reading order, make a total of 64 four-digit numbers.  Clues in the centre of a 2x2 area show its rank among those 64 numbers, where the lowest is 1 and the highest is 64. \n\nThe two “X”s are the same number. \n\nOne or more equal numbers are considered to be at rank N when there are N-1 numbers of strictly lower rank. (Eg, if there are three equal numbers which have 19 numbers lower than them then these three numbers would be rank 20 and the next rank will be 23, i.e. the ranks could go ⋯, 19, 20, 20, 20, 23, ⋯)","solution":"276584913584391762391726458652839147839147625147265839918453276763912584425678391","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Clues in the centre of a 2x2 area show its rank among those 64 numbers, where the lowest is 1 and the highest is 64. The two “X”s are the same number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"q6vqwmsp2k","ctcId":3162,"ctcDifficulty":"HARD","title":"Blockers","author":"Fenners","rules":"Normal 9x9 Sudoku rules apply.\n\nBlockers: Digits in diamonds can never be used on a different clue type than the clue type the diamond lives on.\n\nRenban: Digits on a purple line form a set of consecutive digits in any order.\n\nDutch Whispers: Two adjacent digits on an orange line must differ by at least 4.\n\nGerman Whispers: Two adjacent digits on a green line must differ by at least 5.\n\nRegion Sum: The 3x3 box border divide blue lines into segments; each segment along an individual line must have the same sum.","solution":"917536284853421976462798153675382419389164527124975368791653842538247691246819735","constraints":["custom","dutch-whispers","german-whispers","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Blockers: Digits in diamonds can never be used on a different clue type than the clue type the diamond lives on.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"iovwq0jc5n","ctcId":3163,"ctcDifficulty":"HARD","title":"Exclusive Lines","author":"Nurator","rules":"Normal sudoku rules apply.\nIf two digits are separated by a black dot then one digit is double the other. Digits separated by a white dot are consecutive. Not all dots are given.\n\nDynamic Fog: Deducing the digit in the highest visible checkpoint (marked with a green square and a number) will reveal new cells and potentially a new checkpoint. \n\nEach line follows the rules of one specific constraint type from the following list. It is up to the solver to determine which line belongs to which type. \n\nEach line constraint type may contain NO REPEATED DIGITS anywhere in the puzzle.\n\nAt the start of the puzzle, all lines are Region Sum Lines (ie the 3x3 box borders divide the lines into segments; each segment along an individual line has the same sum). \n\nWhen a new checkpoint is revealed, remove the determined line types and all entered digits EXCEPT those on checkpoints. You are now allowed a new line constraint!\n\nCheckpoint 1: Additionally, the lines can now be German Whisper lines (Adjacent digits differ by at least 5)\n\nCheckpoint 2: Additionally, the lines can now be Parity lines (Digits alternate between odd and even digits)\n\nYou have completed the puzzle when all 3 checkpoints are revealed and the complete grid is filled.","solution":"673254198541986273298713546436872951157439682829165437785691324912348765364527819","fogLight":"R7C2,R7C1,R6C1,R5C1,R4C1,R4C2,R3C2,R2C2","constraints":["custom","german-whispers","kropki","region-sum-line","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"It is up to the solver to determine which line belongs to which type. Each line constraint type may contain NO REPEATED DIGITS anywhere in the puzzle. When a new checkpoint is revealed, remove the determined line types and all entered digits EXCEPT those on checkpoints. Checkpoint 2: Additionally, the lines can now be Parity lines (Digits alternate between odd and even digits)","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8","c10","c13"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"xipcvuhz9y","ctcId":3164,"ctcDifficulty":"HARD","title":"RAT RUN 29: Counterbalance","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, share cells, cross themselves or each other, or pass through any thick maze walls.\n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nONE-WAY DOORS: A purple arrow may only be passed through in the direction it's pointing. An arrow always points to the smaller of the two digits it sits between.\n\nREDCURRANTS: If a redcurrant sits between two digits, one is odd and the other is even.\n\nTEST CONSTRAINT: In this experiment, any digit on Finkz' path indicates exactly how many times that digit appears on Finkz' path. The same rule applies separately for Phinx' path.","solution":"325714869914286357786953214138642975247895136659371428872169543461538792593427681","constraints":["custom","inequality"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, share cells, cross themselves or each other, or pass through any thick maze walls. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. ONE-WAY DOORS: A purple arrow may only be passed through in the direction it's pointing. REDCURRANTS: If a redcurrant sits between two digits, one is odd and the other is even. TEST CONSTRAINT: In this experiment, any digit on Finkz' path indicates exactly how many times that digit appears on Finkz' path. The same rule applies separately for Phinx' path.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7","c8","c9"]},{"slug":"inequality","type":"inequality","variant":"modified","modifiers":[],"params":null,"note":"An arrow always points to the smaller of the two digits it sits between.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]}]},{"id":"23xbq0xofa","ctcId":3165,"ctcDifficulty":"MEDIUM","title":"Odd!","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Along every positive diagonal (ie from south-west to north-east) the difference between neighbouring digits is at least 2. Every green line contains only odd digits. The central 3x3 box is a magic square (ie each row, columns and 3-cell diagonal of this box must sum to the same total).","solution":"456327819389416725172985436941672583638159274725834961894761352563298147217543698","constraints":["custom","odd"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Along every positive diagonal (ie from south-west to north-east) the difference between neighbouring digits is at least 2. The central 3x3 box is a magic square (ie each row, columns and 3-cell diagonal of this box must sum to the same total).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"yj1g5x7n9f","ctcId":3166,"ctcDifficulty":"HARD","title":"Wingspan","author":"Kaktuslav","rules":"Normal sudoku rules apply. The 3x3 box borders divide each blue line into segments; along an individual line each of those segments must have the same sum.","solution":"562943178138725649749816253487392516915684732326157894271438965654279381893561427","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"5ry14x9azl","ctcId":3167,"ctcDifficulty":"VERY HARD","title":"Nearly π","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along an orange line have a difference of at least four.\nThe digits on the gray lines form palindromes. (They read same from both the directions.)\nCells separated by an X sum to ten. Not all possible Xs are necessarily given.","solution":"516794823372815964849263517763942158128576349954381672697458231435129786281637495","constraints":["XV","dutch-whispers","palindrome"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"n44kqgll5s","ctcId":3168,"ctcDifficulty":"MEDIUM","title":"Dutch Flat Mates: Split Ends","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nEvery 5 in the grid must have a 1 directly above it or a 9 directly below it. It may have both, but it doesn't need both.\n\nEach horizontal blonde line sums to a 2 digit number. These two digits are at the start and end of its row, in some order.\n\nEach vertical brunette line also sums to a 2 digit number. These two digits are at the top and bottom of its column, in some order.","solution":"926354781318697425754821396189536274567942138243718569632485917471269853895173642","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every 5 in the grid must have a 1 directly above it or a 9 directly below it. Each horizontal blonde line sums to a 2 digit number. Each vertical brunette line also sums to a 2 digit number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c6"]}]},{"id":"dnu167bzhz","ctcId":3169,"ctcDifficulty":"MEDIUM","title":"Seven Ate Nine","author":"James Sinclair","rules":"Normal sudoku rules apply, and all clues are standard.\nCages: the sum of the digits inside the cage is equal to the small number in the top left corner.\nArrows: the sum of the digits along an arrow is equal to the digit in the connected circle.\nDigits in cells separated by a white dot are consecutive.\n\nThis puzzle appears in Artisanal Sudoku: 150 Handcrafted Puzzles That Go Beyond the Ordinary, from Puzzlewright Press (published March 2026).","solution":"795631842813942657246875193479268315538714926621593478952186734184327569367459281","constraints":["arrow","cage","kropki"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"axfuqiprqj","ctcId":3170,"ctcDifficulty":"HARD","title":"RAT RUN 30: Star Rats","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths may not share cells except for where they meet at the cupcake cell.\n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBOOSTER CELLS: There is one booster cell in every row, column and box, and each contains a different digit. The value of a booster cell equals its digit, plus its row number, plus its column number. Eg: If r7c3 is a booster cell and contains a 6, it will have a value of 16 (7+3+6).\n\nBLACKCURRANTS: If two cells are joined by a blackcurrant then the value of one is double the value of the other.\n\nSTARFRUIT: The sum of the two values joined by a starfruit is always the same, and must be deduced.\n\nTEST CONSTRAINT: In this experiment, both rats visit the same number of cells, and the sequence of VALUES along both paths are identical. Eg: If the first five values visited by Finkz are 7, 4, 12, 3, 8 (in that order) then the same must be true for Phinx.","solution":"758396412624157983319842576985274361263519847147683295596738124432961758871425639","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths may not share cells except for where they meet at the cupcake cell. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. BOOSTER CELLS: There is one booster cell in every row, column and box, and each contains a different digit. The value of a booster cell equals its digit, plus its row number, plus its column number. STARFRUIT: The sum of the two values joined by a starfruit is always the same, and must be deduced. TEST CONSTRAINT: In this experiment, both rats visit the same number of cells, and the sequence of VALUES along both paths are identical.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c7","c10","c11"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"BLACKCURRANTS: If two cells are joined by a blackcurrant then the value of one is double the value of the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]}]},{"id":"aixxhbtkvj","ctcId":3172,"ctcDifficulty":"MEDIUM","title":"EXclusiVe","author":"NurglesGift","rules":"Normal sudoku rules apply. \n\nCells separated by a single knight's move (in chess) cannot contain the same digit. \nThe following constraints operate in this puzzle: \n1) Cells connected by an X must sum to 10; \n2) Cells connected by an V must sum to 5; \n3) Digits in a cage sum to the small number in the cage's top-left corner; \n4) Digits on an arrow sum to the digit in that arrow's circle; and \n5) Digits on a thermometer must increase from the bulb end. \n\nWithin any single constraint type listed above, digits may not repeat.  (Eg If one caged cell contained a 1, no other caged cell anywhere in the puzzle can contain a 1.)","solution":"123456789456789123987231564274365891569178432831924657315642978798513246642897315","constraints":["XV","antiknight","arrow","cage","custom","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Within any single constraint type listed above, digits may not repeat.","evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"4ssf9qr9l9","ctcId":3173,"ctcDifficulty":"VERY HARD","title":"Two Truths and a Region","author":"gdc","rules":"Normal sudoku rules apply.\n𝗗𝘆𝗻𝗮𝗺𝗶𝗰 𝗙𝗼𝗴 hides some clues. Placing a correct digit clears fog from its cell and possibly other cells.\n𝟮𝗧𝟭𝗟:  For each clue type listed below, there are three clues of that type in the grid which don't share cells. Two of them are correct, and one is incorrect ('lying').\n𝗥𝗲𝗴𝗶𝗼𝗻𝗮𝗹 𝗖𝗼𝗻𝘀𝘁𝗿𝗮𝗶𝗻𝘁𝘀: For each clue type, all cells clued by that type (incl. the liar) contain different digits.\n𝗖𝗹𝘂𝗲 𝗧𝘆𝗽𝗲𝘀: Cages, V, arrows, double arrows, renban, and black kropki (no negative constraints, see below).\n\n𝗖𝗟𝗨𝗘 𝗧𝗬𝗣𝗘𝗦 𝗜𝗡 𝗗𝗘𝗧𝗔𝗜𝗟\n\n𝗖𝗮𝗴𝗲𝘀: Digits in a cage sum to the total in the top-left.\n𝗩: Each V joins two digits that sum to 5.\n𝗗𝗼𝘂𝗯𝗹𝗲 𝗔𝗿𝗿𝗼𝘄𝘀 (DA): If two circles in different cells are connected by a line, the sum in the circles is equal to the sum of the remaining (0+ cell) line.\n𝗔𝗿𝗿𝗼𝘄𝘀 (A): Digits along an arrow sum to the digit in the attached circle.\n𝗥𝗲𝗻𝗯𝗮𝗻 (R): Digits on a hollow line form a single consecutive sequence (like 234) in any order.\n𝗥𝗮𝘁𝗶𝗼: If two digits are joined by a black dot then one is double the other.","solution":"569327814138469725427518369395746281246851937781932456673295148954183672812674593","fogLight":"R1C1,R1C2,R6C3","constraints":["XV","arrow","cage","custom","fog","kropki","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"𝗩: Each V joins two digits that sum to 5.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"𝗔𝗿𝗿𝗼𝘄𝘀 (A): Digits along an arrow sum to the digit in the attached circle.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"𝗖𝗮𝗴𝗲𝘀: Digits in a cage sum to the total in the top-left.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Two of them are correct, and one is incorrect ('lying'). 𝗥𝗲𝗴𝗶𝗼𝗻𝗮𝗹 𝗖𝗼𝗻𝘀𝘁𝗿𝗮𝗶𝗻𝘁𝘀: For each clue type, all cells clued by that type (incl. the liar) contain different digits. 𝗗𝗼𝘂𝗯𝗹𝗲 𝗔𝗿𝗿𝗼𝘄𝘀 (DA): If two circles in different cells are connected by a line, the sum in the circles is equal to the sum of the remaining (0+ cell) line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c11"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"𝗥𝗮𝘁𝗶𝗼: If two digits are joined by a black dot then one is double the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c14"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"𝗥𝗲𝗻𝗯𝗮𝗻 (R): Digits on a hollow line form a single consecutive sequence (like 234) in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c13"]}]},{"id":"yymnj1pfww","ctcId":3174,"ctcDifficulty":"MEDIUM","title":"These Two Equal These Two","author":"Eric Rathbun","rules":"Normal Sudoku rules apply.\nNormal Killer Cage rules apply.\nNormal Little Killer Cage rules.\nDigits separated by a white dot have a difference of one. Not all dots are given.\nDigits separated by a king's move in chess do not repeat.","rulesClarified":"Normal Sudoku rules apply.\n\nKiller cages: normal Killer rules. The digits in a cage add up to the total printed in that cage, and no digit repeats within a cage. A cage with no printed total has no given total.\n\nLittle Killer: each number outside the grid is the sum of the run of cells it marks, in the direction the arrow shows. The outside number's own position is not counted.\n\nDots: a white dot between two neighbouring cells means their digits differ by exactly one. Not all dots are given. A pair of neighbouring cells with no dot gives no information.\n\nAntiking: two cells a king's move apart (including diagonal neighbours) never hold the same digit.","solution":"964257138823614597751839642647528319532971486198346275275183964419762853386495721","constraints":["antiking","cage","kropki","little-killer"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"t80utgm1os","ctcId":3175,"ctcDifficulty":"MEDIUM","title":"It's only logical","author":"HalfBakedLunatic (aka David Workman)","rules":"• Normal Sudoku rules apply\n• Digits in cells separated by a white dot must be consecutive, digits separated by a black dot must be in a 2:1 ratio - not all dots are shown\n• Digits in cells separated by an X must sum to 10, digits separated by a V must sum to 5 - not all X's and V's are shown\n• Digits in cages must sum to the value in the corner of the cage","solution":"379485612681932475254671893862319547415726938937854126543167289796248351128593764","constraints":["XV","cage","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"37wqeifgzs","ctcId":3177,"ctcDifficulty":"VERY HARD","title":"RAT RUN 31: Equivalence","author":"Marty Sears and Justin Vitanza","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, share cells, cross themselves or each other, or pass through any thick maze walls. \n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBLACKCURRANTS: If a blackcurrant sits between two digits, one is double the other.\n\nREDCURRANTS: If a redcurrant sits between two digits, one is odd and the other is even.\n\nTELEPORTS: Entering a yellow teleport will cause a rat to be instantly transported to the other yellow teleport. The teleports have identical digits.\n\nMOTION SENSORS: The digit on a pink motion sensor indicates the number of cells that are visited (by either rat) within the (up to 9) cells immediately surrounding the sensor. The sensor itself is counted, if visited.\n\nTEST CONSTRAINT: In this experiment, for any row or column, the digits visited by Finkz must have the same sum as the digits visited by Phinx. This sum must be determined for each row and column.","solution":"273859461961234758584671329695183247132745986847962135358497612419526873726318594","constraints":["clone","custom","kropki"],"constraintFacts":[{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, share cells, cross themselves or each other, or pass through any thick maze walls. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. REDCURRANTS: If a redcurrant sits between two digits, one is odd and the other is even. TELEPORTS: Entering a yellow teleport will cause a rat to be instantly transported to the other yellow teleport. MOTION SENSORS: The digit on a pink motion sensor indicates the number of cells that are visited (by either rat) within the (up to 9) cells immediately surrounding the sensor. TEST CONSTRAINT: In this experiment, for any row or column, the digits visited by Finkz must have the same sum as the digits visited by Phinx.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c6","c7","c9","c11"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"uoypkyxq4g","ctcId":3178,"ctcDifficulty":"HARD","title":"Yin Yang killers","author":"Jonesy","rules":"Hello\n\nNormal Sudoku rules apply.\n\nYin-Yang shading:\nColor the grid using two colors such that:\n\nEach color forms a single orthogonally connected region and no 2×2 block of cells is entirely one color.\n\nThe digits along each line sum to the same total.\n\nAlong each line, the Yin-Yang coloring separates odd and even digits; that is, all odd digits on a line are one color and all even digits are the other color.\n\nDigits separated by a white dot are consecutive.\n\nHave fun.","solution":"781362459936457821452891367524736198368519742179248536647985213215673984893124675","constraints":["custom","kropki","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digits along each line sum to the same total. Along each line, the Yin-Yang coloring separates odd and even digits; that is, all odd digits on a line are one color and all even digits are the other color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"uevzycz28t","ctcId":3179,"ctcDifficulty":"HARD","title":"Wendezäune","author":"Dorlir","rules":"Normal sudoku rules apply.\n\nDraw a single loop that travels orthogonally and passes through the centers of cells. The loop may go straight through a cell or turn within a cell, but it cannot branch or cross itself. Adjacent digits along the loop differ by at least 5.\n\nA digit in a circle indicates how many of the four surrounding cells contain turns of the loop. Additionally, the digit also indicates that at least one of those four surrounding cells contains that digit.","rulesClarified":"Normal sudoku rules apply.\n\nDraw a single loop that travels orthogonally from cell to cell, passing through the centres of cells. The loop may go straight through a cell or turn inside it, but it cannot branch or cross itself.\n\nAdjacent digits along the loop differ by at least 5. Adjacent here means next to each other on the loop, not next to each other in the grid.\n\nA circled digit sits over a 2x2 block of four cells. Those four cells are the surrounding cells for that circle.\n\nA circled digit says how many of its four surrounding cells contain a turn of the loop. A cell that the loop only passes straight through does not count.\n\nA circled digit also says that at least one of its four surrounding cells contains that digit.","solution":"617349582382715469945682731596134278834527916271896345129463857763958124458271693","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single loop that travels orthogonally and passes through the centers of cells. The loop may go straight through a cell or turn within a cell, but it cannot branch or cross itself. A digit in a circle indicates how many of the four surrounding cells contain turns of the loop. Additionally, the digit also indicates that at least one of those four surrounding cells contains that digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c5","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"yya40q1u23","ctcId":3181,"ctcDifficulty":"MEDIUM","title":"Just a killer","author":"Adem Jaziri","rules":"Normal sudoku rules apply.\n\nKiller : digits in cages do not repeat and sum to the number in the top left corner of the cage","solution":"942576831517834296683219547795683124864127953231495768479358612156742389328961475","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"x0xwsud0hq","ctcId":3182,"ctcDifficulty":"MEDIUM","title":"Fibreglass Acoustic Diffusers","author":"ThePedallingPianist","rules":"SUDOKU: Fill each cell with a digit from 1-9 such that digits do not repeat in a row, column or box.\n\nREGION SUM LINE: The blue 'R' is split by a box border into two segments whose digits have the same sum.\n\nPARITY LINE: Each pair of adjacent digits on the red 'A' must contain one odd and one even digit.\n\nGERMAN WHISPER LINE: Each pair of adjacent digits on the green 'H' must have a difference of at least 5.\n\nFIBREGLASS ACOUSTIC DIFFUSERS:\n• A digit on a Fibreglass Acoustic Diffuser (upside-down mushroom) shows how many times that digit appears on Fibreglass Acoustic Diffusers;\n• Fibreglass Acoustic Diffusers prevent echoes in adjacent cells, i.e. a Fibreglass Acoustic Diffuser and its up to four orthogonal neighbours contain different digits.","solution":"371245986869137425425896371786321594932564718514789263147652839658973142293418657","constraints":["custom","german-whispers","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"PARITY LINE: Each pair of adjacent digits on the red 'A' must contain one odd and one even digit. • A digit on a Fibreglass Acoustic Diffuser (upside-down mushroom) shows how many times that digit appears on Fibreglass Acoustic Diffusers; • Fibreglass Acoustic Diffusers prevent echoes in adjacent cells, i.e. a Fibreglass Acoustic Diffuser and its up to four orthogonal neighbours contain different digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c6","c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"uy0r96nw2i","ctcId":3183,"ctcDifficulty":"MEDIUM","title":"Archipelago","author":"Lithium-Ion","rules":"Normal sudoku rules apply. Each cell in the grid belongs to exactly one terrain: Either island (green) or water (blue). All water cells in the grid must form one orthogonally connected region. Each 2x2 region in the grid contains at least one cell from each terrain. Each island contains exactly one clue, which equals the product of the size of the island (i.e. the number of cells that belong to this island) and the sum of the digits in all cells belonging to this island. Digits within an island do not repeat. Island are not allowed to touch each other (neither orthogonally nor diagonally). A digit in a circle equals the size of the island. Not all possible circles are given.","solution":"942761583175834629836952147459613278617428395283579461591286734768345912324197856","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each cell in the grid belongs to exactly one terrain: Either island (green) or water (blue). All water cells in the grid must form one orthogonally connected region. Each 2x2 region in the grid contains at least one cell from each terrain. Each island contains exactly one clue, which equals the product of the size of the island (i.e. the number of cells that belong to this island) and the sum of the digits in all cells belonging to this island. Digits within an island do not repeat. Island are not allowed to touch each other (neither orthogonally nor diagonally). A digit in a circle equals the size of the island.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c7","c8"]}]},{"id":"93r6idydph","ctcId":3184,"ctcDifficulty":"VERY HARD","title":"Figure 8","author":"Antiknight","rules":"Normal Sudoku rules apply. Digits must not repeat in cells that are a chess knight's move apart. The digits along each arrow must sum to the digit in the circled cell. Digits may repeat along an arrow if permitted by other rules. Digits do not repeat along gold Nabner lines. Additionally, no pair of digits anywhere on a Nabner line can be consecutive. Digits along each magenta line must be a set of consecutive digits in any order.","solution":"685724931724931685931685742517842396842396157396157824158473269473269518269518473","constraints":["antiknight","arrow","nabner-line","renban"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"o2u3rfkurb","ctcId":3185,"ctcDifficulty":"HARD","title":"RAT RUN 32: Veracity","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach cupcakes by finding a path through the maze. The paths must not visit any cell more than once, share cells, or pass through any thick maze walls. No diagonal moves are possible in this maze.\n\n• BLACKCURRANTS: If two digits are joined by a blackcurrant, one is double the other.\n• REDCURRANTS: If two digits are joined by a redcurrant, one is odd and the other is even.\n• GOLDENBERRIES: If two digits are joined by a goldenberry, they are non-consecutive.\n• GRAPES: If two digits are joined by a grape, they have a difference of at least 5.\n• MOTION SENSORS: A digit on a motion sensor indicates exactly how many cells in the (up to 9) surrounding cells are visited by a rat.\n\nTEST CONSTRAINT: In this experiment, some clues are fake! (A fake clue breaks its rule in the list above.)\n\nAll clues that Phinx passes through are fake. All other clues are truthful (ie; those passed through by Finkz, and those unvisited by either rat.) It is to be determined which rat is which.","solution":"953172864471836295826945137549613782237598641168724359315487926784269513692351478","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach cupcakes by finding a path through the maze. The paths must not visit any cell more than once, share cells, or pass through any thick maze walls. • REDCURRANTS: If two digits are joined by a redcurrant, one is odd and the other is even. • GOLDENBERRIES: If two digits are joined by a goldenberry, they are non-consecutive. • GRAPES: If two digits are joined by a grape, they have a difference of at least 5. • MOTION SENSORS: A digit on a motion sensor indicates exactly how many cells in the (up to 9) surrounding cells are visited by a rat. All clues that Phinx passes through are fake. All other clues are truthful (ie; those passed through by Finkz, and those unvisited by either rat.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c6","c7","c8","c9","c12","c13"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"• BLACKCURRANTS: If two digits are joined by a blackcurrant, one is double the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"1l8hcd2k4v","ctcId":3186,"ctcDifficulty":"MEDIUM","title":"Entropic islands","author":"Jonesy","rules":"Hello\n\nNormal Sudoku rules apply.\n\nDigits are grouped into entropic sets:\n\nLow → {1, 2, 3}\nMid  → {4, 5, 6}\nHigh→ {7, 8, 9}\n\nA digit placed in a circle indicates the size of the orthogonally connected group of cells that all contain digits from the same entropic set as that digit.\n\nNo region contains more than one circled cell.\nNot all regions contain a circle.\n\nDigits separated by a white dot must be consecutive.\nDigits separated by a black dot have a 2:1 ratio.\n\nHave fun.","solution":"156423798872569314493871652689714523541236987237985146364198275925647831718352469","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit placed in a circle indicates the size of the orthogonally connected group of cells that all contain digits from the same entropic set as that digit. No region contains more than one circled cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10","c11"]}]},{"id":"4tc1g21b3x","ctcId":3187,"ctcDifficulty":"MEDIUM","title":"Pentomino Islands","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Adjacent digits on any pentomino must differ in value by at least 5.","solution":"276549183918736542435281697729458361541673829683192754154967238867324915392815476","constraints":["german-whispers"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"rit0vqqp1o","ctcId":3189,"ctcDifficulty":"HARD","title":"One for the New Year","author":"Fool on Hill","rules":"Normal Sudoku Rules apply.\n\nCells a chess king's move apart must contain different digits.\n\nIn a cage, digits may not repeat and sum to the total in the top left corner (if given).\n\nOn a green German Whisper line, adjacent digits differ by at least 5.\n\nDigits separated by a white dot are consecutive.\n\nIf two digits are separated by a black dot, one is twice the other.\n\nNot all dots are necessarily given.","solution":"256438971948751362731926854867514293529863147413279586685142739174395628392687415","constraints":["antiking","cage","german-whispers","kropki"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"b37xfe4xjf","ctcId":3190,"ctcDifficulty":"MEDIUM","title":"Dancing in a ring","author":"Fool on Hill","rules":"Normal Sudoku rules apply.\n\nAdjacent digits on a green German Whisper line differ by at least 5.\n\nDigits on a pink Renban line form a consecutive set with no repeats. The central cross is a single line.\n\nDigits separated by a white dot are consecutive.\n\nWhere digits are separated by a black dot, one is double the other.\n\nNot all dots are given (no negative constraint)","solution":"974851632863927541251634987736189425489562713512743869697218354148395276325476198","constraints":["custom","german-whispers","kropki","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The central cross is a single line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"pz0wrs1heo","ctcId":3191,"ctcDifficulty":"HARD","title":"N is for Naomi","author":"Fool on Hill","rules":"Normal Sudoku rules apply.\n\nOn an orange Dutch Whisper line adjacent digits differ by at least 4.\n\nThe digits on a pink Renban line form a consecutive set with no repeats.\n\nDigits separated by a white dot are consecutive. Where digits are separated by a black dot, one is double the other. (Partial kropki not all possible dots are necessarily given)","solution":"512798643896435712473162859928654371135879426764321985689517234257943168341286597","constraints":["dutch-whispers","kropki","renban"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"zhsltyic9o","ctcId":3192,"ctcDifficulty":"HARD","title":"Ringing the changes","author":"Fool on Hill","rules":"Normal Sudoku rules apply.\n\nAdjacent digits on a green German Whisper line differ by at least 5.\n\nThe digits on a pink Renban line form a consecutive set with no repeats.; The central cross is a single line.\n\nIf two digits are separated by a black dot, one is double the other. Two digits separated by a white dot are consecutive. Not all dots are given.\n\nThis is a companion to my puzzle \"Dancing in a ring\", which is cleaner and more precise. But I am always interested in exploring related ideas. Both puzzles features four of each of four kinds of clue, with the whispers in four-cell squares and a central cross.","solution":"924376518381459672657821943179534826538762194462198357843917265716285439295643781","constraints":["german-whispers","kropki","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"wnw8v9wxre","ctcId":3196,"ctcDifficulty":"HARD","title":"Mayan Ruins","author":"Riffclown","rules":"Normal sudoku rules apply. \n\nAny sequence of five cells along the long purple lines must contain a run of five consecutive digits in any order without repeats. Lines shorter than five cells must contain a run of consecutive digits in any order without repeats.","solution":"389452716645173829712869453256317948974628531138594267421786395863945172597231684","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any sequence of five cells along the long purple lines must contain a run of five consecutive digits in any order without repeats.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"fhfgpia0vy","ctcId":3197,"ctcDifficulty":"HARD","title":"There's Sum-Thing In The Shadows","author":"sujoyku and ChinStrap","rules":"Normal sudoku rules apply.\n\nYin Yang: Shade some cells such that i) all shaded cells are orthogonally connected; ii) all unshaded cells are orthogonally connected; and iii) every 2x2 contains both shaded and unshaded cells.\n\nYin Yang Split Lines: Yin Yang borders split lines into 2 or more segments with the same sum. (If 2 cells are adjacent along the line, they are in the same segment if and only if they have the same shading). Digits may not repeat within a segment. Every line contains shaded and unshaded cells.\n\nSegment Counters: A digit in a circle on a line indicates how many total segments that line has.","solution":"836941257429567813751328649298154736143796528675832194582479361314685972967213485","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Yin Yang Split Lines: Yin Yang borders split lines into 2 or more segments with the same sum. Digits may not repeat within a segment. Every line contains shaded and unshaded cells. Segment Counters: A digit in a circle on a line indicates how many total segments that line has.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5","c6","c7"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9o9qq364b1","ctcId":3198,"ctcDifficulty":"HARD","title":"Rockingham","author":"damo_89","rules":"Normal sudoku rules apply: Place the digits 1 to 9 once each in every row, column, and 3x3 box\n\nMid Loop: Draw a single 1-cell-wide loop of orthogonally connected cells into the grid that does not branch or enter any cell more than once. The loop must pass through all given dots, and all given dots must be in the middle of a straight loop segment (i.e., the distance from a dot to the next turn along the loop must be identical in both directions)\n\nAmbiguous Kropki: Digits separated by a grey dot are consecutive or one is double the other. Adjacent digits on the loop not separated by a dot must NOT be consecutive or where one is double the other","rulesClarified":"Normal sudoku rules apply: place the digits 1 to 9 once each in every row, column and 3x3 box.\n\nMid Loop: draw a single loop of orthogonally connected cells into the grid. The loop is one cell wide, does not branch, and does not enter any cell more than once.\n\nEach grey dot sits on the edge between two neighbouring cells. The loop must pass through every grey dot, across that edge. At each grey dot the loop runs straight: the distance from the dot to the next turn along the loop is the same in both directions.\n\nAmbiguous Kropki: the two digits on either side of a grey dot are consecutive, or one digit is double the other.\n\nAny two digits that are next to each other on the loop, with no grey dot between them, must not be consecutive, and one must not be double the other.","solution":"359726148416583792872941536564217983731869425298354617183475269627198354945632871","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Mid Loop: Draw a single 1-cell-wide loop of orthogonally connected cells into the grid that does not branch or enter any cell more than once. The loop must pass through all given dots, and all given dots must be in the middle of a straight loop segment (i.e., the distance from a dot to the next turn along the loop must be identical in both directions)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Ambiguous Kropki: Digits separated by a grey dot are consecutive or one is double the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4","c5"]}]},{"id":"nozibzvmcc","ctcId":3199,"ctcDifficulty":"HARD","title":"Modularrows","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply.\n\nMODULAR ARROWS - A digit on an arrow counts how many cells in the indicated direction have the same remainder mod-3 as itself, including itself.\n\n(Eg a 4 on an arrow would indicate that exactly four digits (including the 4 itself) in that direction were selected from the digits 1, 4 & 7 (because each of 1,4 & 7 have the same remainder (ie 1) when divided by 3).","rulesClarified":"Normal Sudoku rules apply.\n\nArrows. Each arrow sits in a cell. The digit in that cell is the arrow's count.\n\nThe count covers the cells in the direction the arrow points, starting with the arrow's own cell, which is included. Count the cells in that direction whose digit has the same remainder when divided by 3 as the arrow's digit. The number of such cells must equal the arrow's digit.\n\nOnly the remainder matters. For remainder 1, the matching digits are 1, 4 and 7.\n\nExample: a 4 on an arrow means that exactly four cells in the arrow's direction, the arrow's own cell included, hold a 1, 4 or 7.","solution":"645281937291357684783496521327168495518924376469573218972615843154839762836742159","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"MODULAR ARROWS - A digit on an arrow counts how many cells in the indicated direction have the same remainder mod-3 as itself, including itself.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"yvkb4l2c2j","ctcId":3200,"ctcDifficulty":"VERY HARD","title":"From A to Zeta : A Zodiac Puzzle","author":"zetamath and friends","rules":"Normal sudoku rules apply.\n\nEach letter from ABCDEFGHZ stands for a different digit from 1-9.  Each labeled gray letter cell in the grid contains that digit.  Other clues in the grid are standard killer, little killer, quadruples, skyscraper, or numbered rooms clues.  Details below.\n\nWhere a ? is used, it always represents a two digit total.  That is, the leading question mark is never 0.\n\nDigits in cages sum to the total given.  Digits cannot repeat within cages.\n\nDigits along indicated diagonals have the indicated sum.  Digits may repeat along such diagonals.\n\nCircles within the grid are quadruples.  The indicated digit appears in at least one of the four surrounding cells.\n\nDigits with a door are numbered rooms.  The indicated digit appears a number of cells into that row or column given by the first number in that row/column.\n\nDigits with a building are skyscrapers.  They indicate how many digits are seen from the perspective of the clue if digits are only seen if they are the highest digit encountered so far.","solution":"356824917497516823812937546671259384245783691983461275539178462128645739764392158","constraints":["cage","custom","little-killer","quadruple","skyscraper"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each letter from ABCDEFGHZ stands for a different digit from 1-9. Each labeled gray letter cell in the grid contains that digit. Where a ? is used, it always represents a two digit total. The indicated digit appears a number of cells into that row or column given by the first number in that row/column.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c6","c15"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]},{"slug":"skyscraper","type":"skyscraper","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c17"]}]},{"id":"gssntzkary","ctcId":3201,"ctcDifficulty":"VERY HARD","title":"The Lost Killer Islands","author":"Patrick Junke","rules":"Normal Sudoku rules apply, matey.\nCells be either 'sea' or 'land'. No 2x2 block can be filled with just sea or land. All sea cells be connected orthogonally like a map. In that way, cells with arrows are like dead ends, that is, sea cells that point to the only other sea cell they touch. Savvy?\nLand cells form 'islands' that don't touch each other, even diagonally, comprising four orthogonally adjacent rugged cells. And each island has a treasure of its own, with four different cells that add up to 14 doubloons.\nX's mark cells that add up to 10 doubloons, and red dots mark them that are worth 12.\nShiver me timbers! : all arrows, X's, and red dots be provided!\nSo hoist the colors and get solving! Or ye'll be walkin' the plank!\nOh, remember also, matey, if ye see an X, it means the two cells be of the same kind, either both saltwater or both solid ground.","solution":"895243167341765892672189354927418635568327941413596278784631529239854716156972483","constraints":["XV","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cells be either 'sea' or 'land'. No 2x2 block can be filled with just sea or land. All sea cells be connected orthogonally like a map. In that way, cells with arrows are like dead ends, that is, sea cells that point to the only other sea cell they touch. Land cells form 'islands' that don't touch each other, even diagonally, comprising four orthogonally adjacent rugged cells. And each island has a treasure of its own, with four different cells that add up to 14 doubloons. X's mark cells that add up to 10 doubloons, and red dots mark them that are worth 12. Shiver me timbers! : all arrows, X's, and red dots be provided! Oh, remember also, matey, if ye see an X, it means the two cells be of the same kind, either both saltwater or both solid ground.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c7","c8","c9","c10","c13"]}]},{"id":"udyn0tghcs","ctcId":3202,"ctcDifficulty":"HARD","title":"RAT RUN 34: On Reflection","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, share cells, or pass through any thick maze walls.\n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBLACKCURRANTS: If a blackcurrant sits between two digits, one is double the other.\n\nREDCURRANTS: If a redcurrant sits between two digits, one is odd and the other is even.\n\nGRAPES: If a grape sits between two digits, they have a difference of at least 5.\n\nVIDEO CAMERAS: The digit on a grey camera indicates the total SUM of the digits in any visited cells that the camera's lens points towards (before a wall is reached, which blocks vision.) A video camera cell itself may not be entered.\n\nTEST CONSTRAINT: In this experiment, all of the low digits in the grid (1s, 2s and 3s) must be visited, but none of the high digits (7s, 8s, and 9s) may be visited. The two rats' paths must be perfect reflections of each other across the positive diagonal (marked with a thin pink line).","solution":"724598316395216784861347952172964835658173429439825167247681593586439271913752648","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, share cells, or pass through any thick maze walls. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. REDCURRANTS: If a redcurrant sits between two digits, one is odd and the other is even. GRAPES: If a grape sits between two digits, they have a difference of at least 5. VIDEO CAMERAS: The digit on a grey camera indicates the total SUM of the digits in any visited cells that the camera's lens points towards (before a wall is reached, which blocks vision.) A video camera cell itself may not be entered. TEST CONSTRAINT: In this experiment, all of the low digits in the grid (1s, 2s and 3s) must be visited, but none of the high digits (7s, 8s, and 9s) may be visited. The two rats' paths must be perfect reflections of each other across the positive diagonal (marked with a thin pink line).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c6","c7","c8","c9","c10","c11"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"5yvmd3yk1m","ctcId":3203,"ctcDifficulty":"MEDIUM","title":"Shh..eep Jo-King","author":"olima","rules":"Normal Sudoku rules apply. Digits a King's move, as in chess, away must be different. Adjacent digits on a green line differ by at least 5. Purple lines contain a set of distinct consecutive digits in any order. Black dots indicate places where one digit is double the other, white dots indicate consecutive digits. Not all dots are necessarily shown.","solution":"852943761976581432314726598493617825285439617167258349741862953629375184538194276","constraints":["antiking","german-whispers","kropki","renban"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"kvqrdqgrr2","ctcId":3204,"ctcDifficulty":"MEDIUM","title":"Not So Simple Miracle","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Two adjacent digits on a purple line must have consecutive values. Two cells separated by a single knight's move (in chess) cannot contain the same digit.","solution":"261594837594837261837261594483726159726159483159483726615948372948372615372615948","constraints":["antiknight","custom"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Two adjacent digits on a purple line must have consecutive values.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"cg5wlayzuj","ctcId":3206,"ctcDifficulty":"VERY HARD","title":"Circus Maximus","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nDigits along a pink line must form a non-repeating group of consecutive digits, but they may appear in any order along the line. \n\nUsing red, green, and blue, color all circles such that:\n-Orthogonally adjacent circles are different colors.\n-The digit inside a circle appears that many times in circles of that color.","solution":"251487369638219754794653218329164875175938642486572193912846537543721986867395421","constraints":["custom","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"-Orthogonally adjacent circles are different colors. -The digit inside a circle appears that many times in circles of that color.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"hn24wxybkz","ctcId":3207,"ctcDifficulty":"MEDIUM","title":"Williwaw","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nBox borders divide each blue line into segments with the same sum.","solution":"584312976629758431137964258715436892863291547492875163276149385958623714341587629","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"2hk0wen7pj","ctcId":3208,"ctcDifficulty":"VERY HARD","title":"Hijinks","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAlong each line, the hexagon is referred to as 'position 1', the next cell along is 'position 2' and so on. Digits never repeat along a line.\n\nPURPLE LINES are thermos. Digits along thermos always increase as you move away from the hexagon. \nEg: 24579 would be a valid thermo.\n\nTURQUOISE LINES are index lines. On an index line, the digit in the Nth position indicates the position along the line where the digit N appears.\nEg: 32154 would be a valid index line. The 3 in the 1st position indicates there is a 1 in the 3rd position, and so on.\n\nLIGHT BROWN LINES are hitlines. Digits can be in any order on a hitline, but the digit in the hexagon  indicates how many digits along the hitline match their position number. \nEg: A hitline might read 27315. The 2 on the hexagon indicates that exactly two digits match their position number; in this case, 3 in the 3rd position and 5 in the 5th position.\n\nSHENANIGANS:\nOne of the digits 1-9 (to be determined) is the 'mischief digit.' Every line follows one (AND ONLY ONE) of the three line rules above, but any line containing the mischief digit has been painted the wrong colour. (Any line NOT containing the mischief digit is the correct colour.)","solution":"215479638378126945469358721854297316926813574137564289781935462692741853543682197","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits never repeat along a line. On an index line, the digit in the Nth position indicates the position along the line where the digit N appears. Digits can be in any order on a hitline, but the digit in the hexagon  indicates how many digits along the hitline match their position number. Every line follows one (AND ONLY ONE) of the three line rules above, but any line containing the mischief digit has been painted the wrong colour.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c8","c12","c17"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"g63hqgbauq","ctcId":3209,"ctcDifficulty":"VERY HARD","title":"There's a Wolf Under There","author":"ViKingPrime","rules":"Normal SUDOKU rules apply.\n\nCells along a pink RENBAN line form a set of consecutive, non-repeating values in any order.\n\nBlack KROPKI dots separate two cells where one is double the value of the other [1:2].\n\nPlace WEREWOLF cells into the grid so that there is exactly one Werewolf cell in each row, column and box; each Werewolf cell must contain the digit that matches its Box number (counted from left-to-right, top-to-bottom); the value of a Werewolf cell is unique from other Werewolf cells and is selected from the remaining digits within its box (e.g. if the digit 1 in Box 1 has a value of 4, the digit 2 in Box 2 could have neither a value of 2 nor 4).","solution":"123654897758932416496871523645397182871526349932148765219785634387469251564213978","constraints":["custom","kropki","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Place WEREWOLF cells into the grid so that there is exactly one Werewolf cell in each row, column and box; each Werewolf cell must contain the digit that matches its Box number (counted from left-to-right, top-to-bottom); the value of a Werewolf cell is unique from other Werewolf cells and is selected from the remaining digits within its box (e.g. if the digit 1 in Box 1 has a value of 4, the digit 2 in Box 2 could have neither a value of 2 nor 4).","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Black KROPKI dots separate two cells where one is double the value of the other [1:2].","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Cells along a pink RENBAN line form a set of consecutive, non-repeating values in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"s64txn1v6l","ctcId":3210,"ctcDifficulty":"HARD","title":"RAT RUN 35: Locked Out","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT:\nFinkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, share cells, or pass through any thick maze walls.\n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBLACKCURRANTS: If two digits are joined by a blackcurrant, one is double the other.\n\nREDCURRANTS: If two digits are joined by a redcurrant, one is odd and the other is even.\n\nTELEPORTS: Entering a teleport will cause a rat to be instantly transported to the matching coloured teleport. Matching teleports always have identical digits, but teleports that don't match always have different digits.\n\nTEST CONSTRAINT: In this experiment, for any path segment connecting two teleports, no other cells along the segment may equal either of the two teleport digits at its ends, or lie numerically between them. Eg: if a path segment joins two teleports with the digits 3 and 6, then the other digits along this path segment may not include a 3, 4, 5 or 6.","solution":"359126478247895361186734529795642183834917652612358947423581796978463215561279834","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, share cells, or pass through any thick maze walls. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. REDCURRANTS: If two digits are joined by a redcurrant, one is odd and the other is even. TELEPORTS: Entering a teleport will cause a rat to be instantly transported to the matching coloured teleport. Matching teleports always have identical digits, but teleports that don't match always have different digits. TEST CONSTRAINT: In this experiment, for any path segment connecting two teleports, no other cells along the segment may equal either of the two teleport digits at its ends, or lie numerically between them.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c7","c8","c9","c10"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"7aatbjdjz8","ctcId":3211,"ctcDifficulty":"VERY HARD","title":"Simple as AB","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nClues outside the grid indicate the sum of the first X digits, where X is the first seen digit.\nA and B represent two numbers to be determined by the solver.\nAny three adjacent digits along a teal modular line have different residues modulo 3 (i.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}).","solution":"391462758284975163765813294913746582548291376627538419839154627452687931176329845","constraints":["custom","modular-line","x-sum"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A and B represent two numbers to be determined by the solver.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7m7iluxxil","ctcId":3212,"ctcDifficulty":"HARD","title":"The Triple Crown","author":"Kennet’s Dad","rules":"Normal sudoku rules apply. \nDigits cannot repeat on the thin blue main diagonal. \nCells that appear in the same relative position of their 3x3 box may not contain the same digit. So, for example, r5c1 (the middle left cell of its 3x3 box) could not contain the same digit as r8c7 (the middle left cell of its 3x3 box.) \nDigits in a cage sum to the small clue in the cage’s top left corner. \nDigits on a pink line form a set of non-repeating, consecutive digits in any order. \nThe 3x3 box borders divide the thick blue lines into segments; each segment along an individual line must have the same sum.","solution":"452367198697185423183492567725843619869571342341629875574236981218954736936718254","constraints":["cage","diagonal","disjoint-groups","region-sum-line","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"disjoint-groups","type":"disjoint-groups","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"kbrkvktac9","ctcId":3214,"ctcDifficulty":"HARD","title":"Douro","author":"Xenonetix","rules":"Normal sudoku rules apply. \n\nThere's a one-cell wide 'river' of orthogonally-connected cells snaking from R9C9 to R1C2 without branching or touching itself orthogonally (but it may touch diagonally). Digits along the 'river' differ by at least 5. All remaining cells are 'land'.\n\n'Bridges' (=) only cross single 'river' cells, and are the sum of the two 'land' cells at each end of the 'bridge' (e.g. if the river cell was a 5, the two land cells could be 2&3 or 1&4). Diagonal 'bridges' only cross 'river' corners. \n\nPlacing a correct digit will clear fog in its cell, and may also clear fog in other cells.","solution":"261375498758194632943628175829467513374951286615283947496832751137546829582719364","fogLight":"R5C4,R6C5,R6C6","constraints":["custom","fog","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"There's a one-cell wide 'river' of orthogonally-connected cells snaking from R9C9 to R1C2 without branching or touching itself orthogonally (but it may touch diagonally). 'Bridges' (=) only cross single 'river' cells, and are the sum of the two 'land' cells at each end of the 'bridge' (e.g. if the river cell was a 5, the two land cells could be 2&3 or 1&4). Diagonal 'bridges' only cross 'river' corners.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5","c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"76p1fymv2s","ctcId":3215,"ctcDifficulty":"HARD","title":"Four Leaf Clover","author":"James Kopp","rules":"Normal sudoku rules apply. Any sequence of four cells along the thinner purple lines must contain a run of four consecutive digits in any order without repeats. The thicker red line contains a set of consecutive digits in any order.\nCells separated by an X sum to ten.\nCells separated by a V sum to five.\nNot all possible Xs and Vs are necessarily given.","solution":"732916458598473126416582397267394581145867239389251674623748915854139762971625843","constraints":["XV","custom","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any sequence of four cells along the thinner purple lines must contain a run of four consecutive digits in any order without repeats.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9q82og2xas","ctcId":3216,"ctcDifficulty":"VERY HARD","title":"Empty Vessels","author":"Die Hard","rules":"Normal sudoku rules apply. If the digit N appears in any of the four cells adjacent to a circle then it appears exactly N times adjacent to a circle across the grid. The 3x3 box borders divide blue lines into segments; each segment along an individual line has the same sum. Adjacent digits on red lines alternate between odd and even. Adjacent digits on green lines differ by at least 5. Digits on a pink line form a non-repeating consecutive set in any order.","solution":"519687342428135976367249185741856293286391754935724861193468527652973418874512639","constraints":["counting-circle","custom","german-whispers","region-sum-line","renban"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent digits on red lines alternate between odd and even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"rwx8a9tkdt","ctcId":3218,"ctcDifficulty":"HARD","title":"Peer Pressure","author":"Cane_Puzzles","rules":"Normal sudoku rules apply. \nCells separated by a single knight's move (in chess) cannot contain the same digit. \nAlong a thermometer digits must increase from the bulb end.  \nEach purple line contains a set of non-repeating, consecutive digits in any order.","solution":"579846312426317589813529746981762435267435198354981627135698274692174853748253961","constraints":["antiknight","renban","thermometer"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"qhcougnkg6","ctcId":3219,"ctcDifficulty":"MEDIUM","title":"Snarky Puppy - Xavi","author":"Aron Lidé (Aspartagcus)","rules":"This sudoku is a tribute to the band Snarky Puppy and their song Xavi.\n\nSudoku: Fill each row, column and region with the digits 1-9.\nGerman Whispers: Neighboring digits along the line must have a difference of at least 5.\nXV: Digits separated by an X sum to 10. Digits separated by a V sum to 5.\nCipher: Each letter (except X and V) corresponds to a unique digit. A cell with a letter in it contains its corresponding digit.\nFog: Some cells are covered in fog, and will be discovered when neighboring digits are filled in.","solution":"265938174193574628874261593732185469618349752459627831946852317381796245527413986","fogLight":"R8C2,R4C3,R3C4,R1C6,R2C8,R5C8,R8C5,R7C6,R6C7,R4C9,R6C1,R5C2,R2C5,R7C1,R8C1,R9C1,R9C2,R9C3,R9C4,R9C5,R8C6,R7C7,R6C8,R5C9,R6C9,R7C8,R8C7,R9C6,R8C4,R8C3,R7C3,R7C2,R6C2,R6C3,R5C3,R5C4,R6C4,R7C4,R7C5,R6C5,R6C6,R5C6,R4C6,R4C5,R4C4,R5C5,R5C1,R4C1,R4C2,R3C2,R3C3,R2C3,R2C4,R1C4,R1C5,R1C7,R2C7,R2C6,R3C6,R3C5,R3C7,R4C7,R5C7,R4C8,R3C8,R3C9,R2C9,R1C9,R1C8,R3C1,R2C2,R1C3,R9C7,R8C8,R7C9","constraints":["XV","custom","fog","german-whispers"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cipher: Each letter (except X and V) corresponds to a unique digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"jewe3tzhy9","ctcId":3220,"ctcDifficulty":"VERY HARD","title":"RAT RUN 36: Alternating Currant","author":"Marty Sears","rules":"SOMEDOKU: Fill the grid with the digits 1-9 so that each row N and column N contain exactly N distinct digits, with the rest of the cells in that row / column being repeats. For example, only 3 distinct digits appear in row 3, and any of these can be repeated multiple times in order to fill the row.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. The paths may only intersect at the cupcake cell.\n\nAs well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell.\n\nBLACKCURRANTS: If a blackcurrant sits between two digits, one is double the other.\n\nREDCURRANTS: If a redcurrant sits between two digits, one is odd and the other is even.\n\nGRAPES: If a grape sits between two digits, they have a difference of at least 5.\n\nCAGES: Digits may not repeat within a cage. Each cage has the same total, to be deduced. If the digit on a cage's electricity symbol is 5 or higher, the cage may not be entered.\n\nTEST CONSTRAINT: In this experiment, both rats visit the same number of cells. Any pair of cells (one on each path) that are an equal distance from the cupcake cell sum to the digit on the cupcake cell. Thus, both paths combined form a valid 'zipper' line, with Finkz and Phinx at the ends and the cupcake cell in the middle.","solution":"222222222227222277212555511227556665216552144227463338216321489217496553217384956","constraints":["cage","custom","kropki","zipper-line"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"SOMEDOKU: Fill the grid with the digits 1-9 so that each row N and column N contain exactly N distinct digits, with the rest of the cells in that row / column being repeats. AIM OF EXPERIMENT: Finkz and Phinx must both reach the cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. As well as moving orthogonally, they may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through a round wall-spot on the corner of a cell. REDCURRANTS: If a redcurrant sits between two digits, one is odd and the other is even. GRAPES: If a grape sits between two digits, they have a difference of at least 5. Each cage has the same total, to be deduced. If the digit on a cage's electricity symbol is 5 or higher, the cage may not be entered. TEST CONSTRAINT: In this experiment, both rats visit the same number of cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c3","c4","c6","c8","c9","c11","c12","c13"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]}]},{"id":"hq2d86hgi0","ctcId":3221,"ctcDifficulty":"HARD","title":"Synergy","author":"Michael Lefkowitz","rules":"Normal Sudoku rules apply. All arrows act as both modular arrows and entropic arrows.\n\nMODULAR ARROWS - A digit on an arrow counts how many cells in the indicated direction have the same remainder mod-3 as itself, including itself.\n\nENTROPIC ARROWS - A digit on an arrow counts how many cells in the indicated direction are in the same entropic group (123, 456, 789) as itself, including itself.","solution":"485739162691528437327416895913264758578391624246875319864953271739182546152647983","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"MODULAR ARROWS - A digit on an arrow counts how many cells in the indicated direction have the same remainder mod-3 as itself, including itself. ENTROPIC ARROWS - A digit on an arrow counts how many cells in the indicated direction are in the same entropic group (123, 456, 789) as itself, including itself.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"yp5cwjsu5m","ctcId":3222,"ctcDifficulty":"MEDIUM","title":"African Daisies","author":"Antiknight","rules":"Normal Sudoku rules apply. Lines in the puzzle act as both Zipper lines and Nabner lines. ie On these lines, digits at equal distance from the lavender central cell must sum to the digit in that central cell. Additionally, along each gold 'Nabner' line, no two digits may be consecutive, and digits may not repeat along the line.","solution":"273946185186275934495138267359827416862314579741659823524761398937482651618593742","constraints":["nabner-line","zipper-line"],"constraintFacts":[{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"yl0n45rfll","ctcId":3223,"ctcDifficulty":"VERY HARD","title":"Yin Yang Doubler Uniqueness","author":"Oddlyeven","rules":"Rules: Normal Sudoku rules apply. Put the digits 1 to 9 once each into every row, column and box.\n\nYin Yang Doublers: Shade some cells in the grid such that all shaded cells are orthoganally connected and all unshaded cells are orthogonally connected. No 2x2 may be all shaded or all unshaded. A shaded cell has a value equal to twice its digit. An unshaded cell has a value equal to twice its digit minus one (double the digit first, then subtract one).\n\nUniqueness: On each of the constraints below, values do not repeat anywhere in the puzzle. For example, if there is a shaded 5 (value 10) on a renban, shaded 5 can't appear anywhere else on a renban, but unshaded 5 could because it has a value of 9.\n\nRenban: Values on a purple line form a set of consecutive numbers with no repeats.\n\nArrows: Values along an arrow sum the value in that arrow's circle.\n\nX: Two cells joined by an X have values that sum to 10.\n\nBlack Dots: Two cells joined by a black dot have values where one is double the other.","solution":"769842513851736924342951786137269845526184379984375261213697458478513692695428137","constraints":["XV","arrow","custom","kropki","renban","yin-yang"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"X: Two cells joined by an X have values that sum to 10.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c11"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A shaded cell has a value equal to twice its digit. An unshaded cell has a value equal to twice its digit minus one (double the digit first, then subtract one). Uniqueness: On each of the constraints below, values do not repeat anywhere in the puzzle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c7"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Black Dots: Two cells joined by a black dot have values where one is double the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Renban: Values on a purple line form a set of consecutive numbers with no repeats.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c9"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"4wlunbtlaq","ctcId":3225,"ctcDifficulty":"HARD","title":"Something Stupid","author":"Marty Sears","rules":"SHUFFLED SOMEDOKU:\nEvery gold circle contains a different digit. In any row or column, its circle indicates the number of distinct digits that appears in that row or column. Any of these digits can be repeated any number of times in order to fill the row / column. Eg: one particular row has a circle containing a 3, meaning that row only contains three distinct digits - a valid example would be 173777131.\n\nFOG:\nEntering a correct digit may clear fog somewhere in the grid. No guessing is necessary.\n\nZIPPER LINES:\nAlong a lavender line, digits that are the same distance from the central spot sum to the digit on that central spot.\n\nGERMAN WHISPERS:\nAdjacent digits along a green line have a difference of at least 5.\n\nRED DOTS:\nIf a red dot sits between two digits, one is odd and the other is even.\n\nBLACK DOTS:\nIf a black dot sits between two digits, one is double the other.","solution":"393919191965417119389725164927511159112122121936128147111111111918423179194916194","fogLight":"R1C1,R9C1,R9C9,R1C9,R2C2,R3C3,R4C4,R5C5,R6C6,R7C7,R8C8,R8C2,R7C3,R6C4,R4C6,R3C7,R2C8","constraints":["custom","fog","german-whispers","kropki","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every gold circle contains a different digit. In any row or column, its circle indicates the number of distinct digits that appears in that row or column. If a red dot sits between two digits, one is odd and the other is even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c14"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c16"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"c325ibxs31","ctcId":3226,"ctcDifficulty":"MEDIUM","title":"Factor Map","author":null,"rules":"Normal sudoku rules apply. Within cages, digits cannot repeat. Each cage has a value equal to the sum of all the digits it contains. Color each cage 1 of 4 colors. Cages of the same color cannot share sides, though they may touch corner-to-corner. All cages with the same color have sums whose prime factorizations contain the same set of prime factors. [E.g. If a red cage is 20 = 2x2x5, then all other red cages must have a prime factorization of 2^X*5^Y. For example, 10, 20, 40, 50, 80, 100, etc could all be valid. 25 would not be valid (no 2's). 30 would not be valid (2x3x5 has a 3). Any other colored cage could not have a 2 nor 5 in its prime factorizations.]","solution":"523479186491638725768125934217396458934581267856742391182964573675213849349857612","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Color each cage 1 of 4 colors. Cages of the same color cannot share sides, though they may touch corner-to-corner. All cages with the same color have sums whose prime factorizations contain the same set of prime factors.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6"]}]},{"id":"9q8gyvfhpm","ctcId":3227,"ctcDifficulty":"HARD","title":"Blind Date","author":"Ul-Rhymm","rules":"Standard sudoku rules apply: each digit, 1-9, appears exactly once in each row, column, and 3x3 region.\n\nIn cages, digits do not repeat and sum to a value that must be deduced. Each cage shares a side with exactly one other cage with the same sum.","solution":"382491657671523894459768132827314965914652378563879241798235416235146789146987523","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each cage shares a side with exactly one other cage with the same sum.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"c2yc4u9yl1","ctcId":3228,"ctcDifficulty":"MEDIUM","title":"Eye of the Storm","author":"Ul-Rhymm","rules":"Standard Sudoku: each digit, 1-9, appears exactly once in each row, column, and 3x3 region. \n\nNonconsecutive: Cells that are orthogonally adjacent cannot contain consecutive digits. \n\nPalindromes: Digits on a grey line read the same forwards and backwards. \n\nFog: correctly placing the first digits in the grid will reveal the hidden cell in the Eye of the Storm.","solution":"158264739726931485493758162269485317831627594574193826947316258615842973382579641","fogLight":"R1C1,R1C2,R1C3,R1C4,R1C5,R1C6,R1C7,R1C8,R1C9,R2C8,R2C7,R2C6,R2C5,R3C5,R3C4,R3C3,R3C2,R2C2,R2C1,R3C1,R3C6,R3C7,R3C8,R3C9,R2C4,R2C3,R4C1,R4C2,R4C3,R4C4,R4C5,R4C6,R4C7,R4C8,R2C9,R4C9,R5C9,R6C9,R7C9,R7C8,R8C8,R9C8,R9C7,R8C7,R8C6,R7C6,R6C6,R5C6,R6C8,R5C8,R5C7,R6C7,R7C7,R8C9,R9C6,R9C5,R9C4,R9C3,R9C2,R9C1,R8C3,R8C4,R8C5,R8C2,R8C1,R7C3,R7C4,R7C5,R7C2,R7C1,R6C2,R6C3,R6C4,R6C5,R6C1,R5C1,R5C2,R5C3,R5C4,R9C9","constraints":["fog","non-consecutive","palindrome"],"constraintFacts":[{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9fjvy1dcyo","ctcId":3229,"ctcDifficulty":"VERY HARD","title":"How to slice a sandwich","author":"Ul-Rhymm","rules":"Sudoku: Each digit, 1-9, appears exactly once in each row, column, and 3x3 box.\n\nRenban: Each pink line contains a set of consecutive, non-repeating digits, in any order.\n\nSandwich: Digits outside the grid indicate the sum of all the digits sandwiched between the 1 and 9 in the row or column.","solution":"546283917173694582829751463958127634714365298362948751285439176437516829691872345","constraints":["renban","sandwich"],"constraintFacts":[{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"wvau08bs7u","ctcId":3230,"ctcDifficulty":"HARD","title":"Wrapped","author":"Sotehr","rules":"Sudoku: Normal Sudoku rules apply; place the digits 1-9 once in every row, column, and 3x3 box.\n\nRenban Line: Solid pink lines contain an unordered set of consecutive values, without repeats.\n\nGerman Whisper Line: Hollow green lines have adjacent cells with a minimum difference of 5.\n\nRegion Sum Line: Dashed blue lines are divided by 3x3 box borders into segments with of equal sums.\n\nBlack Kropki: Cells separated by a black dot have one digit double the other.\n\nWhite Kropki: Cells separated by a white dot have consecutive digits.","rulesClarified":"Normal Sudoku rules apply: place the digits 1-9 once in every row, column and 3x3 box.\n\nSolid pink lines are renbans: the digits on a pink line are consecutive values, with no repeats. Their order along the line is not fixed.\n\nHollow green lines are German whisper lines: any two cells next to each other along a green line differ by at least 5.\n\nDashed blue lines are region sum lines. The 3x3 box borders cut each blue line into segments. Every segment of that line has the same digit total. The totals are not given.\n\nA black dot sits between two cells: one digit is double the other.\n\nA white dot sits between two cells: the two digits are consecutive.","solution":"735941826469382751812567493694215378523478169187693542978124635346859217251736984","constraints":["german-whispers","kropki","region-sum-line","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"oiqfym9ehw","ctcId":3231,"ctcDifficulty":"MEDIUM","title":"This Is Sparta!","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nThe product of the digits along a hollow orange line is equal to 300.\nEvery set of three sequential digits along a teal modular line contains digits with three different remainders when divided by 3. (I.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}).\nAdditionally, the total sum of the modular lines is equal to 300.","solution":"143267598657983214298415736576129843481536927932748165814652379765391482329874651","constraints":["custom","modular-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The product of the digits along a hollow orange line is equal to 300. Additionally, the total sum of the modular lines is equal to 300.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"so6t07h4yh","ctcId":3232,"ctcDifficulty":"HARD","title":"Orientation","author":"zetamath","rules":"Normal sudoku rules apply.  \n\nRossini: Arrows indicate the direction in which the first three digits in that row or column (nearest the arrow) increase or decrease. For instance, r7c1 < r7c2 < r7c3. If no arrow appears adjacent to a row or column, the three nearest digits must not be in increasing or decreasing order (that is, the central digit must be the highest or lowest).","solution":"293567418158342976467891532926175384345928167871436295789214653612753849534689721","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Rossini: Arrows indicate the direction in which the first three digits in that row or column (nearest the arrow) increase or decrease. If no arrow appears adjacent to a row or column, the three nearest digits must not be in increasing or decreasing order (that is, the central digit must be the highest or lowest).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"ceyzcgb9os","ctcId":3233,"ctcDifficulty":"HARD","title":"RAT RUN: One Year Earlier","author":"Marty Sears","rules":"For the final preliminary 'free-roam' trial, the nine shortlisted rats were placed in a 9x9 space, and their movements were observed and recorded. Each of the digits 1-9 appeared in each row and column.\n\nOBSERVATIONS:\n\n• Every cell in the grid was visited, exactly once.\n• No rat's path contained any repeated digits.\n• No rat chose to move diagonally at any point.\n• Every 2x2 area was visited by at least 2 rats.\n• No two rats started on the same digit.\n• No two rats ended on the same digit.\n• All blackcurrants and redcurrants were eaten.\n• No grapes were eaten.\n\nBLACKCURRANTS:\nIf a blackcurrant sits between two digits, one is double the other.\n\nREDCURRANTS:\nIf a redcurrant sits between two digits, one is odd and the other is even.\n\nGRAPES:\nIf a grape sits between two digits, they have a difference of at least 5.","solution":"951348726873694251765432198394127865642815973517263489236981547128579634489756312","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"• Every cell in the grid was visited, exactly once. • No rat's path contained any repeated digits. • No rat chose to move diagonally at any point. • Every 2x2 area was visited by at least 2 rats. • No two rats started on the same digit. • No two rats ended on the same digit. • All blackcurrants and redcurrants were eaten. • No grapes were eaten. If a redcurrant sits between two digits, one is odd and the other is even. If a grape sits between two digits, they have a difference of at least 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6","c7","c8","c9","c10","c11","c15","c17"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]}]},{"id":"4jw7hz9rd1","ctcId":3234,"ctcDifficulty":"HARD","title":"Calm Construction","author":"oskode","rules":"Sudoku: Fill all rows, columns and marked 3x3 boxes with the digits 1-9 without any repeats.\n\nChaos Construction: Divide the grid into 9 additional regions of 9 orthogonally connected cells. Each extra region contain the digits 1-9 without repeats.\n\nCircles: A digit in a circle indicates how many cells (including itself) overlap between its 3x3 box and its additional region.","solution":"428679153739521648615483297951362784246758931387194562562837419894216375173945826","constraints":["custom","region"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Chaos Construction: Divide the grid into 9 additional regions of 9 orthogonally connected cells. Circles: A digit in a circle indicates how many cells (including itself) overlap between its 3x3 box and its additional region.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"jpjbe0lid4","ctcId":3235,"ctcDifficulty":"MEDIUM","title":"Odd Way to Even Out","author":"oskode","rules":"Sudoku: Fill all rows, columns and marked 3x3 regions with the digits 1-9 without any repeats.\n\nKiller Cages: Digits in a cage do not repeat and sum to the number given in its upper left corner.\n\nQuadruples: Cells surrounding a white circle must contain at least one copy of the digits within the circle.","solution":"578631492634892175291547368825916743963274581417358926189725634356489217742163859","constraints":["cage","quadruple"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"bs3y9058h7","ctcId":3236,"ctcDifficulty":"VERY HARD","title":"Count Me In","author":"oskode","rules":"Sudoku: Normal sudoku rules apply. ie Fill all rows, columns and marked 3x3 regions with the digits 1-9 without any repeats.\n\nCounting Loop: Draw a 1-cell wide loop in the grid, passing through the centers of some orthogonally adjacent cells. The loop does not touch itself, not even diagonally. A digit on the loop indicates how many times that digit appears on the loop.\n\nArrows: A digit in a cell containing an arrow counts how many loop cells are in the indicated direction (not including the cell with the arrow). Multiple arrows in the same cell counts loop cells independent of one another. (So, for example, if r6c4 is a 3 then there are three loop cells to its north and three loop cells to its north east).","solution":"284531796317689254659274183726893541841752369935146827492315678573468912168927435","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Counting Loop: Draw a 1-cell wide loop in the grid, passing through the centers of some orthogonally adjacent cells. The loop does not touch itself, not even diagonally. A digit on the loop indicates how many times that digit appears on the loop. Arrows: A digit in a cell containing an arrow counts how many loop cells are in the indicated direction (not including the cell with the arrow).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]}]},{"id":"ayk7228tr8","ctcId":3237,"ctcDifficulty":"VERY HARD","title":"One Of The Two","author":"oskode","rules":"I placed a bunch of constraints in my puzzle but I was stupid enough to use the same colors for similar looking constraints... Can you help me check if the puzzle is still solvable? I know that:\n\nNormal sudoku rules apply.\n\nOne of the cages contains one 5, the other’s digits sum to 15\n\nOne of the red lines contains a set of distinct consecutive digits in any order, while adjacent digits on the other line must differ by at least 5.\n\nAlong one of the dark blue lines, digits read the same from either direction, while any 3 adjacent digits along the other line must have different remainders when divided by 3.\n\nAlong one of the light blue diagonals no digit is repeated, while the digits in the other one sums to the same total in every region it enters.\n\nDigits along one of the grey lines must increase from the digit in the bulb, while digits on the other line must sum to the digit in the bulb.\n\nValues of digits along one green line must lie strictly inbetween the values of the digits in the attached bulbs , while digits along the other must sum to the same value as the digits in the attached bulbs.\n\nOne of the orange dots separate two consecutive digits, while he other one separates digits in a 1:2 ratio.\n\nOne of the Y’s separate digits that sum to 5, the other Y separate digits that sum to 10\n\nOne orientation of the grey triangles contain even digits, the other orientation contain odd digits.","solution":"698325714312947856745168293931586427874239561526714389269873145487651932153492678","constraints":["XV","arrow","between-line","cage","custom","diagonal","even","german-whispers","kropki","modular-line","odd","palindrome","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"One of the Y’s separate digits that sum to 5, the other Y separate digits that sum to 10","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"One of the cages contains one 5, the other’s digits sum to 15","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"One of the cages contains one 5, the other’s digits sum to 15 One of the red lines contains a set of distinct consecutive digits in any order, while adjacent digits on the other line must differ by at least 5. Along one of the dark blue lines, digits read the same from either direction, while any 3 adjacent digits along the other line must have different remainders when divided by 3. Along one of the light blue diagonals no digit is repeated, while the digits in the other one sums to the same total in every region it enters. Digits along one of the grey lines must increase from the digit in the bulb, while digits on the other line must sum to the digit in the bulb. Values of digits along one green line must lie strictly inbetween the values of the digits in the attached bulbs , while digits along the other must sum to the same value as the digits in the attached bulbs. One orientation of the grey triangles contain even digits, the other orientation contain odd digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c7","c8","c9","c10","c13"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"7iiikykquy","ctcId":3238,"ctcDifficulty":"MEDIUM","title":"It's All Basic Calculations","author":"oskode","rules":"Normal sudoku rules apply. \nA letter indicates the same whole number whenever it appears (eg the letter B could represent the number 10 throughout the puzzle); and each letter represents a different number. \nDigits in a cage sum to the total in the cage’s upper left corner. \nRed numbers outside the grid indicate the sum of all digits along the indicated diagonal. \nBlack numbers outside the grid indicate the sum of the first N digits in that row or column (counting from the direction of the clue), where N is the digit in the first cell in that row or column (closest to the clue.)","solution":"184763259739582461562149783943276815621835974875491326456327198298614537317958642","constraints":["cage","custom","little-killer","x-sum"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A letter indicates the same whole number whenever it appears (eg the letter B could represent the number 10 throughout the puzzle); and each letter represents a different number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"190rj9itty","ctcId":3239,"ctcDifficulty":"HARD","title":"Renban Squares","author":"James Kopp","rules":"Normal sudoku rules apply. \nPlacing a correct digit may clear fog somewhere in the grid – no guessing is required. \nThe digits along a purple line contain consecutive digits in any order without repeats. Each purple line is in the shape of a square. Similarly, the digits along a grey line contain consecutive digits in any order without repeats. Each grey line is also in the shape of a square. \nCells separated by an X sum to 10 and, in cells separated by a black dot, one digit is double the other.","rulesClarified":"Normal sudoku rules apply.\n\nPlacing a correct digit may clear fog somewhere in the grid; no guessing is required.\n\nPurple lines: each purple line is a closed loop of cells, and its shape is a square. The digits along each purple line are consecutive digits in any order, with no repeats.\n\nGrey lines: each grey line is a closed loop of cells, and its shape is a square. The digits along each grey line are consecutive digits in any order, with no repeats.\n\nX clue: an X sits between two cells, and those two cells sum to 10.\n\nBlack dot: a black dot sits between two cells, and one of those two digits is double the other.","solution":"234715698165894327789632541357241869921586734648379152516928473872463915493157286","fogLight":"R5C4,R5C5,R4C5,R6C5,R5C6","constraints":["XV","fog","kropki","renban"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5"]}]},{"id":"27z6ar78be","ctcId":3242,"ctcDifficulty":"MEDIUM","title":"Let's Sausage!","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nThe difference between the sums of two linked sausages on a chain must be exactly equal to the number of sausages in that chain.","solution":"476925813192483657538176942813694275647352198259718364784261539921537486365849721","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The difference between the sums of two linked sausages on a chain must be exactly equal to the number of sausages in that chain.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"g78oascrp0","ctcId":3243,"ctcDifficulty":"MEDIUM","title":"Inbetween Taken","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. The values of the digits along a line must lie between the two values of the circles at either end of that line.","solution":"729145863185326974643879512938652147256714398471983256514268739362597481897431625","constraints":["between-line"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"modified","modifiers":[],"params":null,"note":"The values of the digits along a line must lie between the two values of the circles at either end of that line.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"4pmysqeian","ctcId":3244,"ctcDifficulty":"MEDIUM","title":"Mushroom Dance","author":"Florian Wortmann","rules":"Normal sudoku rules apply.\n\nThe 3x3 box borders divide each blue line into segments; each segment along an individual line must have the same sum.","solution":"362781954918425376547369218724953861689172435135648792891534627273816549456297183","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"5gyf7rj813","ctcId":3246,"ctcDifficulty":"HARD","title":"Killers in Hiding","author":"Aron Lidé (Aspartagcus)","rules":"Sudoku: Fill each row, column and region with the digits 1-9.\nHidden sum killer cages: Digits in a cage may not repeat and sum to the two-digit number in the two left-most cells in the top row of that cage.","rulesClarified":"Fill each row, column and region with the digits 1 to 9.\n\nNo cage total is printed. The total of each cage is the two-digit number formed by the digits in the two left-most cells of the cage's top row, read left to right.\n\nThose two cells are cells of the cage, so their digits count toward the total too. The digits in a cage must not repeat.","solution":"184527369329164587576398142837619425612453798945872613453986271791245836268731954","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"gn1gqsglle","ctcId":3248,"ctcDifficulty":"MEDIUM","title":"24 Trios!","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Along each length-3 line, the digits ascend from one end of the line to the other. In every 3x3 box, the digits in every horizontal or vertical threesome are never consecutive in some order.","solution":"264395718831762459597841362742136985189257643356489127418573296975624831623918574","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In every 3x3 box, the digits in every horizontal or vertical threesome are never consecutive in some order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Along each length-3 line, the digits ascend from one end of the line to the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"u3wks9egf5","ctcId":3249,"ctcDifficulty":"MEDIUM","title":"My Original Reality Show Entertainment ","author":"Chip Sounder","rules":"Normal sudoku rules apply. Place the digits 1-9 once each in every row, column and 3x3 box.\n-Clues outside the grid gives the sum the digits between the 1 and 9 in their respective row/column.\n-Cells separated by a white dot are consecutive.\n-Adjacent digits along a green line must differ by at least 5.\n-Adjacent digits along a red line must have alternating parity.\n-Cells separated by a black dot has one digit double the other (1:2 ratio).\n-Digits in a dotted cage without repeat sum to the total given in the top left corner of the cage.\n-The grey line is a palindrome and must read the same forwards as backwards.\nNo negative constraints.","solution":"456712893789356124123498765845963271932871456671245938217634589568129347394587612","constraints":["cage","custom","german-whispers","kropki","palindrome","sandwich"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"-Adjacent digits along a red line must have alternating parity.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c7"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"b3wa450x40","ctcId":3250,"ctcDifficulty":"HARD","title":"Vicissitudes","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nShade some cells so that all shaded cells are orthogonally connected, and all unshaded cells are orthogonally connected. No 2x2 area may be completely shaded or unshaded.\nThe shading splits the line into segments with equal sums. Digits may not repeat within a segment.","solution":"687154329913627548254389617562971483841536972739248165125763894398412756476895231","constraints":["custom","region-sum-line","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits may not repeat within a segment.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"The shading splits the line into segments with equal sums.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"1f9u67dq06","ctcId":3251,"ctcDifficulty":"MEDIUM","title":"Balance lines","author":"Jonesy","rules":"Hello \n\nNormal sudoku rules apply.\n\nOn each line the sum of the odd digits equals the sum of the even digits.\n\nDigits separated by a white dot are consecutive.\nThe digit in the grey square must be even.\n\nHave fun.","solution":"531784692862159473947632185623591748789346251154278936376425819418963527295817364","constraints":["custom","even","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On each line the sum of the odd digits equals the sum of the even digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"0ffc9frb42","ctcId":3252,"ctcDifficulty":"MEDIUM","title":"Epitome","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nWithin a cage, digits must not repeat and they sum to the small number in the top left corner.","solution":"581692743762834951349715628958461372634287519127359486295173864476928135813546297","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"sg7gob420m","ctcId":3254,"ctcDifficulty":"HARD","title":"Auteur","author":"SamuPiano","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\nLoose Tens: In every row, column, and 3x3 box, one cell has a value of ten. These cells form a complete set of the digits from 1 to 9.\nUnique Cages: The sum of the values in each cage is unique.","solution":"375462189962381475184597632596173824238649751741258963423716598659824317817935246","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Loose Tens: In every row, column, and 3x3 box, one cell has a value of ten. These cells form a complete set of the digits from 1 to 9. Unique Cages: The sum of the values in each cage is unique.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]}]},{"id":"up5nrki10o","ctcId":3255,"ctcDifficulty":"HARD","title":"RAT RUN 38: Synchronicity","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. There is no space to move diagonally in this maze.\n\nBLACKCURRANTS: If two digits are joined by a blackcurrant, one is double the other.\n\nONE-WAY DOORS: A purple arrow always points to the smaller of the two digits it sits between, and may only be passed through in the direction it's pointing. \n\nTEST CONSTRAINT: In this experiment, any two digits visited adjacently along a path must be different parities (one is odd and the other is even), and also have a difference of at least 5.","solution":"381965472756124938294837615679481523832756149415293867527649381948312756163578294","constraints":["custom","german-whispers","inequality","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"AIM OF EXPERIMENT: Finkz and Phinx must both reach different cupcakes by finding a path through the maze. The paths must not visit any cell more than once, cross themselves or each other, or pass through any thick maze walls. ONE-WAY DOORS: A purple arrow always points to the smaller of the two digits it sits between, and may only be passed through in the direction it's pointing. TEST CONSTRAINT: In this experiment, any two digits visited adjacently along a path must be different parities (one is odd and the other is even), and also have a difference of at least 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c6","c7"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"inequality","type":"inequality","variant":"modified","modifiers":[],"params":null,"note":"ONE-WAY DOORS: A purple arrow always points to the smaller of the two digits it sits between, and may only be passed through in the direction it's pointing.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"74acwb3vkq","ctcId":3256,"ctcDifficulty":"HARD","title":"Balanced X-Sums","author":"RockyRoer","rules":"[Sudoku] Normal sudoku rules apply -- fill every row, column, and region with the digits from 1 to 9 once each. \n\n[Balanced X-Sums] Each arrow indicates that the sum of the odd digits must equal the sum of the even digits in the first x cells seen in the direction of the arrow where x is the digit in the cell next to the clue.","solution":"798631254341285679526479138839146725214753896657928413173894562982567341465312987","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"[Balanced X-Sums] Each arrow indicates that the sum of the odd digits must equal the sum of the even digits in the first x cells seen in the direction of the arrow where x is the digit in the cell next to the clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"23phi9d5m7","ctcId":3260,"ctcDifficulty":"VERY HARD","title":"Foggy Banana Split","author":"SamuPiano","rules":"SUDOKU: Normal sudoku rules apply.\nFOG (OLD-SCHOOL): The grid is partially covered in fog. Placing correct digits will clear the fog from the surrounding area.\nCHOCO BANANA: Shade all cells either brown (chocolate) or yellow (banana) such that all chocolate areas are rectangular, and no banana areas are rectangular.\nLINES: All lines move orthogonally and end in circles on either end. Lines do not cross, branch, or share cells.\nCIRCLES (SHADING): Circles may be contained in either chocolate or banana cells. Circles indicate the size of the area in which they are contained.\nCIRCLES (COUNT): The digit in a circled cell with a line attached also gives the number of cells of the same shading as the circled cell along the line, including the endpoints.\nSPLIT PEAS: Digits along a line must sum to a two-digit number, where the 'tens' digit is in one circle and the 'ones' digit is in the other.\nXV: Cells separated by an X sum to 10. Cells separated by a V sum to 5.","solution":"832971564549628317167345982624197835718453296395862741473286159951734628286519473","fogLight":"R3C1,R1C2","constraints":["XV","custom","fog"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c11","c12"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"CHOCO BANANA: Shade all cells either brown (chocolate) or yellow (banana) such that all chocolate areas are rectangular, and no banana areas are rectangular. LINES: All lines move orthogonally and end in circles on either end. Lines do not cross, branch, or share cells. Circles indicate the size of the area in which they are contained. CIRCLES (COUNT): The digit in a circled cell with a line attached also gives the number of cells of the same shading as the circled cell along the line, including the endpoints. SPLIT PEAS: Digits along a line must sum to a two-digit number, where the 'tens' digit is in one circle and the 'ones' digit is in the other.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6","c8","c9","c10"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ofafbe2382","ctcId":3261,"ctcDifficulty":"MEDIUM","title":"Battleaxe","author":"Scott Williams","rules":"Apply normal sudoku rules. Box borders divide each blue line into segments with the same sum. Digits in a circle must appear at least once in the surrounding four cells.","solution":"479825613285163479316749528598472361137986254624531897742618935853297146961354782","constraints":["quadruple","region-sum-line"],"constraintFacts":[{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"du9fe2vznz","ctcId":3262,"ctcDifficulty":"MEDIUM","title":"Coterminous","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nThe 3x3 box borders divide the blue lines into segments; each segment along an individual line must have the same sum.","solution":"286374591453189726917256348562431879741598632398627154139845267824763915675912483","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9yho58uz5e","ctcId":3263,"ctcDifficulty":"MEDIUM","title":"Giraffe Hunt 2","author":"bellal","rules":"Normal sudoku rules apply. Anti-giraffe: cells (1,4) apart cannot contain the same digit. (eg the digit in r1c5 cannot appear in r2c1/r2c9/r5c4/r5c6.) Cells joined by black dots contain digits in a 1:2 ratio (ie one digit will be double the other); cells joined by a white dot contain consecutive digits. Along a thermometer, digits increase from the bulb end. The digits in the black cage sum to 12. The blue cages contain the same pair of digits.","solution":"579846321621973548348521679895412763216397854734658192953784216167239485482165937","constraints":["cage","custom","kropki","thermometer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Anti-giraffe: cells (1,4) apart cannot contain the same digit. (eg the digit in r1c5 cannot appear in r2c1/r2c9/r5c4/r5c6.) The blue cages contain the same pair of digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"4dszmln0se","ctcId":3265,"ctcDifficulty":"MEDIUM","title":"Can of worms","author":"bellal","rules":"Normal sudoku rules apply.\nOrange lines are both index lines and entropic lines.\nIndex lines: starting with the diamond at position 1, the digit at position N along the line indicates the position of the digit N on the line.\nEntropic lines: every set of 3 consecutive digits along the line contain one low digit (1,2,3), one medium digit (4,5,6) and one high digit (7,8,9).\nThe arrow points to the smaller of the digits in the cells it occupies.","solution":"576319428921487635438526917214798563385164279697235184742653891159872346863941752","constraints":["custom","entropic-line","inequality"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Index lines: starting with the diamond at position 1, the digit at position N along the line indicates the position of the digit N on the line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"inequality","type":"inequality","variant":"modified","modifiers":[],"params":null,"note":"The arrow points to the smaller of the digits in the cells it occupies.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]}]},{"id":"jfpflqk7pr","ctcId":3266,"ctcDifficulty":"MEDIUM","title":"Pressure Cooker","author":"bellal","rules":"Normal Sudoku rules apply: place digits 1-9 once each in each row, column and 3x3 box.\n\nEqual pressure cages: the sum of the digits inside a gold cage (which may repeat) equals the sum of the digits in the cells outside which share an edge with cells inside.","solution":"567218943238694157491753826814537269376829514925461738752386491689142375143975682","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Equal pressure cages: the sum of the digits inside a gold cage (which may repeat) equals the sum of the digits in the cells outside which share an edge with cells inside.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"65spa2e9w3","ctcId":3267,"ctcDifficulty":"HARD","title":"Eye of the Beholder","author":"oskode & Calvinball","rules":"Sudoku: Fill all rows, columns and marked 3x3 regions with the digits 1-9 without any repeats.\n\nQuestion Marks: Each question mark acts as a stand-in for a digit, which must be deduced for each question mark.\n\nQuadruples: Each circle contains 2 digits. The 2 digits must appear in at least one of the four cells surrounding that circle (if a digit repeats in a circle, it must appear twice).\n\nArrows: Digits along an arrow sum to a two-digit number. This number is a concatenation of BOTH digits in the attached circle.\n\n\n(For clarity: A circle with the digits {1, 9} would be surrounded by at least one copy each of the digits 1 and 9 and could have arrows that summed to either 19 or 91. Its arrows could not sum to 11 nor 99, this would require a {1, 1} circle surrounded by two 1s or a {9, 9} circle surrounded by two 9s respectively.)","solution":"317459682429768315685231479154873926263914857798625134536197248941582763872346591","constraints":["arrow","custom","quadruple"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Arrows: Digits along an arrow sum to a two-digit number.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Question Marks: Each question mark acts as a stand-in for a digit, which must be deduced for each question mark.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"tl8tkze8mn","ctcId":3268,"ctcDifficulty":"HARD","title":"Mind the Gap","author":"Michael Lefkowitz","rules":"Normal sudoku rules apply.\n\nSAFETY STRIPS - Digits separated by a yellow safety strip are in a 2:1 ratio (ie one is double the other.)\n\nGAP LOOP - Extend the 'gap' (ie the grey lines) along cell edges so that it forms a single loop, which cannot touch itself. Even and odd digits may not touch except across the gap.\n\nPATHFINDER - Draw a path from cell centre to cell centre from the blue dot to the red pin, which may move orthogonally or diagonally. It can't cross or touch the gap, except at yellow safety strips. Adjacent digits on the path differ by at least 3.","solution":"739564128564128937821739546982645371173982465456371289218457693397216854645893712","constraints":["custom","german-whispers","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"GAP LOOP - Extend the 'gap' (ie the grey lines) along cell edges so that it forms a single loop, which cannot touch itself. Even and odd digits may not touch except across the gap. PATHFINDER - Draw a path from cell centre to cell centre from the blue dot to the red pin, which may move orthogonally or diagonally. It can't cross or touch the gap, except at yellow safety strips.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"jl4sby2gl2","ctcId":3269,"ctcDifficulty":"MEDIUM","title":"The one and only sum","author":"Lithium-Ion","rules":"Normal sudoku rules apply. Cells separated by a black dot contain digits that are in a 1:2 ratio. Cells separated by a white dot contain consecutive digits. Neighboring digits along a green line must differ by at least 5. Neighboring digits along an orange line must differ by at least 4. A pink line contains a set of non-repeating consecutive digits in any order. Along a gray thermometer, digits must strictly increase from the bulb end. Each set of three consecutive cells along a peach entropic line must contain one low (123), one medium (456) and one high  (789) digit. Box borders dive the blue region sum line into segments with the same sum. The sum of all digits that belong to one constraint type (e.g. all digits on black dots)  is the same for each of the eight constraint types in this puzzle and must be deduced by the solver.","solution":"154978362398162754276534891982346175541297683763815249429681537617453928835729416","constraints":["custom","dutch-whispers","entropic-line","german-whispers","kropki","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of all digits that belong to one constraint type (e.g. all digits on black dots)  is the same for each of the eight constraint types in this puzzle and must be deduced by the solver.","evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"g4olqfawhb","ctcId":3270,"ctcDifficulty":"MEDIUM","title":"Rigmarole","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nClues outside the grid indicate the sum of all continuously diagonally adjacent digits with the same parity, up to (and not including) the first digit with the opposite parity along the indicated diagonal from the direction of the clue (digits may repeat if allowed by other rules).","rulesClarified":"Normal sudoku rules apply.\n\nClues sit outside the grid, at the end of a diagonal. A clue gives the total of a run of digits along its diagonal, counted from the diagonal's first cell inside the grid, in the direction of the clue.\n\nKeep adding digits along that diagonal while each digit has the same parity as the one before it. Stop before the first digit with the opposite parity and do not count it. The total of the digits counted is the clue.\n\nDigits may repeat if the other rules allow it.","solution":"692781354485236791173549628329174586816325479547968132251693847934817265768452913","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Clues outside the grid indicate the sum of all continuously diagonally adjacent digits with the same parity, up to (and not including) the first digit with the opposite parity along the indicated diagonal from the direction of the clue (digits may repeat if allowed by other rules).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"2mltluk4bn","ctcId":3271,"ctcDifficulty":"HARD","title":"20 Almost Balanced Lines","author":"RockyRoer","rules":"Normal sudoku rules apply.\n\nOn lines, the sum of the even digits and the sum of the odd digits are almost equal - that is, they are off by one.  Digits may repeat on lines if sudoku allows.","solution":"624517983931628457785934261493872516276351894158496372549763128817245639362189745","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On lines, the sum of the even digits and the sum of the odd digits are almost equal - that is, they are off by one.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"oso53h7rd2","ctcId":3272,"ctcDifficulty":"HARD","title":"24 Squares!","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Each line contains a square number reading from left to right (or in the case of the line in r3c1, from top to bottom). eg If r8c7 was a 2 then r7c8 must be a 5 (to give the square number 25). (As an aide memoire, all 2-digit squares and 3-digit squares (without zeroes or a repeated digit) are: 16, 25, 36, 49, 64, 81, 169, 196, 256, 289, 324, 361, 529, 576, 625, 729, 784, 841, 961).","solution":"297315486456897231138642957673184592581729364924563178742958613319276845865431729","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each line contains a square number reading from left to right (or in the case of the line in r3c1, from top to bottom). eg If r8c7 was a 2 then r7c8 must be a 5 (to give the square number 25).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9pbfrrmznf","ctcId":3275,"ctcDifficulty":"HARD","title":"Coral Corridor","author":"Sotehr","rules":"Sudoku: Normal Sudoku rules apply; place the digits 1-9 once in every row, column, and 3x3 box.\n\nRenban Line: Solid pink lines contain an unordered set of consecutive digits, without repeats.\n\nRegion Sum Line: Hollow blue lines are divided by 3x3 box borders into segments with sums of equal value.\n\nBlack Kropki: Cells separated by a black dot have one digit double the other.\n\nWhite Kropki: Cells separated by a white dot have consecutive digits.","solution":"358124769927638154416597328273986415861345297549271683135469872682753941794812536","constraints":["kropki","region-sum-line","renban"],"constraintFacts":[{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"2vyd84g6u0","ctcId":3276,"ctcDifficulty":"HARD","title":"Coded Pairs","author":"Mr.Menace","rules":"Classic Sudoku rules apply. \n\nOutlined cages are drawn in the grid, each containing a letter. The same letter represents the same pair of digits across the grid. Different letters must represent different pairs. The order of digits within cages does not matter.","solution":"723894516158726934694351872439678251216435798587219463962543187345187629871962345","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The same letter represents the same pair of digits across the grid. Different letters must represent different pairs.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"1f53g3ay0v","ctcId":3277,"ctcDifficulty":"MEDIUM","title":"Lonely Fives","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nAnti-Queen Fives: No 5 in the grid may be a chess queen's move away from another 5.\n\nTentropy Lines: Every set of 4 adjacent digits on a hollow peach line must contain a digit from each of the X-pair (ten-pair) subsets of {1,9}, {2,8}, {3,7}, and {4,6}. A 5 may not appear on a Tentropy Line.\n\nKropki: A white dot between two digits indicates that those digits are consecutive. A black dot between two digits indicates that one digit is double the other.","solution":"715269384423871695896534712687942153931758426254316879348125967569487231172693548","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Anti-Queen Fives: No 5 in the grid may be a chess queen's move away from another 5. Tentropy Lines: Every set of 4 adjacent digits on a hollow peach line must contain a digit from each of the X-pair (ten-pair) subsets of {1,9}, {2,8}, {3,7}, and {4,6}. A 5 may not appear on a Tentropy Line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"58u9d7sohd","ctcId":3278,"ctcDifficulty":"HARD","title":"Hot or Cold","author":"James Kopp","rules":"Normal sudoku rules apply.\nEach domino crossing a region border must contain digits which differ by at least 4.\nThe digit in each red cell is greater than each orthogonally adjacent neighbour in a white cell. Each digit in a blue cell is less than each orthogonally adjacent neighbour in a white cell.","solution":"534876192286193754971524863425968317168357249397241586742685931653719428819432675","constraints":["custom","maximum","minimum"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each domino crossing a region border must contain digits which differ by at least 4.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"maximum","type":"maximum","variant":"modified","modifiers":[],"params":null,"note":"The digit in each red cell is greater than each orthogonally adjacent neighbour in a white cell.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"minimum","type":"minimum","variant":"modified","modifiers":[],"params":null,"note":"Each digit in a blue cell is less than each orthogonally adjacent neighbour in a white cell.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"f4ec7xtau8","ctcId":3279,"ctcDifficulty":"HARD","title":"Spreading Through The Fog","author":"Rab3aron","rules":"Chaos Construction: Divide the grid into 9 non overlapping regions, each consisting of orthogonally connected cells.\n\nSudoku: Place the digits 1–9 exactly once in each row, column, and region.\n\nCircles: A digit in a circle equals the number of distinct columns occupied by its region. There are 9 circles in total, and exactly one pair of circles share the same digit.\n\nSquares: A digit in a square equals the number of distinct rows occupied by its region. There are 9 squares in total, and exactly one pair of squares share the same digit.\n\nDiamonds: A digit in a diamond equals the number of distinct regions that appear anywhere in its row or column, including its own region (regions seen in both the row and column are still counted once).\n\nEqual sums: The sum of every circled and squared digit within a region is the same for each of the nine regions.\n\nFog: The grid is covered in fog, placing correct digits clears the fog somewhere in the grid.","solution":"123456789234567891345678912456789123567891234678912345789123456891234567912345678","fogLight":"R5C5","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Chaos Construction: Divide the grid into 9 non overlapping regions, each consisting of orthogonally connected cells. Circles: A digit in a circle equals the number of distinct columns occupied by its region. There are 9 circles in total, and exactly one pair of circles share the same digit. Squares: A digit in a square equals the number of distinct rows occupied by its region. There are 9 squares in total, and exactly one pair of squares share the same digit. Diamonds: A digit in a diamond equals the number of distinct regions that appear anywhere in its row or column, including its own region (regions seen in both the row and column are still counted once). Equal sums: The sum of every circled and squared digit within a region is the same for each of the nine regions.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c3","c4","c5","c6","c7","c8"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"nntvpka1p2","ctcId":3280,"ctcDifficulty":"MEDIUM","title":"Fractured Symmetry","author":"Rab3aron","rules":"Normal sudoku rules apply. \nGerman Whisper: Adjacent digits along a green line have a difference of at least 5.\nPalindrome: Digits along a gray line read the same in both directions.\nLittle Killers: A clue outside the grid gives the sum of the digits along the indicated diagonal.\nKropki Dots: Digits in cells joined by a white dot are consecutive.","solution":"973648521216975384584231697745826139369514278821793456452189763197362845638457912","constraints":["german-whispers","kropki","little-killer","palindrome"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"3p3nivu3o6","ctcId":3281,"ctcDifficulty":"HARD","title":"Lupin's Loop 1 - No Shared Factors","author":"Rab3aron","rules":"When the city announced a challenge to design a perfect new road system, there was really only one candidate everyone expected to solve it: Professor Lupin, the mathematician so famous for his love of loops that people joked that was how he got his name. He set out to design a single elegant road network — one continuous road that would eventually close into a loop while connecting every house in the city.\n\nNormal Sudoku rules apply.\nDraw a single road that travels orthogonally from cell to cell, never branching, crossing, or overlapping, and which eventually closes into a loop. The road must pass through every house. Borders marked with traffic lights are controlled intersections that the road cannot cross. The bold 3×3 borders divide the road into segments. Within each segment, all digits must be 'pairwise prime' (that is, any two digits in the same segment share no common factor greater than 1). A digit in a house equals the length of the segment containing it, while a digit in a speed camera counts how many road cells appear in the ENTIRE row of that camera, including the camera cell itself.\n\nNote: A segment does not necessarily contain a house. Any segment of length 1 must contain the digit 1.","rulesClarified":"Draw a single road that travels orthogonally from cell to cell, never branching, crossing, or overlapping, and which eventually closes into a loop.\n\nThe road must pass through every house.\n\nA traffic-light marker sits on the border between the two cells it names. The road cannot cross a border marked with traffic lights.\n\nThe bold 3×3 borders divide the road into segments.\n\nWithin each segment, all digits must be pairwise prime: any two digits in the same segment share no common factor greater than 1. Two copies of the same digit are therefore allowed only when the digit is 1.\n\nA digit in a house equals the length of the segment containing it.\n\nA digit in a camera cell counts how many road cells appear in the entire row of that camera, including the camera cell itself.\n\nA segment does not necessarily contain a house.\n\nAny segment of length 1 must contain the digit 1.\n\nNormal Sudoku rules apply.","solution":"638491275415732968927658413251386794394175826786249351163924587842567139579813642","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single road that travels orthogonally from cell to cell, never branching, crossing, or overlapping, and which eventually closes into a loop. The road must pass through every house. Borders marked with traffic lights are controlled intersections that the road cannot cross. Within each segment, all digits must be 'pairwise prime' (that is, any two digits in the same segment share no common factor greater than 1). A digit in a house equals the length of the segment containing it, while a digit in a speed camera counts how many road cells appear in the ENTIRE row of that camera, including the camera cell itself. Any segment of length 1 must contain the digit 1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6","c8","c9","c11"]}]},{"id":"l00604nlbr","ctcId":3282,"ctcDifficulty":"HARD","title":"Lupin's Loop 2 - Space Invasion","author":"Rab3aron","rules":"Normal sudoku rules apply. \nDigits separated by a white dot are consecutive. \nDraw a single route that travels orthogonally from cell to cell, never branching, crossing, or overlapping, which eventually closes into a loop. The loop must pass through every planet. Thick black borders represent black holes that the route cannot cross. \nA digit in a satellite dish equals the number of loop cells in the 3×3 box centred on that cell. \nAlong the loop, one parity forces the route to turn (making a 90° angle) while the other forces it to continue straight (making a 180° angle), it is up to the solver to determine which parity corresponds to which behaviour. \nAny two cells that are adjacent along the loop must contain non-consecutive digits unless the loop is passing through a white dot (where consecutive digits may appear).","solution":"352796418746831925918524673267349581594182367831657294129475836685213749473968152","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single route that travels orthogonally from cell to cell, never branching, crossing, or overlapping, which eventually closes into a loop. The loop must pass through every planet. Thick black borders represent black holes that the route cannot cross. A digit in a satellite dish equals the number of loop cells in the 3×3 box centred on that cell. Along the loop, one parity forces the route to turn (making a 90° angle) while the other forces it to continue straight (making a 180° angle), it is up to the solver to determine which parity corresponds to which behaviour. Any two cells that are adjacent along the loop must contain non-consecutive digits unless the loop is passing through a white dot (where consecutive digits may appear).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c6","c7","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"zsmtekox43","ctcId":3283,"ctcDifficulty":"HARD","title":"Lupin’s Loop 3 – Successorless","author":"Rab3aron","rules":"Normal Sudoku rules apply. Digits separated by a white Kropki dot are consecutive. \nDraw a single electricity cable that travels orthogonally from cell to cell, never branching, crossing, or overlapping, and eventually closes into a loop. The loop must pass through every hut. Water drops mark river borders that the loop cannot cross. Any two cells that are adjacent along the loop must contain non-consecutive digits, unless the loop is passing through a white dot (where consecutive digits may appear). Any two huts directly connected by the loop form a segment (including both huts). A digit in a hut equals the length of the longest segment containing it.","rulesClarified":"Normal Sudoku rules apply.\n\nDraw a single electricity cable that travels orthogonally from cell to cell, never branching, crossing, or overlapping, and eventually closes into a loop.\n\nThe loop must pass through every hut.\n\nDigits separated by a white Kropki dot are consecutive. Each white dot sits on the border between two neighbouring cells.\n\nAny two cells that are adjacent along the loop must contain non-consecutive digits. The exception is a white dot: where the loop runs across the border that a white dot sits on, the two cells on either side may contain consecutive digits.\n\nWater drops mark river borders that the loop cannot cross. Each water drop sits on the border between the two neighbouring cells it covers.\n\nAny two huts directly connected by the loop form a segment, including both huts. Two huts are directly connected when the loop runs from one to the other without passing another hut.\n\nA digit in a hut equals the length of the longest segment containing it.","solution":"324695178586417293791328645159746832837152469462839751613584927975261384248973516","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single electricity cable that travels orthogonally from cell to cell, never branching, crossing, or overlapping, and eventually closes into a loop. The loop must pass through every hut. Water drops mark river borders that the loop cannot cross. Any two cells that are adjacent along the loop must contain non-consecutive digits, unless the loop is passing through a white dot (where consecutive digits may appear). A digit in a hut equals the length of the longest segment containing it.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c6","c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"vc62zmuo08","ctcId":3284,"ctcDifficulty":"HARD","title":"Ba-King Ratio Recommender","author":"olima","rules":"Normal sudoku rules apply. Digits a king's move (in chess) apart must be different. Adjacent digits on a green line differ by at least 5. Digits on a purple line do not repeat and are a set of consecutive digits in any order. On a black dot, one digit is double the other. Red cells indicate the position of the cell's column number in that row, e. g. a 4 in r6c3 implies a 3 in r6c4.","rulesClarified":"Normal sudoku rules apply.\n\nDigits a king's move (in chess) apart must be different.\n\nAdjacent digits on a green line differ by at least 5.\n\nDigits on a purple line do not repeat, and each purple line holds a set of consecutive digits in any order. Each purple line is its own line, separate from the others.\n\nOn a black dot, one digit is double the other. The dot sits between two cells, and those two cells are the pair.\n\nRed cells indicate a column number. In a red cell in column c holding digit d, the cell in column d of the same row contains the digit c. For example, a 4 in r6c3 implies a 3 in r6c4.","solution":"897534612461928357532617984784396125219785463653142879148279536375461298926853741","constraints":["antiking","custom","german-whispers","kropki","renban"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Red cells indicate the position of the cell's column number in that row, e. g. a 4 in r6c3 implies a 3 in r6c4.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"8df315rarb","ctcId":3285,"ctcDifficulty":"HARD","title":"36 x Even","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Cells containing a grey square must contain even digits. Three adjacent cells in any direction (orthogonal or diagonal) never contain three consecutive digits in some order.","solution":"752183496349256187618749352983612745476395218521874963235961874167438529894527631","constraints":["custom","even"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Three adjacent cells in any direction (orthogonal or diagonal) never contain three consecutive digits in some order.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"0wffw5dssm","ctcId":3287,"ctcDifficulty":"MEDIUM","title":"SVS #470 - Harmonious Thermos","author":"Richard","rules":"Normal sudoku rules apply.\nDigits along a thermometer must strictly increase from the bulb end. Additionally, the sum of the digits along a thermometer must be divisible by the number of cells the thermometer uses.","solution":"134598672568217493279364158342981765896725341751436829685179234927843516413652987","constraints":["custom","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Additionally, the sum of the digits along a thermometer must be divisible by the number of cells the thermometer uses.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"17j9j9bf82","ctcId":3288,"ctcDifficulty":"HARD","title":"Whispering Dominoes","author":"Kaktuslav","rules":"Normal sudoku rules apply. Totals of orthogonally adjacent cages differ by at least 7. No two cages have the same total.","solution":"923814675584967213617523489736158924498372156152496738249735861865241397371689542","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Totals of orthogonally adjacent cages differ by at least 7. No two cages have the same total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"6jmMrgJHLT","ctcId":3291,"ctcDifficulty":"MEDIUM","title":"Deep Space 9x9","author":"Haley Prochilo","rules":"Normal sudoku rules apply. Circles contain odd digits. Each line (purple or grey) contains a sequence of digits in any order. There is a hidden 9 cell ‘thermometer’ entirely contained in one box, along which digits increase from one end to the other. It only moves orthogonally and does not cross itself.","solution":"379512864456873219281946537637294185198365472542187396923751648814629753765438921","constraints":["odd","renban","thermometer"],"constraintFacts":[{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"x07h2149k1","ctcId":3292,"ctcDifficulty":"MEDIUM","title":"The Squaretaker","author":"haleypro","rules":"-Black lines are renbans\n-Blue/red lines are thermos\n-Grey lines are region sum lines\n-Yellow circles are odd\n-There is a hidden thermo that begins and ends at cells α and Δ. It only moves orthogonally. The bulb is to be deduced by the solver. The thermo may not cross any renban lines.\n\nTheme rules:\n-Voyager need to find a way home to the Alpha Quadrant! the best route is along the hidden thermo that begins at cell Δ and ends at cell α. It only moves orthogonally. The bulb is to be deduced by the solver. The path must avoid any Borg Cubes.\n-Borg Cubes (black lines) are renbans\n-Nacelles (blue/red lines) are thermos\n-Starships (grey lines) are region sum lines\n-Stars (yellow circles) are odd","solution":"253146789784295631619387542132678495965412378478539216346821957827953164591764823","constraints":["custom","odd","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"It only moves orthogonally. The bulb is to be deduced by the solver. The thermo may not cross any renban lines.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7","c8"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"-Grey lines are region sum lines","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c5"]}]},{"id":"3xdi7kf6ab","ctcId":3293,"ctcDifficulty":"MEDIUM","title":"North Side","author":"haleypro","rules":"Normal sudoku rules apply. This puzzle must be solved in tandem with South Side. The puzzles overlap at the Loop in R9C9 (so eg. R9C7 in North Side and R1C6 in South Side contain the same digit). All cells with an airplane contain the same digit across both puzzles. Red Line: Parity line (cells alternate in parity). Purple Line: Zipper line (digits an equal distance from the center sum to the digit in the center). Yellow Line: Nabner line (no two digits can be consecutive or identical). Blue Line: Region Sum line (box borders divide the line into segments with an equal sum). Green Line: German Whisper line (adjacent digits differ by 5 or more). Brown Line: Slow thermo (moving from the bulb, each digit is the same or higher). Pink Line: Renban line (a set of consecutive digits in any order).","solution":"156973428428651937937248516264597183591836274783124659875419362619382745342765891","constraints":["custom","german-whispers","nabner-line","region-sum-line","renban","thermometer","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The puzzles overlap at the Loop in R9C9 (so eg. All cells with an airplane contain the same digit across both puzzles. Red Line: Parity line (cells alternate in parity).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5","c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"d05ho9qchh","ctcId":3294,"ctcDifficulty":"MEDIUM","title":"South Side","author":"haleypro","rules":"Normal sudoku rules apply. This puzzle must be solved in tandem with 'North Side'. The puzzles overlap at the Loop in R1C8 (so eg. R9C7 in 'North Side' and R1C6 in 'South Side' contain the same digit). All squares with an airplane contain the same digit across both puzzles.\n\nRed Line: Parity line (cells alternate in parity). Blue Line: Region Sum line (box borders divide the line into segments with an equal sum). Green Line: German Whisper line (adjacent digits differ by 5 or more). Orange Line: Dutch Whisper line (adjacent digits differ by 4 or more). Pink Line: Renban line (a set of consecutive digits in any order).","solution":"427658913851329764936741258543197682168432597792865341675214839384976125219583476","constraints":["custom","dutch-whispers","german-whispers","region-sum-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The puzzles overlap at the Loop in R1C8 (so eg. All squares with an airplane contain the same digit across both puzzles. Red Line: Parity line (cells alternate in parity).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5","c6"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"k01vyssa50","ctcId":3295,"ctcDifficulty":"VERY HARD","title":"Invisible Killers","author":"yttrio","rules":"Normal sudoku rules apply.\n\nSeveral (invisible) killer cages are present in the grid.  Digits in a cage cannot repeat, and sum to the clue in the top-left-most cell of the cage (top-most is evaluated first, followed by left-most).  Cages cannot overlap.\n\nOnly the number for each cage is visible, and it is up to the solver to determine the rest of the cells each cage visits.\n\nEvery cage visits at least two 3x3 boxes and has an equal number of cells in each 3x3 box visited.","solution":"124953678789162345635478912267581493458396721913247586571839264846725139392614857","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a cage cannot repeat, and sum to the clue in the top-left-most cell of the cage (top-most is evaluated first, followed by left-most).","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Cages cannot overlap. Only the number for each cage is visible, and it is up to the solver to determine the rest of the cells each cage visits. Every cage visits at least two 3x3 boxes and has an equal number of cells in each 3x3 box visited.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6"]}]},{"id":"sd02li6q2c","ctcId":3296,"ctcDifficulty":"HARD","title":"Four Octagons","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits in a cage must sum to the small number in the top-left corner of the cage. Adjacent digits along a rose octagon line must differ in value by at least 6.","solution":"693714285275968341841352769529637814468291537317485926956123478134879652782546193","constraints":["cage","german-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"6y7vhnhdof","ctcId":3297,"ctcDifficulty":"MEDIUM","title":"Nabnerfel","author":"Antiknight","rules":"Normal sudoku rules apply. The digits along each arrow must sum to the digit in the circled cell. No digit on a golden line can be consecutive with any other digit on that line. A white dot between two cells indicates that the digits are consecutive. Not all such dots are shown.","solution":"854697213139824657267351894723568149945712368681943572498135726312476985576289431","constraints":["arrow","kropki","nabner-line"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"mea9u6amrt","ctcId":3298,"ctcDifficulty":"MEDIUM","title":"Quiet Room","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nAlong a line that occupies N cells, every pair of adjacent digits must have a difference of at least N.\n\nIf a black dot sits between two digits, one is double the other.","solution":"457819263361274859982563417175486932294351786638792145726138594849625371513947628","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Along a line that occupies N cells, every pair of adjacent digits must have a difference of at least N.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"vrblr4abgp","ctcId":3299,"ctcDifficulty":"HARD","title":"Kelowna","author":"Oddlyeven","rules":"Normal sudoku rules apply. \nOne cell in each row, column and box is a “doubler cell”. Doubler cells have a value equal to twice their digit. Each digit from 1 to 9 appears once in the set of doubler cells. \nEach grey line can be divided into one or more consecutive, non-overlapping sections each of which contains values summing to ten. \nDigits in a cage do not repeat. Values in a cage sum to the total in the upper left corner of the cage. \nValues on a black dot are in a 1:2 ratio (ie one value is double the other).","solution":"546731982182695374973842561798163425614258793325479618267384159451927836839516247","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits in a cage do not repeat. Values in a cage sum to the total in the upper left corner of the cage.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c6","c7"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"One cell in each row, column and box is a “doubler cell”. Doubler cells have a value equal to twice their digit. Each digit from 1 to 9 appears once in the set of doubler cells. Each grey line can be divided into one or more consecutive, non-overlapping sections each of which contains values summing to ten.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"znt0i5zouc","ctcId":3301,"ctcDifficulty":"MEDIUM","title":"No, the other side","author":"Scott Strosahl","rules":"Normal sudoku rules apply\n\nOpposite X-Sums: Numbers outside the grid indicate the sum of the LAST N digits, where N is the FIRST digit in the indicated row/column","rulesClarified":"Normal sudoku rules apply.\n\nNumbers outside the grid are sums. A number outside a row or column applies to that row or column only.\n\nTo read a clue, look at the digit in the cell at the clue's end of that row or column. Call that digit N. The clue is the sum of the last N digits: the N cells at the far end of the row or column, counting from the far side. The clue cell itself is outside the grid and is not counted.\n\nA row or column may have a clue at each end. Each clue is worked out on its own.","solution":"627345198853169724149728536362814975918537462475692813786251349534976281291483657","constraints":["x-sum"],"constraintFacts":[{"slug":"x-sum","type":"x-sum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"9702l0djmf","ctcId":3302,"ctcDifficulty":"VERY HARD","title":"The reckoning","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nDigits cannot repeat within a cage. If the digits in a cage sum to N, there are exactly N cages whose digits sum to N.","solution":"159632874678514293432897516213948657586723149947156382721389465365471928894265731","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If the digits in a cage sum to N, there are exactly N cages whose digits sum to N.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"1b5i3a2d2d","ctcId":3304,"ctcDifficulty":"HARD","title":"Reborn hooligan ghost","author":"Lithium-Ion","rules":"Normal sudoku rules apply. A digit in a circle equals the sum of all orthogonally adjacent cells. All circles are given.","solution":"179543826824916375563782419287659143936421587415378962391264758742895631658137294","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a circle equals the sum of all orthogonally adjacent cells. All circles are given.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"8s7d1v9agq","ctcId":3305,"ctcDifficulty":"MEDIUM","title":"Auralis","author":"Rab3aron","rules":"Normal sudoku rules apply. \nThe 3x3 box borders divide blue lines into segments. The digits on each segment of the same line must sum to the same total. eg r4c9 + r5c9 + r6c9 = r7c8 + r7c9.\nDigits in cells joined by a yellow dot are not consecutive.","solution":"921457836378962145654138792189725463267349581435681279716294358843516927592873614","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in cells joined by a yellow dot are not consecutive.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"encxi3ci5i","ctcId":3308,"ctcDifficulty":"MEDIUM","title":"Proximity","author":"zetamath","rules":"Normal sudoku rules apply.\n\nArrows: Digits along an arrow must sum to the number indicated in the circle from which the arrow emerges. Digits may repeat along arrows if allowed by other rules.\n\nQuadruples: Digits in a Quadruple circle must be placed at least once in the four cells touching that circle.","rulesClarified":"Normal sudoku rules apply.\n\nArrows: each arrow starts at a circle. The digits along the arrow must sum to the number indicated in that circle. The circle's own cell is not part of the sum.\n\nDigits may repeat along arrows if allowed by other rules.\n\nQuadruples: a quadruple circle sits on the corner shared by four cells, and those four cells are the cells it touches. The digits written in a quadruple circle must each be placed at least once in those four cells.","solution":"745826913621397485893154267972468351158239746436715892287641539369582174514973628","constraints":["arrow","quadruple"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"gcyif48z31","ctcId":3309,"ctcDifficulty":"HARD","title":"Just Sum Long Lines","author":"HalfBakedLunatic (aka David Workman)","rules":"• Normal Sudoku Rules Apply\n• Box borders divide the Blue Region Sum Lines into segments with the same sum","solution":"542891376937264581186375294654932817823417965791586432469128753218753649375649128","constraints":["region-sum-line"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"1tzwquyhbb","ctcId":3311,"ctcDifficulty":"VERY HARD","title":"Stishovite","author":"bellsita and Wisteria Fall (supervised by XeonRisq)","rules":"Normal sudoku rules apply. \nNo digit may appear more than once on a particular clue type. \nClue types: \n1) Adjacent digits on a green line differ by 5 or more; \n2) Purple lines must contain a set of consecutive non-repeating digits in any order; \n3) Any sequence of 3 adjacent digits along a teal line must contain a complete set of residuals modulo 3, i.e: one from (1,4,7), one from (2,5,8) and one from (3,6,9); \n4) Digits along a red line must alternate between odd and even; \n5) Digits may not repeat within a cage; \n6) The grey circle contain an odd digit. The grey squares contain even digits. \n7) Cells separated by a black dot have a 1:2 ratio (ie one is double the other); \n8) Cells separated by a white dot must be consecutive.","solution":"365921874814657329792384651481573296237169548956248137129436785548712963673895412","constraints":["cage","custom","even","german-whispers","kropki","modular-line","odd","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No digit may appear more than once on a particular clue type. 4) Digits along a red line must alternate between odd and even;","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c7"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10","c11"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"3fb9325t0p","ctcId":3312,"ctcDifficulty":"HARD","title":"Surrounded by oddness","author":"Jonesy","rules":"Hello.\n\nNormal Sudoku rules apply.\n\nOrthogonally adjacent cells may not both contain even digits.\n\nDigits along an arrow sum to the digit in its circle.\n\nHave fun.","solution":"457163892389452761612987435543678129298315674761294583936741258125836947874529316","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Orthogonally adjacent cells may not both contain even digits.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"y0vht5ywm4","ctcId":3313,"ctcDifficulty":"MEDIUM","title":"Loss for Words","author":"Br1312te","rules":"Place the digits 1-9 in every row, column and box.\n\nGerman Whisper Lines: two cells connected by a green line must have a difference of at least 5. \n\nRenban Lines: digits on a magenta line form a set of consecutive, not-repeating digits in any order. \n\nLove, Brigitte","solution":"964837251512694873783215964257361498839452716641978325398126547476589132125743689","constraints":["german-whispers","renban"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"0do1zxouyi","ctcId":3314,"ctcDifficulty":"VERY HARD","title":"Lupin's Loop 4 - Surrounded","author":"Rab3aron","rules":"Normal sudoku rules apply. \nA greater-than symbol points towards the smaller number. \nDraw two metro lines that travel orthogonally from cell to cell, never branching, crossing, or overlapping, either with themselves or with each other, which eventually close to form two loops. Thick black walls cannot be crossed by the lines. One loop must lie entirely inside the other, so the outer loop completely surrounds the inner loop. \nEvery station must lie on a loop. All cells on the same loop share the same parity (the two loops may have the same or different parities).\nA digit in a red sensor equals the number of cells visited by either loop in the 3×3 box centred on that cell. \nA digit in a station equals the total number of stations containing that digit. \nThe mirror cell has mirrored parity, meaning its parity is considered to be the opposite of its real parity. If a loop passes through it, treat the cell according to this mirrored parity.","solution":"423719568975683124186425379648237915712958643539164287297546831851372496364891752","constraints":["counting-circle","custom","inequality"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw two metro lines that travel orthogonally from cell to cell, never branching, crossing, or overlapping, either with themselves or with each other, which eventually close to form two loops. Thick black walls cannot be crossed by the lines. One loop must lie entirely inside the other, so the outer loop completely surrounds the inner loop. Every station must lie on a loop. All cells on the same loop share the same parity (the two loops may have the same or different parities). A digit in a red sensor equals the number of cells visited by either loop in the 3×3 box centred on that cell. The mirror cell has mirrored parity, meaning its parity is considered to be the opposite of its real parity.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c6","c7","c8","c10"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"8spurrnmcc","ctcId":3315,"ctcDifficulty":"HARD","title":"Coldulo","author":"Kaktuslav","rules":"Normal sudoku rules apply. The nine marked cells contain the digits 1–9, each exactly once.\n\nIf a marked cell contains the digit N, then every vertical group of N consecutive cells in its column has remainders 0, 1, ..., N−1, in some order, when its digits are divided by N. Such a group may start anywhere in the column; it does not need to contain the marked cell.\n\nFor example, if a marked cell contains 4, then every four consecutive cells in its column have remainders 0, 1, 2, 3 modulo 4, in some order.","solution":"517394862463278951982156743836421597194567328725839416241785639379642185658913274","constraints":["custom","region"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If a marked cell contains the digit N, then every vertical group of N consecutive cells in its column has remainders 0, 1, ..., N−1, in some order, when its digits are divided by N. Such a group may start anywhere in the column; it does not need to contain the marked cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region","type":"region","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"et4mh85g07","ctcId":3316,"ctcDifficulty":"HARD","title":"Sulla Via Della Gloria","author":"Playmaker6174","rules":"Normal Sudoku rules apply.\nThe cell marked with a blue diamond contains an even digit, while the cell marked with a red diamond contains an odd digit.\nTwo cells marked with yellow squares must contain the same digits; similarly, two cells marked with yellow circles must contain the same digits.\nDigits along a thin gray arrow sum to the digit in the pink circle cell attached to that arrow.\nThe sum of the digits along the pink line that has two pink circles as its endpoints must equal to the sum of two digits in both circles.\nWithin a cage, digits sum to the small number written in the top left of that cage.\nAlong the green line, two adjacent digits have the difference of at least 5.\nBox borders divide the thicker gray line into smaller segments with the same sum of digits along each segment.","solution":"764981235512364798389257461931475682258619374647832519126593847875146923493728156","constraints":["arrow","cage","clone","custom","even","german-whispers","odd","region-sum-line"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits along the pink line that has two pink circles as its endpoints must equal to the sum of two digits in both circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"191t7peym8","ctcId":3317,"ctcDifficulty":"MEDIUM","title":"Dutch Flat Mates: Multiple Lines","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nEvery 5 in the grid must have a 1 directly above it, or a 9 directly below it. It may have both, but it doesn't need both.\n\nFor two adjacent digits along a coloured line, dividing one by the other gives an exact integer (one is a multiple of the other.)","rulesClarified":"Normal sudoku rules apply.\n\nEvery 5 in the grid must have a 1 directly above it, or a 9 directly below it. A 5 in the top row has no cell above it, so it needs a 9 directly below. A 5 in the bottom row has no cell below it, so it needs a 1 directly above.\n\nA 5 may have both, but it does not need both.\n\nAlong each coloured line, take every pair of adjacent digits. For each pair, one digit must divide exactly into the other, so one is a multiple of the other. Equal digits pass, since each divides the other exactly.","solution":"719258634452396718863471952291543876675982143384617529937825461146739285528164397","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every 5 in the grid must have a 1 directly above it, or a 9 directly below it. For two adjacent digits along a coloured line, dividing one by the other gives an exact integer (one is a multiple of the other.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"gbpdlymn6r","ctcId":3319,"ctcDifficulty":"MEDIUM","title":"Arithmetid Quiy","author":"mnasti2","rules":"Normal sudoku rules apply: Place the digits 1-9 exactly once each in every row, column, and 3x3 box.\n\nOff-By-One Equations: Complete each equation in the grid so that the right hand side is exactly one greater or one less than the value of the left hand side, using standard arithmetic operations. Two-cell pills represent two-digit numbers.\n\nAdjacent digits along a red line differ by at most 2.","solution":"148297563259361784376458921421879356597643218683125479732916845815734692964582137","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Off-By-One Equations: Complete each equation in the grid so that the right hand side is exactly one greater or one less than the value of the left hand side, using standard arithmetic operations. Two-cell pills represent two-digit numbers. Adjacent digits along a red line differ by at most 2.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]}]},{"id":"gf8l5f4s64","ctcId":3320,"ctcDifficulty":"VERY HARD","title":"Reciprocals","author":"Kaktuslav","rules":"Normal sudoku rules apply.\n\nYin–Yang: shade some cells in the grid so that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2×2 region is entirely shaded or entirely unshaded. \n\nEvery shaded cell containing digit x has value 1/x; every unshaded cell has value equal to its digit.\n\nProduct/Sum cages: each cage has a corner mark in the leftmost cell of its top row identifying its type. If it shows Σ=X, the values in the cage sum to X; if it shows Π=X, the values in the cage multiply to X (X is not necessarily an integer). Digits or values MAY repeat within a cage.\n\nDynamic Fog of War: the grid is partially covered in fog. Placing correct digits reveals their own cell and may also lift fog elsewhere in the grid. No guessing is required.","solution":"438912567176548392925376481749623158683751249512894673851267934267439815394185726","fogLight":"R4C4,R5C4,R6C4,R6C5,R5C5,R4C5,R4C6,R5C6,R6C6","constraints":["cage","custom","fog","yin-yang"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"If it shows Σ=X, the values in the cage sum to X; if it shows Π=X, the values in the cage multiply to X (X is not necessarily an integer).","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Every shaded cell containing digit x has value 1/x; every unshaded cell has value equal to its digit. If it shows Σ=X, the values in the cage sum to X; if it shows Π=X, the values in the cage multiply to X (X is not necessarily an integer).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"inhwpyj59k","ctcId":3321,"ctcDifficulty":"VERY HARD","title":"Increasing Differences","author":"Aad van de Wetering","rules":"Normal sudoku rules apply.  Along the marked diagonals the differences between neighbouring digits increase from left to right, such that the difference of the first pair is 1, of the second pair 2, of the third pair 3, etc.","solution":"671459832835162749294873561429385176316947285587216394742598613163724958958631427","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Along the marked diagonals the differences between neighbouring digits increase from left to right, such that the difference of the first pair is 1, of the second pair 2, of the third pair 3, etc.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"pzl2b5oua1","ctcId":3322,"ctcDifficulty":"MEDIUM","title":"A Bouquet Of Complements","author":"RockyRoer","rules":"Normal sudoku rules apply. \nEntering enough correct digits in cells will reveal more of the puzzle – no guessing is required. \nA pair of 2-digit numbers read from left to right are circled. This pair of numbers must add to 90. Each time the fog clears, another pair will appear - each time summing to 90. \nDigits in a cage must sum to the total given in the cage’s upper left corner. \nDigits on a purple “Renban” line form a set of consecutive numbers. \nAny three adjacent digits on a teal “Modular” line must include one digit from each of the sets {147}, {258}, {369}. \nAny two adjacent cells on a green German Whisper line have a difference of at least 5. \nCells separated by a white dot have a difference of 1.","solution":"312697458478215639659843271945126387783459126126378945567932814291584763834761592","fogLight":"R4C4,R4C5,R4C6,R5C6,R5C5,R5C4,R6C5,R6C6","constraints":["cage","custom","fog","german-whispers","kropki","modular-line","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"This pair of numbers must add to 90.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"bq3bqqtcix","ctcId":3323,"ctcDifficulty":"HARD","title":"A Longer Snake in the Grass","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nSNAKE:\nDraw a snake, one cell wide, that starts and ends at two neighbouring cells within the same 3x3 box. The snake only moves orthogonally, and visits every cell in the grid apart from the large grey rock in the central cell. The snake may not enter any cell more than once.\n\nINSECTS:\nThe snake must eat every insect, and these divide the snake into segments. Adjacent segments along the snake have consecutive totals. No two segments have the same total.\n\nGREY PEBBLES:\nThe snake must not pass directly through any grey pebbles. Digits joined by a grey pebble are either consecutive, or have a 1:2 ratio.\n\nEGGS:\nOne of the four digits surrounding an egg indicates the number of spots on that egg.","solution":"591386247627549183843127569765213498489765312132498756216874935378951624954632871","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a snake, one cell wide, that starts and ends at two neighbouring cells within the same 3x3 box. The snake only moves orthogonally, and visits every cell in the grid apart from the large grey rock in the central cell. The snake may not enter any cell more than once. The snake must eat every insect, and these divide the snake into segments. Adjacent segments along the snake have consecutive totals. No two segments have the same total. The snake must not pass directly through any grey pebbles. One of the four digits surrounding an egg indicates the number of spots on that egg.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c7","c8","c9","c11","c14"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"Digits joined by a grey pebble are either consecutive, or have a 1:2 ratio.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c12"]}]},{"id":"xug1fmiw9y","ctcId":3324,"ctcDifficulty":"VERY HARD","title":"Fortress Yin Yang","author":"yttrio","rules":"Normal Sudoku rules apply.\n\nYin Yang: Shade some cells such that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2x2 area is fully shaded or fully unshaded.\n\nShaded cells act as fortress (maximum) cells: shaded cells must be larger than all orthogonal neighbors of the cell that are unshaded.\n\nA digit in a cell with an arrow counts the total number of shaded cells seen in the direction of the arrow (not counting the cell itself).","solution":"329561847814723956657489213546938172973214568182675394761352489438196725295847631","constraints":["custom","maximum","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a cell with an arrow counts the total number of shaded cells seen in the direction of the arrow (not counting the cell itself).","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"maximum","type":"maximum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"6k7r2bex5r","ctcId":3325,"ctcDifficulty":"MEDIUM","title":"Chaotic Zippers","author":"Dorlir","rules":"Chaos Construction: Divide the grid into nine regions each consisting of nine orthogonally-connected cells. Each row, column and region must contain the digits 1 to 9, once each.\n\nZipper line: Digits an equal distance from the center of the purple line must sum to the digit in the center of that purple line. Different zippers don't share cells with each other.\n\nLots: The digit in the center of a purple line counts how many regions contain at least one cell on that purple line.\n\nRegion borders: Some region borders are given.\n\nDynamic fog: Entering a correct digit clears fog in its cell, and may or may not clear fog in other cells.","solution":"512867394128693745286739451869374512673945128937451286394512867745128639451286973","fogLight":"R1C3,R1C4,R1C5,R1C6,R1C7,R1C8,R2C8,R3C7,R4C7,R5C7,R2C1,R3C9,R2C3,R2C4,R3C8,R4C8,R4C9,R5C9,R5C8,R2C7,R6C7,R6C8,R6C9,R7C9,R7C8,R7C7,R8C7,R8C8,R8C9,R9C9,R9C8,R9C7","constraints":["custom","fog","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Chaos Construction: Divide the grid into nine regions each consisting of nine orthogonally-connected cells. Different zippers don't share cells with each other. Lots: The digit in the center of a purple line counts how many regions contain at least one cell on that purple line. Region borders: Some region borders are given.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c4","c5","c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"whrb3lnsey","ctcId":3326,"ctcDifficulty":"VERY HARD","title":"CTC 700k Subs","author":"WombatBreath","rules":"Normal irregular sudoku rules apply - digits (1-9) may not repeat in any row, column, region or cage. Digits on a purple (renban) line must form a non-repeating consecutive set (in any order). A white dot between cells shows they contain consecutive digits, and a black dot between cells indicates that they contain digits in a 2:1 ratio - all black dots _on_lines_ are shown. The 'K' cell may NOT contain a prime factor of 700,000 (2, 5 or 7).","solution":"742936158375812496684751329863495217519263784456129873931687542297548631128374965","constraints":["cage","custom","kropki","renban"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c1"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The 'K' cell may NOT contain a prime factor of 700,000 (2, 5 or 7).","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"A white dot between cells shows they contain consecutive digits, and a black dot between cells indicates that they contain digits in a 2:1 ratio - all black dots _on_lines_ are shown.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Digits on a purple (renban) line must form a non-repeating consecutive set (in any order).","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"wxbluqtoso","ctcId":3327,"ctcDifficulty":"HARD","title":"Rapuzzle, Rapuzzle, Let Down Your Sausage","author":"ThePedallingPianist","rules":"(Artwork by DubiousMobius; puzzle heavily inspired by [Scojo](https://sudokupad.app/xowd4rzqqg))\n---\n\nNormal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nAnti-Knight: Cells a chess knight's move away cannot contain the same digit.\n\nTower Fortress: Cells that are part of the gray tower must be greater than all orthogonally adjacent non-tower cells. Note: any cell that the tower even partially covers is considered a fortress cell.\n\nRapunzel's Sausage: The difference between the sums of two linked sausages on a chain must be exactly equal to the number of sausages in that chain.\n\nRapunzel's Face: The digit on Rapunzel's face shows how many numbers of the opposite odd/even parity to itself appear on the whole sausage chain.","solution":"451926378739841526628735941562173894143298657987654213876512439315489762294367185","constraints":["antiknight","custom"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Tower Fortress: Cells that are part of the gray tower must be greater than all orthogonally adjacent non-tower cells. Rapunzel's Sausage: The difference between the sums of two linked sausages on a chain must be exactly equal to the number of sausages in that chain. Rapunzel's Face: The digit on Rapunzel's face shows how many numbers of the opposite odd/even parity to itself appear on the whole sausage chain.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c7","c8"]}]},{"id":"i8sa44138x","ctcId":3328,"ctcDifficulty":"MEDIUM","title":"Cataract","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nDots divide lines into segments with equal sums. Digits may repeat on lines but not within a segment.","solution":"542781369917563428863294751394672185786915234125348697631459872258137946479826513","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Dots divide lines into segments with equal sums. Digits may repeat on lines but not within a segment.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"4b16rwzym1","ctcId":3329,"ctcDifficulty":"HARD","title":"Unlucky 13","author":"Possible Spam Risk","rules":"⚠️ WARNING ⚠️\nEXTREME PUZZLE AHEAD\n\nExtreme puzzles can cause dangerous reactions in some solvers.\n\nSymptoms include:\n  - shortness of breath\n  - heart palpitations\n  - dizziness/faintness\n\nIf you are unlucky enough to experience these symptoms, consider contacting an appropriate emergency or crisis number — perhaps one of the “Unlucky 13” numbers given in the clues.\n-----------------------------------------------------------------------------------------\n\nJapanese Sums rules apply, with the additions described below. Colors are gray (g), brown (w), blue (u), brick (k), and yellow (y). The shading may resolve before the puzzle does; if so, removing unshaded markings is recommended. Goodliffing will likely be your best friend in this puzzle.\nBonus challenge: Before placing any digits or numerical markings, see how much shading (including unshaded) you can determine. Then count the cells whose shading remains undetermined. My best result leaves 8 cells with undetermined shading.\n\nUnknown Sum rules apply.\n“Unlucky 13” rules apply.\n\nJapanese Sums rules:\nThe squares outside the grid indicate the order of the runs of contiguous cells that sum to the number in the square and are shaded the color of the square. There must be at least one unshaded cell between runs of the same color. All runs are given.\n\nUnknown Sum rules:\nFor many clues, the run’s sum is unknown. If the clue contains a single question mark, the clue is a one-digit number. If the clue contains two question marks, the clue is a two-digit number.\n\n“Unlucky 13” rules:\nThere are 13 three-digit emergency or crisis numbers represented by the listed clues. Every clue with a printed numeric value is part of one of these numbers; no unknown clue (? or ??) is part of any number. Each number is formed by reading clue values in order. For example, the number 615 could appear as a 6 followed by a 15.  Identifying the actual emergency or crisis numbers may be interesting, but it is not necessary to solve the puzzle.","solution":"934276815271958436865341729528764391719823654346519287487135962192687543653492178","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The squares outside the grid indicate the order of the runs of contiguous cells that sum to the number in the square and are shaded the color of the square. There must be at least one unshaded cell between runs of the same color. If the clue contains a single question mark, the clue is a one-digit number. If the clue contains two question marks, the clue is a two-digit number. Every clue with a printed numeric value is part of one of these numbers; no unknown clue (? or ??) is part of any number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c20","c21","c25","c26","c29"]}]},{"id":"utaq8fddwh","ctcId":3330,"ctcDifficulty":"HARD","title":"Segment Counter","author":"Kaktuslav","rules":"Normal sudoku rules apply. The 3x3 box borders divide each blue line into segments. Along any individual blue line, all segments have the same sum. Different blue lines may have different sums. If a circled cell on a blue line contains the digit N, then the digit N appears in exactly N segments of that blue line (including the segment containing the circle).","solution":"351927846269854713487136952572348169648719235193562478916483527834275691725691384","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"If a circled cell on a blue line contains the digit N, then the digit N appears in exactly N segments of that blue line (including the segment containing the circle).","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"n7a6oi1gyy","ctcId":3331,"ctcDifficulty":"MEDIUM","title":"Banksy Wor-King at Queen's Mews","author":"olima","rules":"Normal Sudoku rules apply. Digits a King's move (in chess) apart must be different. Adjacent digits on a green line differ by at least 5. On thermos digits increase from bulb to the tips.","solution":"648193275537248961219657348754326819196584723382971654971865432865432197423719586","constraints":["antiking","german-whispers","thermometer"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"ybaev4x39i","ctcId":3332,"ctcDifficulty":"HARD","title":"Lupin's Loop 5 - Countercount","author":"Rab3aron","rules":"Normal Sudoku rules apply. A greater than sign points to the smaller number.\nDraw a single route for the airplane that travels orthogonally from cell to cell, never branching, crossing, or overlapping, and eventually closes into a loop. The route starts at the airplane, passes through every country, and returns to its starting point. Thick black borders represent heavy turbulence that the airplane cannot cross. If a digit N appears on the route, then the digit N appears exactly N times in cells not on the route. If two countries are directly connected by the route, their digits differ by the length of the segment connecting them. If a country and the airplane are directly connected by the route, the digit in the airplane equals the length of the segment connecting them.\n\nNote: Segment lengths include both endpoints. Two objects are directly connected by the route if no other object lies between them along the route.","solution":"298564317357218964461397582985672431123945678746831295879423156612759843534186729","constraints":["custom","inequality"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single route for the airplane that travels orthogonally from cell to cell, never branching, crossing, or overlapping, and eventually closes into a loop. The route starts at the airplane, passes through every country, and returns to its starting point. Thick black borders represent heavy turbulence that the airplane cannot cross. If a digit N appears on the route, then the digit N appears exactly N times in cells not on the route. If two countries are directly connected by the route, their digits differ by the length of the segment connecting them. If a country and the airplane are directly connected by the route, the digit in the airplane equals the length of the segment connecting them.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c6","c7","c8"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"geypyx7wpd","ctcId":3333,"ctcDifficulty":"HARD","title":"On and Off","author":"Kaktuslav","rules":"Normal sudoku rules apply.\n\nDraw a single path through the centres of cells. The path may not branch, cross itself, or visit any cell more than once. Segments of the path alternate between diagonal segments, joining two cells that touch at a corner, and vertical segments, joining two vertically adjacent cells. Any four consecutive cells along the path contain digits with four different remainders when divided by 4.\n\nEvery square lies on the path; every circle lies off the path. If a square contains digit N, then digit N occurs exactly N times on the path. If a circle contains digit N, then digit N occurs exactly N times in cells not on the path.","solution":"512847639349561872768392514957128346431756928286934157824613795693475281175289463","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single path through the centres of cells. The path may not branch, cross itself, or visit any cell more than once. Segments of the path alternate between diagonal segments, joining two cells that touch at a corner, and vertical segments, joining two vertically adjacent cells. Any four consecutive cells along the path contain digits with four different remainders when divided by 4. Every square lies on the path; every circle lies off the path. If a square contains digit N, then digit N occurs exactly N times on the path. If a circle contains digit N, then digit N occurs exactly N times in cells not on the path.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c7","c8"]}]},{"id":"5luwmmvgku","ctcId":3334,"ctcDifficulty":"HARD","title":"One with the Circus","author":"Jeff Wajes","rules":"Normal Sudoku rules apply.\n\nUsing red, green, and blue, color in all circles such that:\n-Orthogonally adjacent circles are different colors.\n-The digit inside a circle appears that many times in circles of that color.","solution":"875369421614527983329418576562134897498672135731985264986751342257843619143296758","constraints":["counting-circle","custom"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Using red, green, and blue, color in all circles such that: -Orthogonally adjacent circles are different colors.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"vn44db0fft","ctcId":3335,"ctcDifficulty":"HARD","title":"Network","author":"Jobo","rules":"Normal sudoku rules apply.\n\nDigits along an arrow must sum to the digit in that arrow's circle.\n\nThe sum of the digits along a double arrow line connecting two circles is equal to the sum of the digits in the circles.","solution":"426537918975814623381629457843961572697253184152748396219376845764185239538492761","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of the digits along a double arrow line connecting two circles is equal to the sum of the digits in the circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"6si77ldvw5","ctcId":3336,"ctcDifficulty":"MEDIUM","title":"Ten to N","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nIf a black dot sits between two digits, then one is double the other.\n\nIn row N or column N, a clue outside the grid indicates the sum of all the digits that appear in that row or column before reaching the digit N, reading from the end nearest the clue. (The digit N is not included in the sum.)","solution":"251369847789542631643871925374698512195234786826715493917426358468153279532987164","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In row N or column N, a clue outside the grid indicates the sum of all the digits that appear in that row or column before reaching the digit N, reading from the end nearest the clue.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"b2lc8walej","ctcId":3337,"ctcDifficulty":"MEDIUM","title":"Diagonal stretch","author":"Lithium-Ion","rules":"Normal sudoku rules apply. Digits along an arrow may repeat and sum to the digit in the attached circle.","solution":"783254961156937482249861753497186235635729814821543679568392147974615328312478596","constraints":["arrow"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"dk7jgt7xov","ctcId":3338,"ctcDifficulty":"HARD","title":"Factory Loop","author":"Marty Sears","rules":"Normal sudoku rules apply. \n\nDraw a loop, one-cell wide, that moves orthogonally between cells. The loop cannot touch itself, even diagonally: ie If two loop cells are side-by-side, they must be directly connected by the loop; and, if a 2×2 area contains two diagonal loop cells, they must be connected by a third loop cell in that same 2x2. \n\nA green circle is on the loop, and its digit indicates the number of cells in its box that are on the loop. \n\nA red square is NOT on the loop, and its digit indicates the number of cells in its box that are NOT on the loop. \n\nFor any two neighbouring cells along the loop, dividing one by the other gives an exact integer (one is a multiple of the other.)","rulesClarified":"Normal sudoku rules apply.\n\nDraw one loop. It is one cell wide and moves orthogonally from one cell to the next.\n\nThe loop cannot touch itself. If two loop cells sit side by side, the loop must connect them directly. If a 2x2 block contains two loop cells that touch only diagonally, they must be connected by a third loop cell in that same 2x2 block.\n\nEach green circle is on the loop. Its digit is the number of cells of its 3x3 box that are on the loop, and the circle's own cell counts.\n\nEach red square is not on the loop. Its digit is the number of cells of its 3x3 box that are not on the loop, and the square's own cell counts.\n\nFor any two cells that are next to each other along the loop, dividing one digit by the other gives a whole number.","solution":"624819375153472689879365214481527963235986741796143852512798436368254197947631528","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a loop, one-cell wide, that moves orthogonally between cells. The loop cannot touch itself, even diagonally: ie If two loop cells are side-by-side, they must be directly connected by the loop; and, if a 2×2 area contains two diagonal loop cells, they must be connected by a third loop cell in that same 2x2. A green circle is on the loop, and its digit indicates the number of cells in its box that are on the loop. A red square is NOT on the loop, and its digit indicates the number of cells in its box that are NOT on the loop. For any two neighbouring cells along the loop, dividing one by the other gives an exact integer (one is a multiple of the other.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6"]}]},{"id":"or42ce5os1","ctcId":3340,"ctcDifficulty":"HARD","title":"Arrow Dynamics","author":"Newjoyku","rules":"- Normal sudoku rules apply, i.e. each row, column, and 3x3 region has to contain the digits from 1 to 9 once each.\n\n- Arrows: Digits on an arrow sum to the digit in the circle from which the arrow emerges.\n\n- Index Lines: Each turquoise line is an Index Line, i.e. the digit in the Nth cell along such a line (starting from the diamond) indicates the position along the line where the digit N appears. For example, if a diamond cell contains a 3, the third cell along that line must have a 1.","solution":"743852619612379584958416372274195863536748291189623745397281456465937128821564937","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Index Lines: Each turquoise line is an Index Line, i.e. the digit in the Nth cell along such a line (starting from the diamond) indicates the position along the line where the digit N appears. For example, if a diamond cell contains a 3, the third cell along that line must have a 1.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"m64296ezsf","ctcId":3342,"ctcDifficulty":"MEDIUM","title":"Double Arrows","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow's circle. Cells separated by a single king's move (in chess) cannot contain the same digit.","solution":"154629387372851496869743512938162745245978631617435928423517869596284173781396254","constraints":["antiking","arrow"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"j99cp5qm7t","ctcId":3345,"ctcDifficulty":"MEDIUM","title":"Willkommen im Palindrom","author":"billybeth","rules":"Normal Sudoku rules apply\nLine is german palindrome where each consectuive number on the line is at least five apart and the numbers on the line are the same in both directions.\nNumber in the grey cell must be larger than those in the cells surrounding it.","solution":"745286913926713845318549627167935482834172596259468371572394168691857234483621759","constraints":["german-whispers","maximum","palindrome"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"maximum","type":"maximum","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"98offhjkjo","ctcId":3346,"ctcDifficulty":"HARD","title":"Loony Tune","author":"billybeth","rules":"Normal Sudoku rules apply\nThe red/yellow lines are a famous tune put into C major using notes of the scale from 1 to 5 (1=c, 2 =d etc). The yellow line is the first line of the tune and the red line is the second line of the tune. On a green line, adjacent digits have a difference of at least 5. A purple line contains a set of non-repeating consecutive digits, in any order.","rulesClarified":"Normal Sudoku rules apply.\n\nThe yellow line and the red line together are a famous tune, put into C major. The yellow line is the first line of the tune and the red line is the second line.\n\nEach digit on the yellow and red lines is a note of the C major scale from 1 to 5: 1 is C, 2 is D, 3 is E, 4 is F, 5 is G.\n\nOn a green line, adjacent digits differ by at least 5.\n\nA purple line contains a set of non-repeating consecutive digits, in any order.","solution":"125896473789345162643712589392681745814257936576934821957463218431528697268179354","constraints":["custom","german-whispers","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The red/yellow lines are a famous tune put into C major using notes of the scale from 1 to 5 (1=c, 2 =d etc).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"5542oxal82","ctcId":3347,"ctcDifficulty":"VERY HARD","title":"Slow Arrows","author":"billybeth","rules":"Normal Sudoku rules apply\nLines are slow thermometer arrows where in one direction the digits increase or stay the same from one end to the other, and in the other the first digit is the sum of the other digits on the line.","solution":"763895412942163578815274396186427935459638721237951864624389157371546289598712643","constraints":["arrow","thermometer"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"modified","modifiers":[],"params":null,"note":"Lines are slow thermometer arrows where in one direction the digits increase or stay the same from one end to the other, and in the other the first digit is the sum of the other digits on the line.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Lines are slow thermometer arrows where in one direction the digits increase or stay the same from one end to the other, and in the other the first digit is the sum of the other digits on the line.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]}]},{"id":"ski1zlop0c","ctcId":3348,"ctcDifficulty":"MEDIUM","title":"Poison Arrows","author":"billybeth","rules":"Normal Sudoku rules apply.\nOn Poison Arrows the digits in the circles are the sum of the digits on their line (including the tip) divided by the digit on their tip.","solution":"269753148735184629418926573657812394824539716391467285173648952582391467946275831","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On Poison Arrows the digits in the circles are the sum of the digits on their line (including the tip) divided by the digit on their tip.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7si4uhm696","ctcId":3349,"ctcDifficulty":"MEDIUM","title":"Call 999","author":"billybeth","rules":"Normal Sudoku rules apply. \nThe small number in the corner of each cage is the sum of all the digits in that cage including those in the small number itself. All the small numbers are different.\nBlack dots separate cells in the ratio of 1:2","rulesClarified":"Normal Sudoku rules apply.\n\nEach cage has a small number in its corner. That small number is the total of all the digits in the cage. The total includes the digits of the small number itself.\n\nAll the small numbers are different from one another.\n\nA black dot sits between two cells. Their digits are in a 1:2 ratio: one is double the other.","solution":"483579126716423598259681437621345879378192654594867312142936785837254961965718243","constraints":["cage","custom","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All the small numbers are different.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"pyufyvwwpw","ctcId":3350,"ctcDifficulty":"HARD","title":"Tree Squirrel","author":"Derek LeClair","rules":"Normal sudoku rules apply. The 3x3 box borders divide the blue line into segments. Each segment's total is found by summing the digits on that segment. The segment totals must increase by 1 from one end of the line to the other. Adjacent digits on the line must not be consecutive.","solution":"479526183163984527825731694754693218912478356638152479397245861581367942246819735","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent digits on the line must not be consecutive.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"The segment totals must increase by 1 from one end of the line to the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"07innbtid1","ctcId":3351,"ctcDifficulty":"MEDIUM","title":"Delta Line","author":"Derek LeClair","rules":"Normal sudoku rules apply. The 3x3 box borders divide the blue line into segments with the same sum. Adjacent digits along the line have a difference of at most 2.","solution":"968753124327148596451926378643812759175394682892567431286475913714239865539681247","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Adjacent digits along the line have a difference of at most 2.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"7k71v1ey6x","ctcId":3352,"ctcDifficulty":"MEDIUM","title":"Square Pairs","author":"Derek LeClair","rules":"Normal sudoku rules apply. A pair of adjacent digits along a line sum to a square number.","solution":"319724658875936421246815973728591364934678512561342897457263189182459736693187245","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A pair of adjacent digits along a line sum to a square number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"61g1ssiok4","ctcId":3353,"ctcDifficulty":"MEDIUM","title":"Regional Renbans","author":"Derek LeClair","rules":"Normal sudoku rules apply. The 3x3 box borders divide a purple line into segments with the same sum. Each segment is also a non repeating consecutive set of digits in any order.","solution":"321978654568431279479256138983712465614385927257694813895167342746823591132549786","constraints":["region-sum-line","renban"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"The 3x3 box borders divide a purple line into segments with the same sum.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"Each segment is also a non repeating consecutive set of digits in any order.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"pyvvk21c84","ctcId":3354,"ctcDifficulty":"MEDIUM","title":"Rising Regions","author":"Derek LeClair","rules":"Normal sudoku rules apply. The 3x3 box borders divide the blue line into segments. The sum of each segment must increase from one end of the line to the other. Any 2 connected segments have no digits in common. On a black dot, one digit is double the other.","solution":"241563978783192564965784132326457819157938246498621357519846723672319485834275691","constraints":["custom","kropki","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any 2 connected segments have no digits in common.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"The sum of each segment must increase from one end of the line to the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"glhzgch93y","ctcId":3355,"ctcDifficulty":"MEDIUM","title":"Whispering Regions","author":"Derek LeClair","rules":"Normal sudoku rules apply. The 3x3 box borders divide the line into segments. The sum of each segment must increase from one end of the line to the other. Adjacent digits along each segment (not the whole line) differ by at least 5.","solution":"389612457512847396764359821893465172127938645645271938951783264438526719276194583","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The sum of each segment must increase from one end of the line to the other.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"d70u447pn4","ctcId":3356,"ctcDifficulty":"HARD","title":"TDF Stage 1","author":"palpot","rules":"Normal Sudoku rules apply.\n\nThe following standard constraints apply: Dutch whisper, German whisper, Parity line, Ten line, Kropki, and XV. detailed rules below.\n\nStage Rules:\n\n1. Paths and Riders:\n Each line in the grid represents the path of a different rider:\n     - Yellow Rider (Dutch Whisper)\n     - Green Rider (German Whisper)\n     - Red Rider (Parity Line)\n     - Grey Rider (Ten Line)\n\n2. Scoring System:\n   - Yellow Rider: Earns 1 point for every 5 on its path.\n   - Green Rider: Earns 1 point for every 4 or 6 on its path.\n   - Red Rider: Earns 1 point for every adjacent pair of consecutive digits along its path.\n   - Grey Rider: Earns 1 point for every 3-cell segment that sums to 10 along its path.\n\nStage Results:\n1. Yellow Rider\n2. Green Rider\n3. Red Rider\n4. Grey Rider\n\nTo clarify, first place scored the highest amount of points, second place scored the highest after that and so on. There are no draws.\n\nDutch whisper: Two cells connected by a Yellow line must have a difference of at least 4.\nGerman whisper: Two cells connected by a Green line must have a difference of at least 5.\nParity line: Adjacent digits along the red line have a different odd/even parity.\nTen line: The Grey line must be divided into one or more contiguous groups of cells that each sum to 10. These groups of cells cannot overlap.\nKropki: Cells separated by a white dot must contain consecutive digits.\nXV: Cells separated by X must sum to 10. \nNot all dots and X's are necessarily given.","solution":"914685237528397164637421859859163742243978516761254398176542983392816475485739621","constraints":["XV","custom","dutch-whispers","german-whispers","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c28"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"- Yellow Rider: Earns 1 point for every 5 on its path. - Green Rider: Earns 1 point for every 4 or 6 on its path. - Red Rider: Earns 1 point for every adjacent pair of consecutive digits along its path. - Grey Rider: Earns 1 point for every 3-cell segment that sums to 10 along its path. To clarify, first place scored the highest amount of points, second place scored the highest after that and so on. Parity line: Adjacent digits along the red line have a different odd/even parity. Ten line: The Grey line must be divided into one or more contiguous groups of cells that each sum to 10.","evidence":"rules","lessonPolicy":"open","sectionIds":["c11","c12","c13","c14","c20","c24","c25"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c22"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c23"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c27"]}]},{"id":"15rywuvxz9","ctcId":3357,"ctcDifficulty":"MEDIUM","title":"The Composite Thread","author":"palpot","rules":"Normal sudoku rules apply. (ie Place the digits 1-9 once each in every row, column, and 3x3 box). The 3x3 box borders divide each blue line into segments. The digits on each segment of the same line must sum to the same total. (Eg r2c6+r3c6=r4c7+r4c8+r4c9). The digits along each line must sum to a unique number, and the sums of these lines must form a set of consecutive numbers.","solution":"792354816651278439438619572983125764574986123216437985349861257827543691165792348","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digits along each line must sum to a unique number, and the sums of these lines must form a set of consecutive numbers.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"7qo4oi3fi3","ctcId":3358,"ctcDifficulty":"MEDIUM","title":"TDF Odd Mountain Stage","author":"palpot","rules":"Normal Sudoku rules apply. Place the digits 1-9 once in each row, column, and 3X3 box.\n\nStage rules: \nEach line in the grid represents the path of a different rider. Riders earn 1 point for every odd digit on their path. \nDigit in a cell with a rider indicates the amount of points earned by that rider. The Red rider (R4C5) doesn't share a cell with its line.\n\nStage Results:\nThe Yellow rider scored more than the Green rider, who scored more than the Red rider, who scored more than the Teal rider.\n\nDutch Whisper: Two cells connected by a Yellow line must have a difference of at least 4.\n\nGerman Whisper: Two cells connected by a Green line must have a difference of at least 5.\n\nParity Line: Adjacent digits along the red line have a different odd/even parity.\n\nModular Line: Any set of three sequential cells along a dashed teal modular line contains one digit from (1,4,7), (2,5,8), and (3,6,9).","solution":"263497518817563429549218763185746392372985146496321857638159274721634985954872631","constraints":["custom","dutch-whispers","german-whispers","modular-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digit in a cell with a rider indicates the amount of points earned by that rider. The Yellow rider scored more than the Green rider, who scored more than the Red rider, who scored more than the Teal rider. Parity Line: Adjacent digits along the red line have a different odd/even parity.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c9","c12"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]}]},{"id":"7d9f9mb2y3","ctcId":3359,"ctcDifficulty":"MEDIUM","title":"TDF: The Route","author":"palpot","rules":"Normal sudoku rules apply. Place the digits 1 to 9 in each Row, Column, and 3X3 box.\n\nPath: Draw a one-cell-wide path through the centers of cells, starting at the rider (R1C9) and ending at the medal (R3C5). The path moves orthogonally between cells. It may not branch or visit any cell more than once.\n\nEntropy Path: Every set of three consecutive digits along the path must contain a low (1,2,3), a medium (4,5,6), and a high digit (7,8,9).\n\nMountain Stages: Each mountain cell lies on the path. The path must travel straight vertically through each mountain cell. If the digit in a mountain cell is N, then that mountain is part of a vertical straight section of length N. The sums of the digits above and below the mountain within that section must differ by N.\n\nFlat Stages: Each flat road cell lies on the path. The path must travel straight horizontally through each flat road cell. If the digit in a flat road cell is N, then that road is part of a horizontal straight section of length N. The sums of the digits to the left and right of the road within that section must differ by N.\n\nChequered Flags: Each chequered flag lies on the path. The path must turn at each flag, with one straight horizontal stage and one straight vertical stage meeting at the flag. If the digit in a flag cell is N, then both stages have length N, including the flag cell itself. The sums of the non-flag digits in the two stages must differ by N.\n\nSoigneurs: Soigneur (standing man) cells are not on the path. A digit in a Soigneur cell indicates the number of path cells in the (up to) 8 surrounding cells.","solution":"359168247627439815814275963438591672275386194961742358596824731742913586183657429","constraints":["custom","entropic-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Path: Draw a one-cell-wide path through the centers of cells, starting at the rider (R1C9) and ending at the medal (R3C5). The path moves orthogonally between cells. It may not branch or visit any cell more than once. Mountain Stages: Each mountain cell lies on the path. The path must travel straight vertically through each mountain cell. If the digit in a mountain cell is N, then that mountain is part of a vertical straight section of length N. The sums of the digits above and below the mountain within that section must differ by N. Flat Stages: Each flat road cell lies on the path. The path must travel straight horizontally through each flat road cell. If the digit in a flat road cell is N, then that road is part of a horizontal straight section of length N. The sums of the digits to the left and right of the road within that section must differ by N. Chequered Flags: Each chequered flag lies on the path. The path must turn at each flag, with one straight horizontal stage and one straight vertical stage meeting at the flag. If the digit in a flag cell is N, then both stages have length N, including the flag cell itself. The sums of the non-flag digits in the two stages must differ by N. Soigneurs: Soigneur (standing man) cells are not on the path. A digit in a Soigneur cell indicates the number of path cells in the (up to) 8 surrounding cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c7","c8","c9","c10","c11","c12","c13","c14","c15","c16","c17","c18"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"zh83rmuwoq","ctcId":3360,"ctcDifficulty":"MEDIUM","title":"Yin Yang Dominoes","author":"PuzzleTank","rules":"Normal Sudoku Rules: Place the digits 1-9 in every row, column and 3x3 box\nKiller: Digits in a cage must not repeat and sum to the number in the top left corner (if given)\nYin Yang: Shade some cells such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected. No 2x2 area can be entirely shaded or unshaded\nShading: All cages have 1 shaded cell and 1 unshaded cell. The largest digit in a cage is always shaded and the smallest digit is always unshaded. ALL GIVEN DIGITS ARE OF THE SAME SHADING\nKropki: Digits separated by a black dot are in a 1:2 ratio (not all black dots are given)","solution":"628157394147239658953486127386514972471392586592678413235861749764925831819743265","constraints":["cage","custom","kropki","yin-yang"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Shading: All cages have 1 shaded cell and 1 unshaded cell. The largest digit in a cage is always shaded and the smallest digit is always unshaded. ALL GIVEN DIGITS ARE OF THE SAME SHADING","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"at4s2p5e5e","ctcId":3361,"ctcDifficulty":"MEDIUM","title":"7 Greens 7 Cages","author":"PuzzleTank","rules":"Normal Sudoku: Place the digits 1-9 in every row, column and 3x3 box\nGerman Whisper: Adjacent digits on a Green line must differ by at least 5\nKiller: Digits in a cage cannot repeat and must sum to the number in the top left corner if given","solution":"365742891178935642942186375459613287813297564726854139681429753597361428234578916","constraints":["cage","german-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"gh20vntsxl","ctcId":3362,"ctcDifficulty":"MEDIUM","title":"Slice of Balance (YY Sandwich)","author":"PuzzleTank","rules":"Normal Sudoku Rules: Place the digits 1-9 in each row, column, and 3x3 box\nKropki: If digits are separated by a white dot, they must be consecutive\nYin Yang: Shade some cells such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected. No 2x2 area can be entirely shaded or unshaded\nSandwich: Clues outside the grid give the sum of the digits strictly between the 1 and 9 in the respective row or column. The full sandwich must be shaded if a sandwich clue is given. (i.e. in the case of a sandwich clue of 6 the string of digits 1429 MUST be shaded in that row)","solution":"375924861612538947498617523521749638786153492934862715247395186869271354153486279","constraints":["custom","kropki","sandwich","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The full sandwich must be shaded if a sandwich clue is given. (i.e. in the case of a sandwich clue of 6 the string of digits 1429 MUST be shaded in that row)","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"sandwich","type":"sandwich","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"yv10lru0u1","ctcId":3363,"ctcDifficulty":"MEDIUM","title":"Just Around the Corner","author":"PuzzleTank","rules":"- Normal Sudoku: Place the digits 1-9 once each in the rows, columns, and 3x3 region.\n- Quadruples: Digits given inside a circle must appear at least once in the surrounding four cells.\n- Arrows: Digits along arrows must sum to the digit in the arrow's circle.","solution":"257986431941327865386514792825643917134879256769251348678495123413762589592138674","constraints":["arrow","quadruple"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"quadruple","type":"quadruple","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qc37ejydvj","ctcId":3364,"ctcDifficulty":"MEDIUM","title":"Xin Yang v2","author":"PuzzleTank","rules":"Normal Sudoku: Place the digits 1-9 once each in every row, column, and 3x3 region.\n\nKropki: Digits separated by a white dot must be consecutive. Not all white dots are given.\n\nArrows: Digits along an arrow must sum to the two digit total given in the arrow's attached pill. The two digit value in the pill is read from left to right.\n\nYin Yang: Shade some cells such that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected. No 2x2 area can be either entirely shaded or unshaded\n\nShading: Each arrow total is a two digit number to be read as (X,Y). The X value (tens digit) indicates how many SHADED cells can be seen from that cell in ONLY the HORIZONTAL direction including itself. The Y value (ones digit) indicates how many UNSHADED cells can be seen from the cell in ONLY the VETRICAL direction including itself. (The other shading blocks vision)\n\nCells separated by a Kropki Dot MUST be of opposite shading.","solution":"861459273792316485435287619246891357153764928978523146317645892589132764624978531","constraints":["arrow","custom","kropki","yin-yang"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The X value (tens digit) indicates how many SHADED cells can be seen from that cell in ONLY the HORIZONTAL direction including itself. The Y value (ones digit) indicates how many UNSHADED cells can be seen from the cell in ONLY the VETRICAL direction including itself. Cells separated by a Kropki Dot MUST be of opposite shading.","evidence":"rules","lessonPolicy":"open","sectionIds":["c9","c10","c12"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"ohqf2rxsno","ctcId":3365,"ctcDifficulty":"MEDIUM","title":"Minimum Maximum","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nMost of the grid is obscured with fog. Entering correct digits may clear fog somewhere in the grid.\n\nA digit on a lime green 'minimum line' must be equal to or greater than the number of cells that the line occupies.\n\nA digit on a blue 'maximum line' must be equal to or less than the number of cells that the line occupies.\n\nLines do not branch, cross each other, or share cells.","solution":"968721534247653981135948267386572149729814653514396728651489372493267815872135496","fogLight":"R6C4,R5C4,R4C4,R4C5,R4C6,R5C6,R6C6,R6C5,R5C5","constraints":["custom","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit on a lime green 'minimum line' must be equal to or greater than the number of cells that the line occupies. A digit on a blue 'maximum line' must be equal to or less than the number of cells that the line occupies. Lines do not branch, cross each other, or share cells.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"musrlacrf2","ctcId":3366,"ctcDifficulty":"MEDIUM","title":"In-Between Extra","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits on a grey line have values between the two circled digits at the ends of that line. In addition, the digit in one circle is equal to the sum of the digits on the line AND the digit in the other circle.","solution":"374658912658129473912374685841563729735942861296817354529486137163795248487231596","constraints":["between-line","custom"],"constraintFacts":[{"slug":"between-line","type":"between-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In addition, the digit in one circle is equal to the sum of the digits on the line AND the digit in the other circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"z3vyld3vm7","ctcId":3367,"ctcDifficulty":"MEDIUM","title":"Bends","author":"Kaktuslav","rules":"Normal sudoku rules apply. Each L-shaped blue line is divided by box borders into segments with the same sum. Different lines may have different sums. The digit at the bend of each line equals the number of distinct digits appearing on that line.","solution":"721895436465137892389426751132589674976214583854763219517342968298651347643978125","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The digit at the bend of each line equals the number of distinct digits appearing on that line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"prg8idgvw2","ctcId":3368,"ctcDifficulty":"HARD","title":"Turbulence","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nArrows: Digits along an arrow must sum the number in the attached circle.\n\nDouble Arrows: Digits along a line sum to the same total as the digits in the attached circles.","solution":"145729638269384157783165294351276849426938571978451326832647915694512783517893462","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Double Arrows: Digits along a line sum to the same total as the digits in the attached circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"rdahf4598m","ctcId":3369,"ctcDifficulty":"HARD","title":"Massive W, Little L","author":"Mr.Menace","rules":"- Normal sudoku rules apply.\n- Colored lines are disconnected palindromes. Identically colored lines contain the same sequence of digits in the same order. They may be read in any direction.","solution":"139268475586417329724539816847156932952783164613924758361845297475392681298671543","constraints":["palindrome"],"constraintFacts":[{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"pvo44ijd8p","ctcId":3370,"ctcDifficulty":"MEDIUM","title":"Unusually Hot","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nDivide the grid into two orthogonally connected regions; one green and one orange. No 2x2 area may be fully within one region.\n\nIn the green region, the value of a cell equals its digit, as normal. In the orange region, the value of a cell equals its row number plus its column number, regardless of what digit appears in the cell.\n\nValues along a thermo strictly increase from bulb to tip.\n\nIf a black dot sits between two cells, the value of one is double the value of the other.","rulesClarified":"Normal sudoku rules apply.\n\nDivide the grid into two regions, one green and one orange. Each region is orthogonally connected. No 2x2 square lies entirely inside one region.\n\nIn a green cell, the value is the digit written in the cell.\n\nIn an orange cell, the value is the cell's row number plus its column number, whatever digit is written there. The digit still follows normal sudoku rules.\n\nThermos and black dots work on values, not on digits.\n\nValues along a thermo strictly increase from bulb to tip.\n\nA black dot sits between two cells. The value of one of them is double the value of the other.","solution":"219386754358472916674951832537864291462197385981523467846719523193245678725638149","constraints":["custom","kropki","thermometer","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In the green region, the value of a cell equals its digit, as normal. In the orange region, the value of a cell equals its row number plus its column number, regardless of what digit appears in the cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"If a black dot sits between two cells, the value of one is double the value of the other.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c7"]},{"slug":"thermometer","type":"thermometer","variant":"modified","modifiers":[],"params":null,"note":"Values along a thermo strictly increase from bulb to tip.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"01lue6wf81","ctcId":3373,"ctcDifficulty":"MEDIUM","title":"Dorlir's unsquished sudoku","author":"Jonesy","rules":"Hello.\n\nNormal sudoku rules apply.\n\nCounting circles : A digit in a circle indicates how many times that digit must appear in circles.\n\nEach counting circle is the center of a 3x3 area which contains 9 unique digits. (the circle on the edge of the grid only reaches 6 cells)\n\nDigits separated by an X sum to 10.\n\nHave fun.","solution":"173628594628594173594713628416382957382957461957461832761839245849275316235146789","constraints":["XV","counting-circle","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each counting circle is the center of a 3x3 area which contains 9 unique digits. (the circle on the edge of the grid only reaches 6 cells)","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"zt3l4bqwuj","ctcId":3374,"ctcDifficulty":"VERY HARD","title":"Consecutive Regional Constraints","author":"Belamis","rules":"Normal sudoku rules apply.\nDynamic Fog: The grid is partially covered in fog. Correctly placed digits may remove fog from other cells. \nAny constraint type can not have a repeated digit. (E.g. if a 2 appears on a parity line, another 2 may not appear on any parity line)\nIn addition, digits across a constraint type must make up a consecutive set of digits. (E.g. if a 2 and 4 exist on dutch whisper line(s), there must also be a 3 somewhere on a dutch whisper line.)\n\nConstraint types:\nArrow - Digits along an arrow sum to the digit in the connected circle. Each circle is associated with exactly one arrow.\nRegion Sum (RS) - The 3x3 box borders divide a blue line into segments;  each segment along an individual line must have the same sum. Each line crosses at least 1 box border and does not branch.\nRenban (R) - Purple lines contain a non-repeating set of consecutive digits in any order.\nDutch Whispers (DW): Adjacent digits along an orange line have a difference of at least 4.\nEntropic (E) - Any three adjacent digits along a peach line are from one each of low(1,2,3), medium(4,5,6), and high(7,8,9) digits. Entropic lines must be at least 3 cells long.\nKropki - Digits in cells separated by a white dot are consecutive.\nParity (P) - Along a red line, adjacent digits must alternate between odd and even.","solution":"936521847542387169781469253274693518863154792159872634627945381415238976398716425","fogLight":"R3C7,R4C9,R9C6,R4C6","constraints":["arrow","custom","dutch-whispers","entropic-line","fog","kropki","region-sum-line","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any constraint type can not have a repeated digit. In addition, digits across a constraint type must make up a consecutive set of digits. Parity (P) - Along a red line, adjacent digits must alternate between odd and even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c6","c18"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c14"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c15"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c17"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13"]}]},{"id":"3eipqnv8xm","ctcId":3375,"ctcDifficulty":"MEDIUM","title":"Whispering Cube","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Neighbouring digits on the orange line must differ in value by at least 4.","solution":"468395172537241689912876453826159347395724861741638295274963518683517924159482736","constraints":["dutch-whispers"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"qs53ivj39n","ctcId":3376,"ctcDifficulty":"MEDIUM","title":"Maximum Effort","author":"Chris Napolitano","rules":"Normal sudoku rules apply. Standard Arrows: Digits along an arrow must sum to the number in its attached circle. Double Arrows: Digits along a line sum to the same total as the sum of the digits in its attached circles. Adjacent digits along green lines must differ by at least 5. The three digits in the killer cage sum to 7.","solution":"742938165658412739193567824279156483814329657365784912587643291921875346436291578","constraints":["arrow","cage","custom","german-whispers"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Double Arrows: Digits along a line sum to the same total as the sum of the digits in its attached circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"ujnp27j7ir","ctcId":3378,"ctcDifficulty":"HARD","title":"Ratio lines - Dynamic fog","author":"Jonesy","rules":"Hello.\n\nNormal Sudoku rules apply.\n\nOn each line, the sum of either the odd digits or the even digits is exactly *half* or *double* the sum of the other parity.\n\nAdditionally, all end cells of any line contain digits of the same parity (all odd or all even).\n\nDigits separated by a white dot are consecutive.\n\nEntering correct digits may lift fog somewhere in the grid. No guessing is required.\n\nHave fun.","solution":"718395624654278931329614578263789415197456283845123796986532147572841369431967852","fogLight":"R4C6,R4C5,R4C4,R5C4,R5C5,R5C6,R6C6,R6C5,R6C4","constraints":["custom","fog","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"On each line, the sum of either the odd digits or the even digits is exactly *half* or *double* the sum of the other parity. Additionally, all end cells of any line contain digits of the same parity (all odd or all even).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"o4u3kz1764","ctcId":3379,"ctcDifficulty":"VERY HARD","title":"Summetry","author":"Kaktuslav","rules":"Normal sudoku rules apply.\n\nShade some cells in the grid so that all shaded cells are orthogonally connected, all unshaded cells are orthogonally connected, and no 2×2 region is entirely shaded or entirely unshaded. The shading must also be centrally symmetric: cells mapped to each other by a 180∘ rotation about the center of the grid have the same shading. \n\nDigits may not repeat within a cage. Each cage contains at least one shaded and one unshaded cell, and the sum of its unshaded digits equals the product of its shaded digits (a sum or product consisting of a single digit is simply that digit).","solution":"429153768178496235653278194946812357385947621712635489267581943534729816891364572","constraints":["cage","custom","yin-yang"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"The shading must also be centrally symmetric: cells mapped to each other by a 180∘ rotation about the center of the grid have the same shading. Each cage contains at least one shaded and one unshaded cell, and the sum of its unshaded digits equals the product of its shaded digits (a sum or product consisting of a single digit is simply that digit).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c5"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"d4aamhonge","ctcId":3381,"ctcDifficulty":"MEDIUM","title":"Easy as 1, 2, 3 ...","author":"Patrick Junke","rules":"1. Normal Sudoku rules apply. (Place each digits from 1 to 9 in each row, in each column and in each 3x3 region.)\n\n2. Standard killer cages rules apply. (In dotted regions, digits don't repeat and sum to the indicated total.)\n\n3. Two orthogonally adjacent digits sum to 10 if there is an X between them, and sum to a value other than 3, 10, 12, or 17 if there is no X between them.","solution":"132459678865327941794168235259786314417235869386941527678513492923874156541692783","constraints":["XV","cage","custom"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"3. Two orthogonally adjacent digits sum to 10 if there is an X between them, and sum to a value other than 3, 10, 12, or 17 if there is no X between them.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"9snrpdy9fe","ctcId":3382,"ctcDifficulty":"VERY HARD","title":"Lupin's Loop 6 - Between Worlds","author":"Rab3aron","rules":"Normal Sudoku rules apply.\n\nDigits separated by a white dot are consecutive. Digits separated by a yellow dot are non-consecutive. Digits separated by a red dot must contain one even digit and one odd digit.\n\nDraw a single cable that travels orthogonally from cell to cell, never branches, crosses, or overlaps itself, and eventually closes into a loop. The cable must pass through every electricity sign and may not cross rivers (blue borders).\n\n90-degree turns split the loop into segments (including endpoints).\n\nIf a segment of length N exists, then the total number of segments of length N in the loop is M, where M > 1 and M and N share the same parity.\n\nAdditionally, if a segment has length N, then the digit N must appear in one of that segment’s endpoints.\n\nA digit in a purple sensor counts the number of loop cells in the 3×3 box centered on that sensor, up to a maximum of 9.\n\nCells on the marked diagonals may not be part of any segment of length exactly 5.","solution":"386795412429613857175824396768531924512947683934268175651479238297386541843152769","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits separated by a yellow dot are non-consecutive. Digits separated by a red dot must contain one even digit and one odd digit. Draw a single cable that travels orthogonally from cell to cell, never branches, crosses, or overlaps itself, and eventually closes into a loop. The cable must pass through every electricity sign and may not cross rivers (blue borders). If a segment of length N exists, then the total number of segments of length N in the loop is M, where M > 1 and M and N share the same parity. Additionally, if a segment has length N, then the digit N must appear in one of that segment’s endpoints. A digit in a purple sensor counts the number of loop cells in the 3×3 box centered on that sensor, up to a maximum of 9. Cells on the marked diagonals may not be part of any segment of length exactly 5.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5","c6","c8","c9","c10","c11"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"zrk69de373","ctcId":3384,"ctcDifficulty":"MEDIUM","title":"Thermo Bunches","author":"Aad van de Wetering","rules":"Normal sudoku rules apply (ie place the digits 1-9, once each, in every row, column and 3x3 box). Digits along a thermometer must increase from the bulb end.","solution":"823765194916843257754921683238617945175394862649582731387159426562478319491236578","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"yporyghx5a","ctcId":3386,"ctcDifficulty":"HARD","title":"Galaxies Collide (Again!)","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nDivide the grid into two galaxies of orthogonally connected cells. No 2x2 area may be completely within one galaxy. Both galaxies must be symmetrical through 180 degrees.\n\nA digit in a green circle indicates how many cells in its sudoku box are in its galaxy.\n\nA digit in a red square indicates how many cells in its sudoku box are NOT in its galaxy.\n\nOne of the two galaxies is special. In that galaxy, for any two orthogonally adjacent cells, dividing one digit by the other always gives an exact integer (one is a multiple of the other.)","rulesClarified":"Normal sudoku rules apply.\n\nDivide the grid into two galaxies of orthogonally connected cells.\n\nNo 2x2 area may be completely within one galaxy.\n\nBoth galaxies must be symmetrical through 180 degrees.\n\nA digit in a green circle is the number of cells in its sudoku box that are in its galaxy. The circled cell counts itself.\n\nA digit in a red square is the number of cells in its sudoku box that are NOT in its galaxy. The square's own cell never counts, because it is in its own galaxy.\n\nOne of the two galaxies is special. In that galaxy, for any two orthogonally adjacent cells, one digit is a multiple of the other.","solution":"485371692726549813193628475539467281864132759271895364658213947942756138317984526","constraints":["custom","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Both galaxies must be symmetrical through 180 degrees. A digit in a green circle indicates how many cells in its sudoku box are in its galaxy. A digit in a red square indicates how many cells in its sudoku box are NOT in its galaxy. In that galaxy, for any two orthogonally adjacent cells, dividing one digit by the other always gives an exact integer (one is a multiple of the other.)","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c6","c8"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"djo2zcf7eo","ctcId":3387,"ctcDifficulty":"MEDIUM","title":"Heart Brea-King","author":"olima","rules":"Normal Sudoku rules apply. Digits a King's move (as in chess) apart must be different. Adjacent digits on a green line differ by at least 5. On black dots one digit is double the other and on white dots digits are consecutive. Not all dots are necessarily given.","solution":"936514278517283946284967531193742685745698312628351794879126453452839167361475829","constraints":["antiking","german-whispers","kropki"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"9xec41tr2z","ctcId":3388,"ctcDifficulty":"VERY HARD","title":"Blue Cages","author":"Kaktuslav","rules":"Divide the grid into nine non-overlapping regions, each consisting of nine orthogonally connected cells. Some borders between the regions are already given. Fill the grid with digits 1–9 so that each row, column, and region contains each digit exactly once.\n\nDigits may not repeat within a cage, and no cage is entirely contained within a single region. Region borders divide each cage into pieces with equal sums. That is, in each region containing cells of a cage, those cells form a single orthogonally connected piece, and all pieces of that cage have the same sum (different cages may have different sums).\n\nDigits separated by a white dot are consecutive. Not all possible dots are necessarily given.","solution":"871596324642839751538961247927415836415387692763254189254178963189623475396742518","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into nine non-overlapping regions, each consisting of nine orthogonally connected cells. Some borders between the regions are already given. Digits may not repeat within a cage, and no cage is entirely contained within a single region. Region borders divide each cage into pieces with equal sums.","evidence":"rules","lessonPolicy":"open","sectionIds":["c1","c2","c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"yavvjksg60","ctcId":3389,"ctcDifficulty":"MEDIUM","title":"Intricacies","author":"zetamath","rules":"Normal sudoku rules apply.\n\nGerman Whispers: Adjacent digits along a green line differ by at least 5.\n\nArrows: The digit in a circle is the sum of the digits along the connected arrow.","solution":"827165349513947628649382157194273865356891274278456913782519436435628791961734582","constraints":["arrow","german-whispers"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"3nizvqv1u9","ctcId":3391,"ctcDifficulty":"MEDIUM","title":"I See No Dots","author":"billybeth","rules":"Normal Sudoku rules apply.\nCells joined by black dots are in the ratio of 1:2 or 1:3. All dots are given.\nAdjacent digits along the green line differ by five or more.","solution":"253871964718649253496532718325187496871964325649253871532718649187496532964325187","constraints":["german-whispers","kropki"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"fstz89rrrr","ctcId":3392,"ctcDifficulty":"MEDIUM","title":"This Way Up","author":"99%Sneaky","rules":"Normal sudoku rules apply. Digits in cages may not repeat and sum to the small number printed in the corner. Digits along arrows sum to the digit in the attached circle. The two cells containing a blue diamond contain the same digit.","solution":"519782643376145892842639157487216539195378264263594781728463915654921378931857426","constraints":["arrow","cage","clone"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"clone","type":"clone","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"2gk2npegiz","ctcId":3394,"ctcDifficulty":"HARD","title":"X-ray","author":"Kaktuslav","rules":"Normal sudoku rules apply. Place nine circles in the grid: one in each row, column, and 3×3 box, with the digits in the circled cells forming a complete set of 1–9. Digits may not repeat within a cage. If an X is in a row with circled digit A and a column with circled digit B, the digits in the cage containing this X sum to A×B (A and B need not be distinct).","solution":"859716234136248795724359618218465379395871462467923851582137946643592187971684523","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Place nine circles in the grid: one in each row, column, and 3×3 box, with the digits in the circled cells forming a complete set of 1–9. If an X is in a row with circled digit A and a column with circled digit B, the digits in the cage containing this X sum to A×B (A and B need not be distinct).","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]}]},{"id":"pwvd13opgn","ctcId":3395,"ctcDifficulty":"MEDIUM","title":"Double Thermos","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Along a thermometer, digits must increase from the bulb end.","solution":"584293671367185924219647538195368247842571369736924815673459182928716453451832796","constraints":["thermometer"],"constraintFacts":[{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"l50613nsxb","ctcId":3398,"ctcDifficulty":"MEDIUM","title":"Feeding Friendsy","author":"Marty Sears","rules":"Normal sudoku rules apply. \n\nNine unlikely friends must each find a path through their box, to reach something that will give them an energy boost.\n\nFEEDING MISSIONS:\n• BOX 1: The frog must reach the fly resting on a waterlily.\n• BOX 2: The mad scientist must reach his lettuce.\n• BOX 3: The digital snake must reach the cake.\n• BOX 4: The robot must reach the battery.\n• BOX 5: The dolphin must reach the fish.\n• BOX 6: The flamingo must reach the pancakes.\n• BOX 7: The cat must reach the milk.\n• BOX 8: The zebra must reach the broccoli.\n• BOX 9: The hippo must reach the doughnut.\n\nMOVEMENT:\nCharacters each stay in their own box, but do not necessarily need to visit all 9 cells. They may not pass through any thick walls, visit any cell more than once, or cross their own paths. As well as moving orthogonally, they may also move diagonally if there is a 2x2 space in which to do so, but may never pass through the end of a wall on the corner of a cell.\n\nMATCHING PATHS: Every character visits exactly the same sequence of digits, in the same order.\n\nONE WAY DOORS: A purple arrow points towards the smaller of the two digits it sits between, and may only be passed through in the direction it's pointing.\n\nEXTRA ITEMS: If two digits are separated by a test tube (in box 2), a metal gear (in box 4), a black sea urchin (in box 5), or a cookie (in box 7),  then one digit is double the other. Extra items may or may not be visited.","solution":"312689475865347912974125836698713254543298167721564389459836721286971543137452698","constraints":["custom","inequality","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Nine unlikely friends must each find a path through their box, to reach something that will give them an energy boost. • BOX 1: The frog must reach the fly resting on a waterlily. • BOX 2: The mad scientist must reach his lettuce. • BOX 3: The digital snake must reach the cake. • BOX 4: The robot must reach the battery. • BOX 5: The dolphin must reach the fish. • BOX 6: The flamingo must reach the pancakes. • BOX 7: The cat must reach the milk. • BOX 8: The zebra must reach the broccoli. • BOX 9: The hippo must reach the doughnut. Characters each stay in their own box, but do not necessarily need to visit all 9 cells. They may not pass through any thick walls, visit any cell more than once, or cross their own paths. As well as moving orthogonally, they may also move diagonally if there is a 2x2 space in which to do so, but may never pass through the end of a wall on the corner of a cell. MATCHING PATHS: Every character visits exactly the same sequence of digits, in the same order. ONE WAY DOORS: A purple arrow points towards the smaller of the two digits it sits between, and may only be passed through in the direction it's pointing.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4","c5","c6","c7","c8","c9","c10","c11","c12","c14","c15","c16","c17","c18"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c18"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c19"]}]},{"id":"r9hx4s0yib","ctcId":3399,"ctcDifficulty":"HARD","title":".357 Magnum","author":"Eric Rathbun","rules":"Normal Sudoku rules apply.\nDigits in a cage must sum to the small clue in the cage's top left corner.\nThe clue outside the grid gives the sum of the digits along the indicated diagonal. \nDigits cannot repeat along the main diagonal marked with a blue line.\nThe grey square contains an even digit.\nGray lines are palindromes ie they read the same forwards and backwards.\nDigits separated by a white dot have a difference of one. If two digits are separated by a black dot then one is double the other.","solution":"782156394931824657465397812843571926527639481196248573219465738374982165658713249","constraints":["cage","diagonal","even","kropki","little-killer","palindrome"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7","c8"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"tnsd7b86gv","ctcId":3400,"ctcDifficulty":"HARD","title":"Diamondback","author":"IcyFruit","rules":"Normal sudoku rules apply.\nA digit in a large diamond indicates the number of cells it can see in its row and column that are larger than itself, where digits smaller than itself block vision.\nA small diamond separates two digits whose difference is a multiple of three.","solution":"548621739129374568376985412637158294295467381481239657714596823952843176863712945","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in a large diamond indicates the number of cells it can see in its row and column that are larger than itself, where digits smaller than itself block vision. A small diamond separates two digits whose difference is a multiple of three.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]}]},{"id":"jkljkw93m8","ctcId":3401,"ctcDifficulty":"MEDIUM","title":"Renbarrows: Consecutive Consequences","author":"LogzMort & MaizeGator","rules":"Normal Sudoku Rules Apply\n\nRenban: Digits along a pink line form a non-repeating consecutive set.\n\nArrow: Digits along an arrow tip sum to the digit in the arrow's bulb.\n\nAll arrow tips are also renban lines (note this does NOT include the arrow's bulb)","rulesClarified":"Normal sudoku rules apply.\n\nRenban: digits along a pink line form a non-repeating consecutive set.\n\nArrows: each arrow starts in a bulb, the circle at its start. The tip of an arrow is the cells after its bulb. The digits along the tip sum to the digit in the bulb.\n\nAll arrow tips are also renban lines: the digits along each arrow tip form a non-repeating consecutive set. The bulb is not part of this renban line.","solution":"261894573438752196975136428526947381743281659819563742194678235687325914352419867","constraints":["arrow","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"modified","modifiers":[],"params":null,"note":"All arrow tips are also renban lines (note this does NOT include the arrow's bulb)","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c2","c4"]}]},{"id":"gfx29v36nv","ctcId":3402,"ctcDifficulty":"MEDIUM","title":"Every Hit Counts","author":"Ratfinkz","rules":"Normal sudoku rules apply (place each digit from 1-9 once each in every row, column and box)\n\nBeige lines are hit point lines. Counting the diamond as position one, digits in their correct position must sum to the number in the diamond (eg a line who's diamond was the value 9 may be made up 93145 as 4&5 are in the 4th and 5th position and sum to 9 fulfilling the diamonds requirements).\n\nDigits may not repeat along a line (the digit in the diamond is considered on the line and may not appear elsewhere along its line).\n\nDigits in the diamonds also count how many different lines they appear on, including themselves (eg if a diamond contained the number 3 it would appear,  in any position, on two more lines). Digits which don't appear in a diamond have no limitations to how many lines they appear on.\n\nI hope you have fun!","solution":"671834925239157864548296713394615278826379451715482396487961532153728649962543187","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Counting the diamond as position one, digits in their correct position must sum to the number in the diamond (eg a line who's diamond was the value 9 may be made up 93145 as 4&5 are in the 4th and 5th position and sum to 9 fulfilling the diamonds requirements). Digits may not repeat along a line (the digit in the diamond is considered on the line and may not appear elsewhere along its line). Digits in the diamonds also count how many different lines they appear on, including themselves (eg if a diamond contained the number 3 it would appear,  in any position, on two more lines).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5"]}]},{"id":"2jar2lhcc5","ctcId":3403,"ctcDifficulty":"MEDIUM","title":"Querulous","author":"Nicolas Duhail","rules":"Normal sudoku rules apply.\nCells separated by a knight's move cannot contain the same digit.\nAll lines sum to the same total.\nAny three adjacent digits along the teal \"modular\" line have different residues modulo 3 (i.e. one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}).\nBox borders divide the blue \"region sum\" line into segments with the same sum.\nAlong the pink \"renban\" line, digits form a consecutive sequence in any order.\nAlong the orange \"dutch whisper\" line, adjacent digits differ by at least 4.\nAlong the gold \"nabner\" line, digits do not repeat and no two digits appearing anywhere on the line can be consecutive.\nAny three adjacent digits along the peach \"entropic\" line contains one low digit (123), one middle digit (456), and one high digit (789).\nAlong the green \"german whisper\" line, adjacent digits differ by at least 5.\nDigits along the red \"parity\" line must alternate between odd and even.","solution":"548639217917245638632718549765183492284597163193462785479326851851974326326851974","constraints":["antiknight","custom","dutch-whispers","entropic-line","german-whispers","modular-line","nabner-line","region-sum-line","renban"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All lines sum to the same total. Digits along the red \"parity\" line must alternate between odd and even.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c11"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"fghtxbkux0","ctcId":3404,"ctcDifficulty":"HARD","title":"Ascents Traversed Evenly","author":"Kaktuslav","rules":"Normal sudoku rules apply. Digits along each line sum to the same total as the digits in the two circles at its ends. Digits in cells with grey squares are even.","solution":"647382915821596473953417286482739561396251847715648392179825634264973158538164729","constraints":["custom","even"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits along each line sum to the same total as the digits in the two circles at its ends.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"even","type":"even","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"yp4utzkw3i","ctcId":3405,"ctcDifficulty":"MEDIUM","title":"Blue Waves","author":"Antiknight","rules":"Normal Sudoku rules apply. Box borders divide each blue line into segments with the same sum. Digits along each cyan thermometer must strictly increase from the bulb.","solution":"679451823123786459485239671896345712712698345354127986241863597537914268968572134","constraints":["region-sum-line","thermometer"],"constraintFacts":[{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"3uz3y611dl","ctcId":3406,"ctcDifficulty":"HARD","title":"Twinned","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nBLACK DOTS: If two digits are joined by a black dot, one is double the other.\n\nWHITE DOTS: If two digits are joined by a white dot, they are consecutive.\n\nX: If two digits are joined by an X, they sum to 10.\n\nTWIN TOTALS:\nTwo lines of the same colour are twins, meaning their digits have the same sum.\n\n• GERMAN WHISPERS - Adjacent digits on a green line have a difference of at least 5.\n\n• RENBANS - Digits on a pink line form a non-repeating, conseuctive sequence which can be arranged in any order along the line.\n\n• REGION SUM LINES - Box borders divide a blue line into segments, each of which have the same sum.\n\n• THERMOMETERS - Digits along a grey thermometer must strictly increase as they get further away from the bulb.\n\n• PARITY LINES - On a red line, digits must alternate between even and odd.\n\n• NABNERS - No two digits anywhere on a yellow line may be consecutive.","solution":"654128739972435861183679425546791283728356194319284657495867312261543978837912546","constraints":["XV","custom","german-whispers","kropki","nabner-line","region-sum-line","renban","thermometer"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Two lines of the same colour are twins, meaning their digits have the same sum. • PARITY LINES - On a red line, digits must alternate between even and odd.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c11"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"nabner-line","type":"nabner-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"eoucbc58v9","ctcId":3407,"ctcDifficulty":"HARD","title":"High Bars","author":"Jobo","rules":"Normal sudoku rules apply.\n\nDigits on a line can never be lower than the length of the line.\n\nDigits separated by a white dot must be consecutive. Not all dots are given.","solution":"981452736324967158567183492452736819619248573873591624736819245248375961195624387","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits on a line can never be lower than the length of the line.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"auifpnq2st","ctcId":3408,"ctcDifficulty":"MEDIUM","title":"Whispering Diabolo","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Adjacent digits on an orange line must differ in value by at least 4.","solution":"951627384342581697768934152826475931417398265539162478685213749194756823273849516","constraints":["dutch-whispers"],"constraintFacts":[{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"p676oglsv8","ctcId":3410,"ctcDifficulty":"VERY HARD","title":"Lupin's Loop 7 - Where It All Began","author":"Rab3aron","rules":"Normal Sudoku rules apply.\n\nRegions: Divide the grid into four distinct regions. Each region is formed of orthogonally connected cells and touches each of the other three regions orthogonally (ie shares at least one edge). No 2×2 block may be entirely within one region. At least two regions are the same size.\n\nPaths: Draw two distinct orthogonally connected, non-branching paths, each joining a pair of hourglasses determined by the solver. The paths share exactly one cell, marked by the red pin, and otherwise do not overlap. Along one path, adjacent digits have opposite parity, along the other, adjacent digits are consecutive.\n\nHourglass Clues: A digit in an hourglass equals the number of times its path crosses the border of the region containing that hourglass.\n\nPurple Sensors: A digit N in a Sensor means the digit N appears exactly N times within that sensor's region.\n\nBlue dots: Neither path may pass through a blue dot.\n\nGreen Dots: Digits in cells joined by a green dot differ by at least 5.\n\nWhite Dots: Digits in cells joined by a white dot are consecutive.\n\nBlack Dots: If two digits are joined by a black dot one is TRIPLE the other.\n\nCages: Digits in a cage sum to the value in its top-left corner and do not repeat within a cage.\n\nArrows: A digit in a cell with arrows equals the total number of cells containing any part of either path in all indicated directions, including the clue cell itself.\n\nDiagonal Sums: Numbers outside the grid on a diagonal indicate the sum of the first X cells along that diagonal. The value of X is not 6 and must be determined by the solver.\n\nOutside Clues: A number N outside a row/column means the first N cells from that side are in the same region, and the (N+1)th cell is in a different region.\n\nNote: You may finish one part before the others (digits, paths, and regions), but the puzzle is only solved once all three parts are completed.","solution":"543298761926317854781456923192543678857621349634789215419872536378165492265934187","constraints":["cage","custom","kropki","little-killer"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c15"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Regions: Divide the grid into four distinct regions. Each region is formed of orthogonally connected cells and touches each of the other three regions orthogonally (ie shares at least one edge). No 2×2 block may be entirely within one region. At least two regions are the same size. Paths: Draw two distinct orthogonally connected, non-branching paths, each joining a pair of hourglasses determined by the solver. The paths share exactly one cell, marked by the red pin, and otherwise do not overlap. Along one path, adjacent digits have opposite parity, along the other, adjacent digits are consecutive. Hourglass Clues: A digit in an hourglass equals the number of times its path crosses the border of the region containing that hourglass. Purple Sensors: A digit N in a Sensor means the digit N appears exactly N times within that sensor's region. Blue dots: Neither path may pass through a blue dot. Green Dots: Digits in cells joined by a green dot differ by at least 5. Arrows: A digit in a cell with arrows equals the total number of cells containing any part of either path in all indicated directions, including the clue cell itself. Outside Clues: A number N outside a row/column means the first N cells from that side are in the same region, and the (N+1)th cell is in a different region.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6","c7","c8","c9","c10","c11","c12","c16","c19"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c13","c14"]},{"slug":"little-killer","type":"little-killer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c17"]}]},{"id":"avvo3j3xng","ctcId":3411,"ctcDifficulty":"VERY HARD","title":"Halo Loop","author":"Derek LeClair","rules":"Normal sudoku rules apply. Draw a single loop that moves orthogonally from cell to cell and never crosses or overlaps itself. A digit in a circle indicates how many of the up to 8 surrounding cells the loop passes through. The loop cannot pass through the circles. Adjacent digits along the loop differ by at least 5.","solution":"167932548239485761485617293816524937392876154754391826623158479978243615541769382","constraints":["custom","german-whispers"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a single loop that moves orthogonally from cell to cell and never crosses or overlaps itself. A digit in a circle indicates how many of the up to 8 surrounding cells the loop passes through. The loop cannot pass through the circles.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"6qpgdgsw4j","ctcId":3412,"ctcDifficulty":"HARD","title":"Saws","author":"Kaktuslav","rules":"Normal sudoku rules apply. For each blue line, box borders divide the line into segments of equal sum. The two lines may have different sums. If a digit N appears on either blue line, it appears exactly N times on the two blue lines combined.","solution":"847953621296814357135762849463129578952487136781536492528371964374698215619245783","constraints":["counting-circle","region-sum-line"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"ib3ewxrhep","ctcId":3413,"ctcDifficulty":"MEDIUM","title":"Outlier","author":"Daniel Hanson","rules":"Normal sudoku rules apply. Digits along a palindrome line read the same forwards and backwards. Digits along an arrow must sum to the digit in that arrow’s circle. Where two cells are separated by a black dot, the digit in one cell is double the digit in the other; all possible black dots are given.","solution":"314658927987432615256197384821749536739265841645381792468523179573914268192876453","constraints":["arrow","kropki","palindrome"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"1b7rrbig2u","ctcId":3414,"ctcDifficulty":"MEDIUM","title":"Quadrants","author":"Daniel Hanson","rules":"Normal sudoku rules apply. The grid is divided into four quadrants. Each quadrant obeys a constraint, and no constraint extends outside of its quadrant. In the NW quadrant (boxes 1, 2, 4, 5), cells separated by a single knight’s move (in chess) cannot contain the same digit. In the NE quadrant (boxes 2, 3, 5, 6), where two cells are separated by a black dot, the digit in one cell is double the digit in the other; all possible black dots for that quadrant are given. In the SW quadrant (boxes 4, 5, 7, 8), where two cells are separated by a white dot, the digit in one cell is consecutive with the digit in the other; all possible white dots for that quadrant are given. In the SE quadrant (boxes 5, 6, 8, 9), digits separated by a V sum to 5 and digits separated by an X sum to ten; all possible V's and X's for that quadrant are given.","solution":"853267419297314685416598327162459873938172564745836192529683741384721956671945238","constraints":["XV","antiknight","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"antiknight","type":"antiknight","variant":"modified","modifiers":[],"params":null,"note":"In the NW quadrant (boxes 1, 2, 4, 5), cells separated by a single knight’s move (in chess) cannot contain the same digit.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In the SE quadrant (boxes 5, 6, 8, 9), digits separated by a V sum to 5 and digits separated by an X sum to ten; all possible V's and X's for that quadrant are given.","evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]}]},{"id":"fc9t0o7etr","ctcId":3415,"ctcDifficulty":"HARD","title":"Magical Constellation","author":"Daniel Hanson","rules":"Normal sudoku rules apply. Cells separated by a single knight’s move (in chess) cannot contain the same digit. Where two cells are separated by a black dot, the digit in one cell is double the other. All possible black dots are given. Digits in the cells in the red box form a magic square (made from nine distinct digits arranged in a square such that every row, column, and diagonal sum to the same total).","solution":"937816524546723819281594763618349275793265148452187396165478932874932651329651487","constraints":["antiknight","custom","kropki"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Digits in the cells in the red box form a magic square (made from nine distinct digits arranged in a square such that every row, column, and diagonal sum to the same total).","evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]}]},{"id":"6ukcd457re","ctcId":3416,"ctcDifficulty":"HARD","title":"Searching High & Low","author":"Daniel Hanson","rules":"Normal sudoku rules apply. Cells separated by a single knight’s move (in chess) cannot contain the same digit. A cell marked as a MAX cell (wedges pointing outward) is larger than all orthogonal and diagonal neighbours; a cell marked as a MIN cell (wedges pointing inward) is smaller than all orthogonal and diagonal neighbours. All possible MAX and MIN cells are shown. Cells marked with a cage are either BIG or SMALL; a BIG/SMALL cell is larger/smaller than its orthogonal neighbors but is not larger/smaller than at least one diagonal neighbour. (In other words, a BIG/SMALL cell cannot be a MAX/MIN cell.) All possible BIG and SMALL cells are shown. Whether a marked cell is BIG or SMALL must be determined by the solver. Somewhere in the grid is a single magic square made from nine distinct digits arranged in a square such that every row, column, and diagonal of the square sum to the same total.","solution":"143257869698314257725896314854769132931425786276183495467538921582941673319672548","constraints":["antiknight","custom","maximum","minimum"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All possible MAX and MIN cells are shown. Cells marked with a cage are either BIG or SMALL; a BIG/SMALL cell is larger/smaller than its orthogonal neighbors but is not larger/smaller than at least one diagonal neighbour. All possible BIG and SMALL cells are shown. Whether a marked cell is BIG or SMALL must be determined by the solver. Somewhere in the grid is a single magic square made from nine distinct digits arranged in a square such that every row, column, and diagonal of the square sum to the same total.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5","c7","c8","c9"]},{"slug":"maximum","type":"maximum","variant":"modified","modifiers":[],"params":null,"note":"A cell marked as a MAX cell (wedges pointing outward) is larger than all orthogonal and diagonal neighbours; a cell marked as a MIN cell (wedges pointing inward) is smaller than all orthogonal and diagonal neighbours.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]},{"slug":"minimum","type":"minimum","variant":"modified","modifiers":[],"params":null,"note":"A cell marked as a MAX cell (wedges pointing outward) is larger than all orthogonal and diagonal neighbours; a cell marked as a MIN cell (wedges pointing inward) is smaller than all orthogonal and diagonal neighbours.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c3"]}]},{"id":"4pd5gy143h","ctcId":3417,"ctcDifficulty":"HARD","title":"Goalie","author":"Daniel Hanson","rules":"Normal sudoku rules apply. Cells separated by a single knight’s move (in chess) cannot contain the same digit. Where two cells are separated by a black dot, the digit in one cell is double the digit in the other. Where two cells are separated by a white dot, the digit in one cell is consecutive with the digit in the other. Not all possible dots are given. Adjacent digits along a green line must differ by at least 5. Digits along a grey line must read the same way backwards and forwards. The digit in the grey circle is odd.","solution":"275914386619283574483675912748369125592148763361752849837526491924831657156497238","constraints":["antiknight","german-whispers","kropki","odd","palindrome"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"palindrome","type":"palindrome","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c7"]}]},{"id":"vdnlyzrag0","ctcId":3418,"ctcDifficulty":"HARD","title":"Lettuce Experiment","author":"Ratfinkz","rules":"Normal sudoku rules apply.\n\n#FRIENDSHIPGOALS:\nProf Sears has been immersing himself in a lot of mad science lately, and frankly has been neglecting his own health. Time for him to try a vegetable instead... he must find his way through the lab to reach his super-lettuce - genetically modified for extra minerals and nutrients. His path must not visit any cell more than once, cross itself or pass through any thick maze walls.\nAs well as moving orthogonally, he may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through the rounded end / corner of a wall.\n\nONE-WAY DOORS: \nProf Sears may only pass directly through a purple arrow if moving in the direction the arrow is pointing. An arrow always points to the smaller of the two digits it sits between.\n\nTEST TUBES:\nDigits separated by a test tube have a 1:2 ratio (one is double the other).\n\nTRIALS and TRAILS:\nIn this mission, Prof Sears's path is divided into segments by box borders (if he enters a box more than once, each instance counts as a new segment.) Each segment is a hitline, with the first cell visited on the segment being position 1. Any cell that equals its position number along its segment is a HITPOINT (eg: if the 2nd digit visited along a segment is a 2.) The HIT TOTAL of a segment equals the sum of its hitpoints. (Eg: a segment reading 127854 would have a hit total of 8; the sum of 1, 2 and 5, which are the only digits in their correct position.) Every clipboard must display the hit total for each and every segment in its 3x3 box (and each box contains at least one segment).  Eg: if a clipboard reads 7, then any and all path segments in its box each individually have a HIT TOTAL of 7.","solution":"369214587781395642542786391615978423974523816823461975458132769196857234237649158","constraints":["custom","inequality","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"His path must not visit any cell more than once, cross itself or pass through any thick maze walls. As well as moving orthogonally, he may move diagonally if there's a 2x2 space in which to do so, but may never pass diagonally through the rounded end / corner of a wall. Prof Sears may only pass directly through a purple arrow if moving in the direction the arrow is pointing. In this mission, Prof Sears's path is divided into segments by box borders (if he enters a box more than once, each instance counts as a new segment.) Every clipboard must display the hit total for each and every segment in its 3x3 box (and each box contains at least one segment).","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c8","c13","c18"]},{"slug":"inequality","type":"inequality","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]}]},{"id":"db1522df7f","ctcId":3420,"ctcDifficulty":"VERY HARD","title":"Mexican Standoff","author":"starwarigami","rules":"Normal Killer Sudoku rules apply.\n\nFully colour the grid with three colours A, B, and C, such that each cage is completely filled with only one colour, all cells of the same colour are orthogonally connected, and no 2x2 area of the grid is completely filled by one colour. The colour of certain cells has been given.\n\nDigits may not repeat in a cage, and each cage sums to a unique total.\nCages marked with a letter in the top left corner sum to the number of squares in the grid filled with that colour.\nCages filled with the same colour all have the same remainder when divided by 3.","solution":"514928376923756841786341592852614937691537428347892165478163259135279684269485713","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Fully colour the grid with three colours A, B, and C, such that each cage is completely filled with only one colour, all cells of the same colour are orthogonally connected, and no 2x2 area of the grid is completely filled by one colour. The colour of certain cells has been given. Digits may not repeat in a cage, and each cage sums to a unique total. Cages marked with a letter in the top left corner sum to the number of squares in the grid filled with that colour. Cages filled with the same colour all have the same remainder when divided by 3.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4","c5","c6"]}]},{"id":"mwz7l2lvoi","ctcId":3422,"ctcDifficulty":"MEDIUM","title":"Right Angles Wrong Quads","author":"Scojo","rules":"Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.\n\nAnti-Quadruples: Digits in a red circle may not appear in any of the four cells touching that circle.\n\nZipper Lines: On lavender lines, pairs of digits equidistant from the center of the line sum to the digit in the center of the line.","solution":"951362874467518293823497615534821967692734581718956342286173459149285736375649128","constraints":["custom","zipper-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Anti-Quadruples: Digits in a red circle may not appear in any of the four cells touching that circle.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"f93bjjsyai","ctcId":3423,"ctcDifficulty":"MEDIUM","title":"Pointer Arrow Sudoku","author":"Piatato","rules":"Normal Sudoku rules apply. Every row, column, and box must contain the digits 1-9 with no repeats.\n\nPointer Arrows: Digits along an arrow must sum to the digit in that arrow's bulb. Additionally, arrow tips point towards a cell containing the digit within the arrow's bulb. The digit in the arrow tip indicates the distance from the arrow tip to the pointed-to cell.","rulesClarified":"Normal Sudoku rules apply. Every row, column and box contains the digits 1 to 9 with no repeats.\n\nEach arrow starts at a circle, its bulb, which holds one digit. The arrow runs through the cells drawn for it, ending at its tip.\n\nThe digits along the arrow sum to the digit in its bulb. The bulb is not one of the arrow's digits. The cell at the tip is one of the arrow's cells.\n\nThe arrow tip points in the direction of the arrow's last step. The digit in the arrow tip gives the distance from the tip to the cell it points to, counted in steps in that direction. The cell the arrow points to contains the digit in the bulb.","solution":"328179564961458327475623891586247139142396758739581642854762913617934285293815476","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Additionally, arrow tips point towards a cell containing the digit within the arrow's bulb. The digit in the arrow tip indicates the distance from the arrow tip to the pointed-to cell.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]}]},{"id":"70njbfg1zs","ctcId":3424,"ctcDifficulty":"MEDIUM","title":"Sort by Size","author":"Marty Sears","rules":"ISOFILL:\nDivide the grid into 9 regions, each containing 9 orthogonally connected cells. All cells in the same region must contain the same digit. All of the digits 1-9 must appear in the grid.\n\nENTROPIC LINES:\nEach peach line must contain one low digit (1, 2 or 3), one medium digit (4, 5 or 6) and one high digit (7, 8 or 9.)\n\nTHERMOMETERS:\nDigits along a thermometer must keep increasing as they move from bulb to tip.","solution":"888999961848976661448976111488976661489975561477777511455555522443222222333333332","constraints":["custom","entropic-line","thermometer"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into 9 regions, each containing 9 orthogonally connected cells. All cells in the same region must contain the same digit. All of the digits 1-9 must appear in the grid.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c4"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]}]},{"id":"nz9u2li1vk","ctcId":3425,"ctcDifficulty":"MEDIUM","title":"Border Arrows","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Cells separated by a single king's move (in chess) cannot contain the same digit. Digits along an arrow must sum to the digit in the attached circle.","rulesClarified":"Normal sudoku rules apply.\n\nCells separated by a single king's move (in chess) cannot contain the same digit.\n\nEach arrow starts at a circle. The digits in the arrow's cells, after the circle, add up to the digit placed in that circle.\n\nThe circle's own cell is not part of the sum.","solution":"698275314237914658451863729164592837972386145385147296743629581519738462826451973","constraints":["antiking","arrow"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"2oeacznw5t","ctcId":3426,"ctcDifficulty":"MEDIUM","title":"Thanks Testers","author":"99%Sneaky","rules":"Normal sudoku rules apply. Adjacent digits along dashed orange lines must have a difference of 4 or more. Digits along solid purple lines form a consecutive set. Each set of three consecutive digits along a hollow peach line will contain one low digit (1,2,3), one medium digit (4,5,6) and one high digit (7,8,9).\n\nIn each box containing a cage, sum all digits which are on two lines, and write that number into the cage. Two digit numbers must be entered left-to-right or top-to-bottom. For example, in box 1, the digit in R3C3 will be the sum of R1C2+R2C2. \n\nThe digit in the cell with the green square is equal to the sum of all of the ten's digits from every two digit number. The digit in the cell with the blue circle is equal to the sum of all of the one's digits from every two digit number.","solution":"453682197718593624296471853849736215531924786627815349162349578374158962985267431","constraints":["custom","dutch-whispers","entropic-line","renban"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In each box containing a cage, sum all digits which are on two lines, and write that number into the cage. Two digit numbers must be entered left-to-right or top-to-bottom. The digit in the cell with the green square is equal to the sum of all of the ten's digits from every two digit number. The digit in the cell with the blue circle is equal to the sum of all of the one's digits from every two digit number.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c8","c9"]},{"slug":"dutch-whispers","type":"dutch-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"entropic-line","type":"entropic-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"x6z9xkvdjb","ctcId":3427,"ctcDifficulty":"HARD","title":"Slithering Heights","author":"Marty Sears","rules":"Normal sudoku rules apply.\n\nDraw a loop that travels along cell edges and does not touch itself.\n\nEvery cell is surrounded by eight dots. The digit in a gold circle indicates how many of its cell's dots are visited by the loop.\n\nIf two digits are joined by a black dot, one is double the other.","solution":"782954361635218749491367852813479526927685134564123978248531697379846215156792483","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Draw a loop that travels along cell edges and does not touch itself. The digit in a gold circle indicates how many of its cell's dots are visited by the loop.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]}]},{"id":"mmsgaq4ylr","ctcId":3428,"ctcDifficulty":"HARD","title":"Diagonal π","author":"James Kopp","rules":"Normal sudoku rules apply.\nAdjacent digits along a green line have a difference of at least five.\nCells separated by a black dot are in the ratio 1 to 2. Not all possible black dots necessarily are given.","solution":"376241598912685734854973612637124859149857326285369147461598273598732461723416985","constraints":["german-whispers","kropki"],"constraintFacts":[{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"mhfpkgyo52","ctcId":3429,"ctcDifficulty":"HARD","title":"The Vault","author":"Nurator","rules":"Normal sudoku rules apply. \n\nIf two digits are separated by a black dot then one digit is double the other. Digits separated by a white dot are consecutive. \n\nDeducing the digit in a visible checkpoint (marked with a green square) will reveal new cells and potentially a new checkpoint.  \n\nEach line follows a specific constraint type from a list of constraints. It is up to the solver to determine which line belongs to which type.  \n\nEach line constraint type may contain no repeated digits anywhere in the puzzle. \n\nAt the start of the puzzle, all lines are German Whisper Lines (ie Adjacent digits differ by at least 5). Whenever new lines are revealed, remove all entered digits except those on checkpoints. After the first new lines are revealed, all lines can now be Region Sum Lines as well as Whispers. (ie The 3x3 box borders divide the lines into segments, each having the same sum). After the second new set of lines are revealed, the lines can now also be Modular lines (ie Every 3 consecutive cells along a modular line must contain a digit from (3,6,9), a digit from (1,4,7) and a digit from (2,5,8)).","solution":"314267985582934671769851432157492863936578124428316597271649358645783219893125746","fogLight":"R5C2,R6C2,R7C2,R7C3,R6C3,R7C4,R8C4,R8C5,R7C5,R7C6,R7C7,R1C2","constraints":["custom","german-whispers","kropki","modular-line","region-sum-line","fog"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"It is up to the solver to determine which line belongs to which type. Each line constraint type may contain no repeated digits anywhere in the puzzle. Whenever new lines are revealed, remove all entered digits except those on checkpoints.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7","c9"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"modular-line","type":"modular-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c10"]}]},{"id":"o9w2xjxagb","ctcId":3430,"ctcDifficulty":"VERY HARD","title":"Flax","author":"Jay Dyer","rules":"Normal sudoku rules apply. \n\nEach row/column/box contains one 'doubler' cell, whose value is double its digit. Each digit appears in exactly one doubler.\n\nThe 3x3 box borders split blue lines into segments, and the values of cells on each segment of a line must sum to the same total.","solution":"123798465854263197697451823742685319389127654516934782461572938278319546935846271","constraints":["custom","region-sum-line"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each row/column/box contains one 'doubler' cell, whose value is double its digit. Each digit appears in exactly one doubler.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3"]},{"slug":"region-sum-line","type":"region-sum-line","variant":"modified","modifiers":[],"params":null,"note":"The 3x3 box borders split blue lines into segments, and the values of cells on each segment of a line must sum to the same total.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c4"]}]},{"id":"tmwfllzail","ctcId":3431,"ctcDifficulty":"HARD","title":"Nonconsecutive Spoons","author":"Phistomefel","rules":"1. Normal thermo sudoku rules apply.\n2. Orthogonally adjacent squares may not contain consecutive digits.","solution":"582963147714285369936417582258639714471852936693174258825396471147528693369741825","constraints":["non-consecutive","thermometer"],"constraintFacts":[{"slug":"non-consecutive","type":"non-consecutive","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c1"]}]},{"id":"bh7z9bwzxx","ctcId":3433,"ctcDifficulty":"MEDIUM","title":"Horses Sliding through a Field of Oil and Water","author":"Merdock","rules":"Normal Sudoku Rules apply:\nPlace the digits 1-9 in every row, column, and box\n\nKiller Cages: \nDigits in a cage cannot repeat. If a number is given in the upper left corner of the cage, then the digits in the cage must sum to that number. \n\nAnti-Knight:\nDigits a knights move away can not be identical\n\nOil and Water:\nEach cage is either full of \"oil\" (even digits), full of \"water\" (odd digits), or a mix of both. In cases where cells of a cage are connected to each other horizontally, those cells must only contain one type (oil or water). If two cells are a part of the same cage and in the same row, but they are not connected horizontally (r5c6 & r5c8 for example), then they can be different types. Oil floats on water, so even digits will always be in rows above odd digits in mixed cages.","solution":"394528716815764392267391485573219648148657923629843157751932864486175239932486571","fogLight":"R9C1,R9C2,R8C2,R8C3,R8C4,R9C4,R9C5,R9C6,R9C7,R9C8,R9C9,R8C9,R7C9,R7C8,R7C7,R8C7,R8C6,R8C5,R7C5,R7C4,R7C3,R7C2,R5C9,R6C9,R6C8,R6C7,R5C7,R4C7,R4C8,R4C9,R5C8,R2C9,R3C9,R2C7,R2C8,R1C8,R5C6,R6C6,R5C4,R6C4,R6C5,R2C5,R3C5,R3C6,R2C6,R1C6,R1C4,R1C3,R2C3,R3C3,R3C4,R2C4,R2C2,R3C2,R2C1,R1C1,R4C3,R4C2,R4C1,R5C1,R6C1,R6C2,R6C3,R5C3,R9C3,R8C1,R8C8,R1C2,R5C5,R4C5,R4C6,R5C2,R7C6,R1C7,R1C5,R1C9","constraints":["antiknight","cage","custom","fog"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"In cases where cells of a cage are connected to each other horizontally, those cells must only contain one type (oil or water). Oil floats on water, so even digits will always be in rows above odd digits in mixed cages.","evidence":"rules","lessonPolicy":"open","sectionIds":["c10","c12"]}]},{"id":"6maya5z2ou","ctcId":3434,"ctcDifficulty":"HARD","title":"Border Square Difference","author":"Phistomefel","rules":"1. Normal sudoku rules apply.\n2. Digits along an arrow must sum to the digit in that arrow's circle.\n2. A border square is a 2x2 square that crosses at least one box border. For all border squares, the sums of the two diagonals differ by a multiple of 4 (0 is also a valid multiple of 4).","solution":"351924876287361594469587321825143769736259148914876253598432617643715982172698435","constraints":["arrow","custom"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"2. A border square is a 2x2 square that crosses at least one box border. For all border squares, the sums of the two diagonals differ by a multiple of 4 (0 is also a valid multiple of 4).","evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"o9rylnnnw1","ctcId":3435,"ctcDifficulty":"HARD","title":"Ying Yang Yogn","author":"Marty Sears","rules":"YIN YANG YONG:\nDivide the grid into three regions of orthogonally connected cells. No 2x2 area can be entirely within one region.\n\nTWO TRUTHFUL REGIONS AND A LIAR REGION:\nClues always sit entirely within one region. For two of the regions, all of its clues tell the truth, obeying the rules listed below. But the 3rd region is a liar region. All of the clues in the liar region break their rule.\n\nCLUES TYPES:\n\n• If a V sits between two digits, they sum to 5.\n\n• If a BLACK DOT sits between two digits, one is double the other.\n\n• If a WHITE DOT sits between two digits, they are consecutive.\n\n• If a YELLOW SQUARE sits between two digits, they are not consecutive.\n\n• If a GREEN DIAMOND sits between two digits, they have a difference of at least 5.\n\n• If a RED DOT sits between two digits, one is odd and the other is even.\n\n• A digit in a CIRCLE indicates the sum of all the digits seen in the direction of its arrow that are in the same region as the circle, until the first region border is reached.","rulesClarified":"Divide the grid into three regions of orthogonally connected cells. No 2x2 area can be entirely within one region. Clues always sit entirely within one region.\n\nTwo of the three regions are truthful. Every clue in them obeys the clue rules below.\n\nThe third region is a liar region. Every clue in it breaks its rule.\n\nClue types. A clue that sits between two digits is drawn across the edge between two adjacent cells, and those two cells are the two digits.\n- A V sits between two digits. They sum to 5.\n- A black dot sits between two digits. One is double the other.\n- A white dot sits between two digits. They are consecutive.\n- A yellow square sits between two digits. They are not consecutive.\n- A green diamond sits between two digits. They have a difference of at least 5.\n- A red dot sits between two digits. One is odd and the other is even.\n- A digit in a circle gives the sum of all the digits seen in the direction of its arrow that are in the same region as the circle, until the first region border is reached.","solution":"927658314631429785584137269259346178376981542418572693863214957792865431145793826","constraints":["XV","custom","kropki"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"modified","modifiers":[],"params":null,"note":"• If a V sits between two digits, they sum to 5.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Divide the grid into three regions of orthogonally connected cells. No 2x2 area can be entirely within one region. For two of the regions, all of its clues tell the truth, obeying the rules listed below. All of the clues in the liar region break their rule. • If a GREEN DIAMOND sits between two digits, they have a difference of at least 5. • If a RED DOT sits between two digits, one is odd and the other is even. • A digit in a CIRCLE indicates the sum of all the digits seen in the direction of its arrow that are in the same region as the circle, until the first region border is reached.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2","c3","c6","c8","c14","c15","c16"]},{"slug":"kropki","type":"kropki","variant":"modified","modifiers":[],"params":null,"note":"• If a BLACK DOT sits between two digits, one is double the other. • If a WHITE DOT sits between two digits, they are consecutive.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c11","c12","c13"]}]},{"id":"f94f3zm4s1","ctcId":3436,"ctcDifficulty":"MEDIUM","title":"Hitpoint Arrows","author":"damo_89","rules":"Normal sudoku rules apply: Place the digits 1 to 9 once each in every row, column, and 3x3 box\n\nHitpoint Arrows: A digit on an arrow is the sum of all digits that are the correct number of steps away from that arrow. For example, if the digits in the direction of an arrow were 32947 then the arrow would contain a 6 (2 + 4) because the 2 is 2 steps away, the 4 is 4 steps away, and all other digits are the wrong number of steps away.","solution":"423865791915247863876931245198324576652718934347596128561472389789653412234189657","constraints":["custom"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Hitpoint Arrows: A digit on an arrow is the sum of all digits that are the correct number of steps away from that arrow.","evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"a9z92eaf6s","ctcId":3437,"ctcDifficulty":"MEDIUM","title":"Slightly intoxicated ","author":"Eric Bader","rules":"Normal sudoku rules apply \nIn this puzzle 4 or 5 of the boxes have become intoxicated. You must determine which boxes are intoxicated. Cages within those intoxicated boxes all use drunken math and are summed by their digits values; digits 1-3 values are equal to 0; digits 4-6 values equal 5; and digits 7-9 equal 10. The intoxicated boxes are all orthogonally connected. The remaining boxes are all not intoxicated and the cages within their digits sum to the cage total.","solution":"965483712431276589287195346319627458546839127728514693194762835652348971873951264","constraints":["cage","custom"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"The remaining boxes are all not intoxicated and the cages within their digits sum to the cage total.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c6"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"You must determine which boxes are intoxicated. Cages within those intoxicated boxes all use drunken math and are summed by their digits values; digits 1-3 values are equal to 0; digits 4-6 values equal 5; and digits 7-9 equal 10. The intoxicated boxes are all orthogonally connected.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5"]}]},{"id":"skuy1x5ywn","ctcId":3438,"ctcDifficulty":"MEDIUM","title":"Fünfzehn","author":"Eric Bader","rules":"Normal sudoku rules apply. Digits within a cage must total indicated; digits may repeat within cages if allowed by other rules. Adjacent digits along a green line (German whisper) must differ by at least 5. A white dot joins consecutive digits.","solution":"126573498378294651945816327834925716769481235512367984281649573657132849493758162","constraints":["cage","german-whispers","kropki"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"modified","modifiers":[],"params":null,"note":"Digits within a cage must total indicated; digits may repeat within cages if allowed by other rules.","evidence":"both","lessonPolicy":"open-with-caveat","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"3ahh9s2agf","ctcId":3439,"ctcDifficulty":"MEDIUM","title":"Counting Foggy Whispers","author":"Eric Bader","rules":"Normal sudoku rules apply\nDigits within a cage must total to the sum in the upper left corner\nGerman whisper adjacent digits along a line must differ by at least 5.\nDynamic fog placing a correct digit may clear fog in other areas of the puzzle.","solution":"584231679913768254267495183856912437492573816731846925145687392329154768678329541","fogLight":"R5C1,R5C2,R5C3,R6C4,R4C5,R5C5,R4C6,R5C7,R5C8,R5C9,R6C5,R6C3,R6C2,R6C1","constraints":["cage","fog","german-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"fgjbhx3iyr","ctcId":3440,"ctcDifficulty":"HARD","title":"Tangled Vines","author":"Eric Bader","rules":"Normal Sudoku rules apply\nAlong the marked positive and negative diagonals digits may not repeat\nGreen Line (German Whisper)- neighbors along the line must differ by 5\nPink line (Renban) - digits must be in a sequence in any order\nWhite Dots- digits must be consecutive, not all white dots are given\nDynamic fog - placing correct digits will reveal the digit in center of the grid","solution":"164957832985362741273841569749618325528493617631725498456179283812534976397286154","fogLight":"R8C1,R7C1,R6C1,R5C1,R4C1,R3C1,R2C1,R1C1,R1C2,R2C2,R3C2,R4C2,R5C2,R6C2,R7C2,R8C2,R9C2,R9C3,R8C3,R7C3,R6C3,R5C3,R4C3,R3C3,R2C3,R1C3,R1C4,R1C5,R1C6,R1C7,R1C8,R1C9,R2C9,R3C9,R4C9,R5C9,R6C9,R7C9,R8C9,R9C9,R9C8,R9C7,R9C6,R9C5,R9C4,R8C4,R7C4,R7C5,R7C6,R7C7,R7C8,R8C8,R8C7,R8C6,R8C5,R6C8,R5C8,R4C8,R3C8,R3C7,R2C7,R4C7,R5C7,R6C7,R4C6,R4C5,R4C4,R5C4,R6C4,R6C5,R6C6,R5C6,R3C6,R2C6,R2C5,R2C4,R3C4,R3C5,R9C1,R2C8","constraints":["diagonal","fog","german-whispers","kropki","renban"],"constraintFacts":[{"slug":"diagonal","type":"diagonal","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"n837muu8j6","ctcId":3441,"ctcDifficulty":"VERY HARD","title":"Anti & Pro Knights","author":"Eric Bader","rules":"Normal sudoku rules apply. Digits in a cage sum to the number shown. Adjacent digits on a green line differ by at least 5. A pink line contains a consecutive group of digits in any order without repeats. Each digit 9 must not be a chess knight’s move away from another 9. Each digit 1 must be a chess knights move away from at least TWO different 1s. All knight’s moves see the grid cylindrically/as a torus, for example R1C2 would see R2C9, R8C1, R8C3, and R9C4  wrapping around the grid; as well as normal knight’s moves like R2C4.","solution":"163249758974856213258371649745968132632415987891732564529183476317624895486597321","constraints":["antiknight","cage","custom","german-whispers","renban"],"constraintFacts":[{"slug":"antiknight","type":"antiknight","variant":"modified","modifiers":[],"params":null,"note":"Each digit 9 must not be a chess knight’s move away from another 9.","evidence":"rules","lessonPolicy":"open-with-caveat","sectionIds":["c5"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each digit 1 must be a chess knights move away from at least TWO different 1s.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]}]},{"id":"TRFJDDjmjt","ctcId":3442,"ctcDifficulty":"VERY HARD","title":"One of these things ...","author":"Jrosas","rules":"Normal sudoku rules apply. All cells in the grid can be divided into two orthogonally connected regions with no 2x2 square entirely in either region. Each cage contains one cell that is not like the others, ie. one digit in each cage is in a different region than are all the others in that cage. The sum clue in a cage is the sum of the “others” in that cage, eg. if the cage sum is 3 and there are three cells in the cage, there is an unknown digit that is in the opposite region from the other two, which are a 1 and a 2. Digits do not repeat within cages. A black dot joins digits that are in a 1:2 ratio. A white dot joins consecutive digits.","solution":"126357849378496251495182637812749365953261784764835192647523918531978426289614573","constraints":["custom","kropki","yin-yang"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Each cage contains one cell that is not like the others, ie. one digit in each cage is in a different region than are all the others in that cage. The sum clue in a cage is the sum of the “others” in that cage, eg. if the cage sum is 3 and there are three cells in the cage, there is an unknown digit that is in the opposite region from the other two, which are a 1 and a 2. Digits do not repeat within cages.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c6","c7"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"y6ivkzi761","ctcId":3443,"ctcDifficulty":"HARD","title":"Outside the Box","author":"Jrosas","rules":"Normal sudoku rules apply\nDigits on a thermometer increase away from the bulb end.\nA digit in a circle indicates the number of circles that contain the digit.\nA digit in the center cell of an bold outlined 3x3 box is the sum of all circled digits in cells outside the box adjacent to the box, including diagonally.","solution":"923465817574821693186973542397516284851294376462738159645389721239157468718642935","constraints":["counting-circle","custom","thermometer"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"A digit in the center cell of an bold outlined 3x3 box is the sum of all circled digits in cells outside the box adjacent to the box, including diagonally.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"n2v6rs916k","ctcId":3444,"ctcDifficulty":"MEDIUM","title":"Ornithological Adjacency","author":"Jrosas","rules":"Ordinary sudoku rules.\n\nAcross the white dot the two digits are consecutive.\n\nAvian variant ratio/fraction rule:\nSome orthogonally adjacent cells are separated by birds.  Each bird indicates a specific ratio.  All pairs of digits on the same kind of bird are in an equal ratio.\n\nIf you prefer to use the term “fractions”, the smaller digit on a bird is a fraction of the larger digit, and all pairs of digits separated by that particular bird share the same fraction or equivalent fractions. \n\nExample.  A pelican might lie between pairs of digits that share a 3:4 ratio (3/4 fraction.)  If so, the ornithologically related pairs across pelicans would be 3/4, 6/8, 4/3, and 8/6.  This is only an example.  There are no pelicans.  \n\nNot all possible birds are given.  (I did not give you all the birds.)","solution":"962158347783429156451367928275693481846571293319842675137984562698215734524736819","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"All pairs of digits on the same kind of bird are in an equal ratio.","evidence":"rules","lessonPolicy":"open","sectionIds":["c6"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"p8ushghwpc","ctcId":3445,"ctcDifficulty":"VERY HARD","title":"Return of the Birds","author":"Jrosas","rules":"Ordinary sudoku rules.\n\nThe pair of digits across each white dot differ by 1.\n\nOrnithologically adjacent rule: Birds indicate ratios.  Any pair of digits across a bird are in the same ratio to each other as are all pairs of digits across that type of bird.  Different birds might share a ratio, but different ratios do not share a bird.\n\nNot all birds are given.","rulesClarified":"Ordinary sudoku rules apply.\n\nEach white dot sits on the border between two cells. The two digits either side of a white dot differ by 1.\n\nEach bird sits across two neighbouring cells. The two digits under a bird are in a ratio to each other.\n\nEvery bird of the same kind has the same ratio. Each kind of bird has one ratio, but different kinds of bird may share a ratio.\n\nNot all birds are given. A pair of neighbouring cells with no bird has no ratio.\n\nFlavour: the rule is called 'ornithologically adjacent'. Birds indicate ratios.","solution":"467132958139857642582649137714593286625781394893426571256978413971364825348215769","constraints":["custom","kropki"],"constraintFacts":[{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"Any pair of digits across a bird are in the same ratio to each other as are all pairs of digits across that type of bird. Different birds might share a ratio, but different ratios do not share a bird.","evidence":"rules","lessonPolicy":"open","sectionIds":["c4","c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"4gausxmp2d","ctcId":3446,"ctcDifficulty":"HARD","title":"Setting Things Straight","author":"Jrosas","rules":"Ordinary sudoku rules: place the digits 1 to 9 in each row, column, and 3x3 bold outlined box.\n\nOrdinary yin Yang rules.  The grid is divided into exactly two regions of orthogonally connected cells.  No 2x2 square of cells is entirely in either region.\n\n+/-1 lines: adjacent cells along a line share differ by 1 and share their yin Yang region.  ALL possible lines are given.\n\nCounting circles: There are 12 circles in the grid.  A digit in a circle indicates how many circles contain that digit and a digit in a circle in a yin Yang region indicates how many cells in that yin Yang region contain the digit.  ALL possible circles are given.\n\nDynamic fog.  One cell is covered with fog.   Correctly placing a digit in a particular cell will clear the fog.","solution":"175938426682574931439216578597321684341865792268497315926153847714689253853742169","fogLight":"R1C8,R1C7,R1C6,R1C5,R1C4,R1C3,R1C2,R1C1,R2C1,R2C2,R2C3,R2C4,R2C5,R2C6,R2C7,R2C8,R2C9,R3C9,R3C8,R3C7,R3C6,R3C5,R3C4,R3C3,R3C2,R3C1,R4C1,R4C2,R4C3,R4C4,R4C5,R4C6,R4C7,R4C8,R4C9,R5C9,R5C8,R5C7,R5C6,R5C5,R5C4,R5C3,R5C2,R5C1,R6C1,R6C2,R6C3,R6C4,R6C5,R6C6,R6C7,R6C8,R6C9,R7C9,R8C9,R9C9,R9C8,R8C8,R7C8,R7C7,R8C7,R9C7,R9C6,R8C6,R7C6,R7C5,R8C5,R9C5,R9C4,R8C4,R7C4,R7C3,R8C3,R9C3,R9C2,R8C2,R7C2,R7C1,R8C1,R9C1","constraints":["counting-circle","custom","fog","yin-yang"],"constraintFacts":[{"slug":"counting-circle","type":"counting-circle","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c8"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"+/-1 lines: adjacent cells along a line share differ by 1 and share their yin Yang region. ALL possible lines are given. A digit in a circle indicates how many circles contain that digit and a digit in a circle in a yin Yang region indicates how many cells in that yin Yang region contain the digit. ALL possible circles are given.","evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6","c8","c9"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c12"]},{"slug":"yin-yang","type":"yin-yang","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"llgqh0kzve","ctcId":3447,"ctcDifficulty":"HARD","title":"No Peeking - Markov's Order","author":"Belamis","rules":"Normal Sudoku rules apply\nDynamic Fog: The grid is partially covered in fog.\nNo Peeking: Digits must be placed in visible cells only. Placing a digit in the last visible cell will reveal the next set of cells.\nDigits in this puzzle must be placed in the correct order (And this requires thinking ahead). Each digit you place must be a factor or multiple of the previously placed digit. E.g. since the first placed (given) digit is 4, the next placed digit must be selected from 1,2,4,8.\nDigits may be placed in any order once ALL fog is revealed.\nGerman Whispers: Adjacent digits along a green line have a difference of at least 5.\nKiller: Digits do not repeat in cages, and sum to the small clue in the top left corner.\nTip: You may want to colour or mark the (currently) last placed digit, to help keep track.","solution":"856392741219746835734815629491568372567123984328974156183259467675431298942687513","fogLight":"R4C1,R4C2,R4C3","constraints":["cage","custom","fog","german-whispers"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"custom","type":"custom","variant":"standard","modifiers":[],"params":null,"note":"No Peeking: Digits must be placed in visible cells only. Each digit you place must be a factor or multiple of the previously placed digit.","evidence":"rules","lessonPolicy":"open","sectionIds":["c3","c6"]},{"slug":"fog","type":"fog","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c9"]}]},{"id":"20ag6yhrrg","ctcId":3448,"ctcDifficulty":"HARD","title":"Wickerwork","author":"Phistomefel","rules":"Normal sudoku rules apply. Digits in a cage cannot repeat and must sum to the small clue given in the top left corner of the cage.","solution":"914268357528731946367495182281379465459612738673854291192583674846927513735146829","constraints":["cage"],"constraintFacts":[{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]}]},{"id":"lrechjs7h8","ctcId":3449,"ctcDifficulty":"HARD","title":"Border Thermos","author":"Aad van de Wetering","rules":"Normal sudoku rules apply. Digits separated by a single king's move (in chess) cannot contain the same digit. Digits along a thermometer must increase from the bulb end.","solution":"461529873582743619793168542826497135357812964149356728235681497914275386678934251","constraints":["antiking","thermometer"],"constraintFacts":[{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"0mapot84dm","ctcId":3451,"ctcDifficulty":"MEDIUM","title":"Hang in the Balance","author":"James Kopp","rules":"Normal sudoku rules apply.\nDigits on an arrow sum to the digit in the circle of that arrow.\nEach purple line contains a set of consecutive digits in any order. \nAdjacent digits along a green line have a difference of at least five.\nCells separated by a black dot are in the ratio 1 to 2. Cells separated by a white dot are consecutive. Not all possible black or white dots necessarily are given.","solution":"945687213712534968836291745428973651691452387573168429267819534159346872384725196","constraints":["arrow","german-whispers","kropki","renban"],"constraintFacts":[{"slug":"arrow","type":"arrow","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c2"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c5","c6"]},{"slug":"renban","type":"renban","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"rules","lessonPolicy":"open","sectionIds":["c3"]}]},{"id":"sv-kader","ctcId":null,"ctcDifficulty":null,"title":"Kader","author":"Sudokuvia","rules":"Sudoku: Normal sudoku rules apply. Place the digits 1 to 9 once each in every row, column and 3x3 box.\nKiller cage: Digits in a cage do not repeat and sum to the total in its corner.\nThermometer: Digits increase from the bulb to the other end.\nGerman whispers (green): Neighbouring digits along a green line differ by at least 5.\nZipper line (red): On a red line, two digits at equal distance from the centre sum to the digit in the centre.\nKropki: Digits joined by a white dot are consecutive. Not all white dots are given.\nXV: Digits joined by an X sum to 10. Not all X's and V's are given.","solution":"196453782823179546754268319512746893478391625369825174931682457645917238287534961","constraints":["XV","cage","german-whispers","kropki","thermometer","zipper-line"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c9","c10"]},{"slug":"cage","type":"cage","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c3"]},{"slug":"german-whispers","type":"german-whispers","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c5"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7","c8"]},{"slug":"thermometer","type":"thermometer","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4"]},{"slug":"zipper-line","type":"zipper-line","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c6"]}]},{"id":"sv-schaakwonder","ctcId":null,"ctcDifficulty":null,"title":"Schaakwonder","author":"Sudokuvia","rules":"No digit is given: six marks and three global rules are enough.\nSudoku: Normal sudoku rules apply. Place the digits 1 to 9 once each in every row, column and 3x3 box.\nKropki: Digits joined by a white dot are consecutive. No black dot is drawn and none would fit: adjacent digits are never one double the other. Not all white dots are given.\nXV: Digits joined by an X sum to 10; digits joined by a V sum to 5. Not all X's and V's are given.\nOdd: A digit in a circle is odd.\nAnti-knight: Two cells a chess knight's move apart never hold the same digit.\nAnti-king: Two cells a chess king's move apart, diagonal neighbours included, never hold the same digit.","solution":"654183972183972546972546831546831729831729465729465318465318297318297654297654183","constraints":["XV","antiking","antiknight","kropki","odd"],"constraintFacts":[{"slug":"XV","type":"XV","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c7","c8"]},{"slug":"antiking","type":"antiking","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c11"]},{"slug":"antiknight","type":"antiknight","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c10"]},{"slug":"kropki","type":"kropki","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c4","c5","c6"]},{"slug":"odd","type":"odd","variant":"standard","modifiers":[],"params":null,"note":null,"evidence":"both","lessonPolicy":"open","sectionIds":["c9"]}]}]}