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Sudoku and its mathematics

10 articles

Anti-Knight Sudoku

Anti-Knight Sudoku, also called Knight Sudoku or No Knight Step Sudoku, is a 9×9 sudoku variant banning identical digits a chess knight's move apart; introduced 2006, famous via Mitchell Lee's 2-given Miracle Sudoku in 2020.

Hoshi

Hoshi (星, Star Sudoku) is a Sudoku variant on a six-pointed star grid of triangular cells: six large triangles of nine cells each take digits 1-9, and every straight line, even across the central hole, must have no repeated digits. Distinct from the Hoshi Star Battle and Go apps.

Killer sudoku

Killer sudoku, also samunamupure, sumdoku or addoku, is a Sudoku variant with dashed cages whose digits sum to a corner clue without repeats; created by Tetsuya Nishio from Miyuki Nisawa's idea, first printed by The Times on 31 August 2005.

Mathematics of Sudoku

Mathematics of Sudoku: the 9×9 puzzle as a Latin square with 3×3 box constraints; 6.67×10^21 completed grids, 5.47×10^9 essentially different, 17-clue minimum (McGuire et al.), exact cover, and NP-completeness of generalized Sudoku.

Samurai Sudoku

Samurai Sudoku, also called Gattai-5 or 5-way Sudoku, is a Sudoku variant of five overlapping 9×9 grids in an X shape with four shared 3×3 boxes, 369 cells total, solved as one puzzle.

Sudoku

Sudoku, also called Number Place, is a logic puzzle played on a 9×9 grid where every row, column, and 3×3 box contains the digits 1 through 9.

Sudoku Mine

Sudoku Mine, also called Minesweeper Sudoku or Minesweeper (Sudoku), is a logic puzzle hybrid: place exactly three mines in each 9×9 Sudoku row, column and 3×3 box so every printed number counts its adjacent mines.

Sudoku solving algorithms

Sudoku solving algorithms fill 9×9 grids under row, column, and box constraints: backtracking with MRV, Norvig-style constraint propagation, Knuth's Dancing Links exact cover, ILP, and human-style logical solvers used for generation and difficulty grading.

Sujiken

Sujiken is a Sudoku variation invented by George Heineman and played on a right triangle of 45 cells, adding diagonal constraints and triangular regions to standard Sudoku rules.

Tridoku

Tridoku (Triangular Sudoku, Tri-Doku) is a triangular Sudoku variant invented by Japheth Light: 81 triangular cells in nine nonets, with outer-edge and inner-triangle lines of 1-9 and a rule that touching cells, up to 12 neighbors, never match.