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A Sudoku whose regions are not (necessarily) square or rectangular is known as a Jigsaw Sudoku. In particular, an N × N square where N is prime can only be tiled with irregular N -ominoes . For small values of N the number of ways to tile the square (excluding symmetries) has been computed (sequence A172477 in the OEIS ). [ 10 ]
A Sudoku starts with some cells containing numbers (clues), and the goal is to solve the remaining cells. Proper Sudokus have one solution. [1] Players and investigators use a wide range of computer algorithms to solve Sudokus, study their properties, and make new puzzles, including Sudokus with interesting symmetries and other properties.
However, after this problem was proved to be NP-complete, proof by reduction provided a simpler way to show that many other problems are also NP-complete, including the game Sudoku discussed earlier. In this case, the proof shows that a solution of Sudoku in polynomial time could also be used to complete Latin squares in polynomial time. [12]
The next two chapters look at two different mathematical formalizations of the problem of going from a Sudoku problem to its solution, one involving graph coloring (more precisely, precoloring extension of the Sudoku graph) and another involving using the Gröbner basis method to solve systems of polynomial equations.
A Sudoku is a type of Latin square with the additional property that each element occurs exactly once in sub-sections of size √ n × √ n (called boxes). Combinatorial explosion occurs as n increases, creating limits to the properties of Sudokus that can be constructed, analyzed, and solved, as illustrated in the following table.
Killer sudoku (also killer su doku, sumdoku, sum doku, sumoku, addoku, or samunanpure サムナンプレ sum-num(ber) pla(ce)) is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, depending on the solver's skill at mental arithmetic ; the hardest ones ...
Numbrix puzzles, which appear in Parade magazine, are similar to Hidato except diagonal moves are not allowed. [9] (vos Savant has only used 7×7 and 9×9 grids). [10]Jadium puzzles (formerly Snakepit puzzles), created by Jeff Marchant, are a more difficult version of Numbrix with fewer given numbers and have appeared on the Parade web site regularly since 2014, along with a daily online ...
The Sudoku Cube or Sudokube is a variation on a Rubik's Cube in which the aim is to solve one or more Sudoku puzzles on the sides or rows. The toy was originally created in 2006 by Jay Horowitz in Sebring, Ohio. [11] It was subsequently produced in China, marketed and sold internationally. A scrambled colorless Sudoku Cube
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