Sudoku - Downloads, Articles, News & Resources

Sudoku is a logic-based number-placement puzzle. The objective is to fill a 9×9 grid so that each column, each row, and each of the nine 3×3 boxes (also called blocks or regions) contains the digits from 1 to 9 only one time each. The puzzle setter provides a partially completed grid.

Completed Sudoku puzzles are usually a type of Latin square with an additional constraint on the contents of individual regions. Leonhard Euler is sometimes incorrectly cited as the source of the puzzle, based on his related work with Latin squares.

The modern puzzle was invented by an American architect, Howard Garns, in 1979 and published by Dell Magazines under the name "Number Place". It became popular in Japan in 1986, after it was published by Nikoli and given the name Sudoku, meaning single number. It became an international hit in 2005

Computer solutions

There are three general approaches taken in the creation of serious Sudoku-solving programs: human solving methods, rapid-style methods, and pure brute-force algorithms. Human-style solvers will typically operate by maintaining a mark-up matrix, and search for contingencies, matched cells, and other elements that a human solver can use to determine and exclude cell values.

Many rapid-style solvers employ backtracking searches, with various pruning techniques in order to help reduce the size of the search tree. The term rapid-style may be misleading: Most human-style solvers run considerably faster than a rapid-style solver, although the latter takes less time to write and is more easily adapted to larger grids. A purely brute-force algorithm is very simple and finds a solution to a puzzle essentially by "counting" upward until a string of eighty-one digits is constructed which satisfies the row, column, and box constraints of the puzzle.

Rapid solvers are preferred for trial-and-error puzzle-creation algorithms, which allow for testing large numbers of partial problems for validity in a short time; human-style solvers can be employed by hand-crafting puzzlesmiths for their ability to rate the difficulty of a created puzzle and show the actual solving process their target audience can be expected to follow.

Although typical Sudoku puzzles (with 9×9 grid and 3×3 regions) can be solved quickly by computer, the generalization to larger grids is known to be NP-complete. Various optimization methods have been proposed for large grids.

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