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# Sudoku

## Sudoku Rules

Sudoku is a logic-based, combinatorial number-placement puzzle. A Sudoku puzzle consists of a 9x9 grid partitioned into nine 3x3 sub-grids (also called "submatrices", "boxes", "blocks", "regions", or "sub-squares") .The objective is to fill a 9×9 matrix with digits so that each column, each row, and each of the nine 3×3 submatrices that compose the matrix contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, and the puzzle is to find the remaining entries, which typically has a unique solution. If both players have the same number of pieces at the end then the game is tied. Although the 9×9 grid with 3×3 regions is by far the most common, variations abound.

## Sudoku History

Number puzzles appeared in newspapers in the late 19th century, when French puzzle setters began experimenting with removing numbers from magic squares. Since 1895, French newspapers published a partially completed 9×9 magic square with 3×3 sub-squares, that was almost a modern Sudoku. These weekly puzzles were a feature of French newspapers for about a decade but then disappeared.

The modern Sudoku was designed by Howard Garns, a 74-year-old retired architect and freelance puzzle constructor from Indiana, and first published in 1979 by Dell Magazines. Garns died in 1989 before getting a chance to see his creation as a worldwide phenomenon.

The puzzle was popularized in 1986 by the Japanese puzzle company Nikoli, under the name Sudoku, meaning single number. In 1997, a retired Hong Kong judge Wayne Gould, then in his early 50s, saw a Sudoku puzzle in a Japanese bookshop. Over six years he developed a computer program to produce puzzles quickly. He promoted Sudoku to The Times in Britain, which launched it on 12 November 2004. The first letter to The Times regarding Sudoku was published the following day on 13 November from Ian Payn of Brentford, complaining that the puzzle had caused him to miss his stop on the tube.

In the United States, the first newspaper to publish a Sudoku puzzle by Wayne Gould was The Conway Daily Sun (New Hampshire), in 2004.

## Mathematics of Sudoku

A completed Sudoku grid is a special type of Latin square with the additional property of no repeated values in any of the 9 blocks of contiguous 3×3 cells. The relationship between the two theories is now completely known, after Denis Berthier proved in his book The Hidden Logic of Sudoku (May 2007) that a first-order formula that is valid for Sudoku if and only if it is valid for Latin Squares.

The first known calculation of the number of classic 9×9 Sudoku solution grids was posted on the USENET newsgroup rec.puzzles in September 2003 and is 6,670,903,752,021,072,936,960.

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