## Su Doku

Su Doku is usually played on a 9 by 9 board, divided into 3 by 3 cells. You can generalize this into playing on an M×M square board broken into non-overlapping rectangular cells, each containing M squares (an obvious question is to how define a puzzle where M is a prime number). The solution of the puzzle is to place M symbols on the board such that each row, column or cell contains each symbol exactly once, without moving the initial clues. Puzzles with M<9 are called Sub Dokus, those for M>9 are called Super Dokus.

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# Related puzzles

## The mathematics of Su Doku

### Latin Squares

An M×M Latin square is a variant of Su Doku without the rule that each cell should contain each symbol exactly once. In other words, one is required to fill up the grid so that each row and each column contain each of the M symbols exactly once. The first systematic study of this problem is due to the Swiss mathematician Leonhard Euler, and dates from 1782. Since there are less conditions to be satisfied, the number of Latin Squares is larger than the number of Su Doku solutions (every Su Doku solution is a Latin Square, but there are Latin Squares which are not Su Doku solutions).