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From Wikipedia, the free encyclopedia
Sudoku (originally called Number Place) is a logic-based, combinatorial number-placement puzzle.
In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid
(also called "boxes", "blocks", or "regions") contain all of the digits from 1 to 9.
The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.
Most Sudoku puzzles published have only one solution.
If there is more than one solution, it is probably a mistake.
That said, puzzles with incomplete clues can have multiple solutions.
In the extreme case, a puzzle with no clues has 6,670,903,752,021,072,936,960 solutions according to Wikipedia.
The number of classic 9×9 Sudoku solution grids is 6,670,903,752,021,072,936,960 (sequence A107739 in the OEIS), or around 6.67×1021.
This is roughly 1.2×10-6 times the number of 9×9 Latin squares.
Various other grid sizes have also been enumerated.
The number of essentially different solutions, when symmetries such as rotation, reflection, permutation, and relabelling are taken into account,
was shown to be just 5,472,730,538 (sequence A109741 in the OEIS).