The rules of Sudoku

Short version

You have to fill the rows and columns of the 9×9 grid in a way that each digit from 1 to 9 can only appear once in every row and in every column. In every 3×3 subgrid of the board each digit can appear only once.

Longer version

Sudoku is an excellent logic-based, combinatorial number-placement puzzle. The goal is to fill a 9×9 grid with digits in such a way that each column, each row and each 3×3 subgrid that compose the table contain all of the digits from 1 to 9. At the beginning you start with a partially completed grid, which generally has only one solution. The completed game is always like a Latin square, with an additional constraint about the contents of the individual regions. For example, a certain number can’t appear more than once in the same row, column or in any of the 9 3×3 subgrids. The game was popularized in 1986 by a Japanese puzzle company called Nikoli, under the name ‘Sudoku’, which means ‘digit’. Since 2005, it has enjoyed huge popularity all over the world.

The general problem of solving Sudoku puzzles on n2×n2 grids of n×n blocks is known to be NP-complete. The number of classic 9×9 Sudoku solution grids is 6,670,903,752,021,072,936,960, or around 6.67×1021