Sudoku Solver
Sudoku is a popular single player game (ie. a puzzle) which is played on a 9x9 board of 81 cells. These cells are in turn grouped into 3x3 subunits of 9 cells each, as in the following diagram
Each cell can either be blank or can accommodate a single digit between 0 and 9. The board is initialized with digits in some of the cells and the play proceeds by filling in the blank cells with other digits until all the cells are full. The player is constrained by the rule that no row, column or subunit may have a repeated digit.
For example, consider the following initial puzzle
The red letters are not part of the puzzle, but I will use them for reference in this example. Examining the column with the letters in it, we realize that cells A, B and C must contain the digits 1, 3 and 8, because all other digits are already represented in the column. However, at this point, we can't say which digit goes in which letter. The row containing A already has a 1 and a 3 in it, so A must be 8. By elimination, this means that B and C contain 1 and 3. The row containing B already has 1 so B must be 3. Finally, we conclude that C must be 1. We continue playing this way until all the cells are filled with digits.