PDF] Sudoku puzzles and how to solve them

A Sudoku puzzle (of ‘classical type’) consists of a 9-by-9 matrix partitioned into nine 3- by-3 submatrices (‘boxes’), under the condition that the nine rows, the nine columns, and the nine boxes all contain a permutation of the symbols of some given alphabet of size 9. A Sudoku puzzle (of ‘classical type’) consists of a 9-by-9 matrix partitioned into nine 3-by-3 submatrices (‘boxes’). Some of the entries are given, and the puzzle is to find the remaining entries, under the condition that the nine rows, the nine columns, and the nine boxes all contain a permutation of the symbols of some given alphabet of size 9, usually the digits 1-9, or the letters A-I. Some mathematicians will claim that since this is a finite problem, it is trivial. The time needed to solve a Sudoku puzzle is O(1) indeed, one can always try the 9 possible ways of filling the grid. But one can still ask for efficient ways of finding a solution. Or, if one knows the solution already, one can ask for a sequence of logical arguments one can use to convince someone else of the fact that this really is the unique solution.

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