If you are interested behind the story of solving Sudoku puzzles with math then you must read the article “Sudoku Squares and Chromatic Polynomials”, by Agnes M. Herzberg and M. Ram Murty, which appears in the June/July 2007 issue of the Notices of the AMS.
The article [in pdf 224 kb] “Sudoku Squares and Chromatic Polynomials” is also available on the web site of the Notices of the AMS. The authors use tools from the branch of mathematics called graph theory to systematically analyze Sudoku puzzles. They also find that analyzing Sudoku’s leads to some unsolved problems in graph theory.
Well this is a bit too much much math for a puzzle website but they also found/proved some thinks which I think is nice knowing about Sudoku’s. For example they proved that, in order for any Sudoku puzzle to have only one solution, at least 8 of the 9 numbers must appear as given entries in the puzzle; if only 7 numbers are given, then the puzzle has at least two solutions. Happy Puzzling!