Sudoku puzzles, and their variants, have become extremely popular in the last decade. They can now be found in major U.S. newspapers, puzzle books, and web sites; almost as pervasive are the many guides to Sudoku strategy and logic. We give a class of solution strategies-encompassing a dozen or so differently named solution rules found in these guides-that is at once simple, popular, and powerful. We then show the relationship of this class to the modeling of Sudoku puzzles as assignment problems and as unique nonnegative solutions to linear equations. The results provide excellent applications of principles commonly presented in introductory classes in finite mathematics and combinatorial optimization, and point as well to some interesting open research problems in the area.
“You don’t have to know any mathematics to solve a Sudoku puzzle,” one of the major Norwegian newspaper claimed when the Sudoku wave started a couple of years ago. I have always disagreed strongly with this, and it seems that Provan J. Scott, who has written an article about this in American Mathematical Monthly, has a similar opinion. The article is entitled Sudoku: strategy versus structure. Here is the article abstract: