Math has helped place a man on the moon and has counted the genes in our DNA.
But never mind all that. A mathematician says he has finally produced something that people really care about: a foolproof way to beat Sudoku puzzles.
“Sudoku has become the passion of many people the world over,” says computer scientist J. F. Crook of Winthrop University in Rock Hill, S.C., in the current Notices of the American Mathematical Society. “The interesting fact about Sudoku is that it is a trivial puzzle to solve.”
Not everyone would agree. Since the introduction of the numerical puzzle in London’s The Times in 2004, Sudoku has taken quiz fans by storm. It has appeared on websites, cellphones and in newspapers, including USA TODAY.
“Sudoku requires a kind of math sense,” says mathematician M. Ram Murty of Canada’s Queen’s University in Kingston, an expert in number theory. “Everyone wants a mental challenge, and Sudoku provides it.”
The puzzles are generally grids of 81 squares, nine across and nine down. Some boxes have a number filled in; the rest are blank. Players must fill in the blank squares with numbers between 1 and 9 without repeating any numbers in a row, column or the nine interior 3-by-3 boxes of the puzzle.
Many players and strategy guides intuitively take steps like those Crook outlines, but he says his study offers the first mathematically guaranteed way of solving the puzzles.
Even using his method, there may be two possibilities for a particular box. In that case, the player would have to guess which one is right and then repeat the steps to see whether they lead to a solution. He counsels switching pencil colors at this stage. If the first guess doesn’t work, erase and try the other option.
Murty, who has published theoretical work on Sudoku, says Crook’s steps follow well-worn mathematical approaches to puzzles such as chess problems. “Sudoku is really just a kind of math in action,” he says.
UPDATE : Crook’s Sudoku theory can be found at http://www.ams.org/notices/200904/rtx090400460p.pdf (pdf. 616kB)