Mathematician's foolproof Sudoku solution — Solve any puzzle, no matter how hard

So big the news appears on the front page of today's USA Today.

Computer scientist J.F. Crook of Winthrop University in Rock Hill, South Carolina published his solution in the current issue of Notices of the American Mathematical Society.

Reporter Dan Vergano wrote in his USA Today article that "many players and strategy guides intuitively take steps like those Crook outlines, but that he [Crook] says his study offers the first mathematically guaranteed way of solving the puzzles."

All set?

Just follow these steps:

1. Scan the puzzle for any "forced" numbers in blank squares within the 3-by-3 boxes — ones in which there are enough surrouding numbers filled in that it could be only one number.

2. Mark up the rest of the puzzle, noting in the open squares every possible number that might occupy the square.

3. After you've marked up the puzzle, look at the number combinations by row, column by column and interior box by interior box. If one number stands out as unique in that row, column or box, it belongs in the square in which you've written it.

4. Repeat this search until only one of the numbers you've written in each of the squares is left. It will be the right number.

Important note: "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."

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Crook's paper is online here.