If you haven’t heard about it, Sudoku is the new numbers puzzle now sweeping the world. The Star Ledger recently started publishing the puzzle along with the crosswords. The puzzle is reminiscent of magic squares, but is really much simpler. To solve it, merely fill in numbers such that each row, column, and 3×3 box contains all nine digits. Someone has figured out (apparently) the minimum number of blanks to fill in to make the puzzle unique.

A logical question is how many of these puzzles are there? I haven’t done much research on it, but I haven’t seen any reference to the total number of possible Sudokus. When Rubik’s cube came out, you will remember, the number of possible positions (a few billion?) was known and published. I followed a few entries in the readers forum on the Sudoku website, but no one seems to have solved the “number” problem as yet. A comment plugging the Sudoku computer program calls the number of games “endless” but this is obviously wrong. “Countless” seems more appropriate, but this too is obviously wrong (unless you define this term as meaning “nobody has done it yet”). I think the number of puzzles is likely to be “astronomical” and possibly already known. My own belief, after reading a little and thinking a little (and, yes, calculating a little) is the number of possible Sudokus is in the range of, but less than Avogadro’s number.

Probably a more difficult calculation is determining how many and which numbers to reveal to make the solution unique. It seems to me there might be many ways of doing this. So maybe each unique puzzle can be presented in many different ways, multiplying the possibilities. On the other hand, mathematics is full of surprises, and maybe there is only one way to provide the minimum number of “hints” that allow the puzzle solution to be unique. Anyway, it’s a clever idea. This is one of those games you have to try, just so you’ll know what everybody’s talking about.

DadGames06/18/05 0 comments

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