How many Sudoku problems are there? If you visit your local bookstore, where Sudoku puzzle books abound, you would think there are millions. The Sudoku craze is boffo box office (so to speak).
And it looks like there are plenty of puzzles to be had. Actually, for a typical 9 x 9 Sudoku grid, there are 6,670,903,752,021,072,936,960 possible arrangments where every number from 1 through 9 appears in every row and column (and no numeral appears twice in any row or column).
That’s a lot of Sudoku puzzles.
Actually, it’s not that high. For example, if you have a valid Sudoku arrangement, and turn it 90 degrees, that counts as a different arrangement. Also, if you have a valid Sudoku arrangment, and (for example) switch all the 6’s and 7’s, that counts as a different arrangement. So the 6,670,903,752,021,072,936,960 number is a little exaggerated.
Therefore, the number of Sudoku patterns is substantially less. In a 9 x 9 grid, there are only 3,546,146,300,288 distinct patterns. I say "only", but really, it is still enough to keep you busy for a while.
For more Sudoku trivia, history, strategy and mathematrical geekdom, read here at The American Scientist.