Number of distinct Sudokus

[bobman0330]

OK, for those who don't know, a Sudoku is a 9x9 grid of numbers subdivided into 9 smaller 3x3 grids. Each row, column, and 3x3 grid contains each number from 1-9 once. How many are there?

My g/f and I tried to figure this out last night. There are 9! ways to set up the top left square. The square below and the square to the right can be set up in, we think, 110 * 6^3. (Derived by finding how many ways the numbers 1-9 can be assigned to a column, then accounting for different arrangements w/in columns.) The bottom left and far rights squares can be set up in 6^3 ways. After that.... ??

[LetYouDown]

5524751496156892842531225600 latin squares and 6670903752021072936960 Sudoku solutions for a 9x9 grid.

http://theory.tifr.res.in/~sgupta/sudoku/expert.html

[bobman0330]

awesome. thanks.

[KenProspero]

While there are 6670903752021072936960 distinct solutions for a 9x9 grid, there are many more possible puzzles, since there would be multiple 'clue sets' that can be derived for any distinct solution.