# How many different sudoku puzzles are there?

The answer: 6, 670, 903, 752, 021, 072, 936, 960, according to this site:

http://www.technologyreview.com/view/426554/mathematicians-solve-minimum-sudoku-problem/

I have tried to get this number using direct methods but basically I have found the question too hard. There are too many possibilities, but I am likely missing some strategic ways to solve the problem. Any help would be greatly appreciated, thanks.

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You should be more precise about when two give sudokus are different. For example given some sudokus you can use a rotation to get a new one. Or another way is just renaming the 1 into 2 and vice versa – Dominic Michaelis Nov 20 '13 at 6:04
So as in Wikipedia stand there are actually 5,472,730,538 different sudokus (taken symmetries in account) – Dominic Michaelis Nov 20 '13 at 6:06

http://www.afjarvis.staff.shef.ac.uk/sudoku/sudoku.pdf ${}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}$

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Beat me to it (again) – Mark Bennet Jan 10 '13 at 20:55
Super. Thanks Chris. – Adam Rubinson Jan 10 '13 at 21:19

Try Wikipedia for an introduction and overview and additional references.

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I think it would be (9!)squared X 9 The 9 is from the 9 different puzzles with the center number changed. Then you would have to subtract all the puzzles with 0 thru 7 solved numbers(if you had the 8th solved, the empty spaces would be the next solved number and the puzzle)

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Based on the equation (9!^2(9)), the number of possible sudoku puzzles is exactly 1,185,137,049,600.

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