# of different structures

Advanced methods and approaches for solving Sudoku puzzles

# of different structures

Postby vinays84 » Mon Apr 17, 2006 5:40 am

More of a math question here:
How many different possible sudoku grid structures are there and how would one reach this conclusion? By different grid structure, I mean: If you take any finished puzzle and switch all the 3's and 5's (choose any 2 numbers), then it is the same structure.


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Postby keith » Mon Apr 17, 2006 5:47 am


Wikipedia has a section on the mathematics of Sudoku which answers your question.

I presume you are asking about unique grids, ignoring reflections.

Look at:


Best wishes,

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Postby vinays84 » Mon Apr 17, 2006 6:45 am

Thanks keith. They give a number there, but I believe this is the number of unique grids, not unique grid structures. I suppose you can find the number of unique grids by simply dividing this number by 9!. This yields 72^2 × 2^7 × 27,704,267,971, which they say was derived through logic and brute force computation. However, the exact logical methods are not stated. If anyone has a basic idea to how these numbers were found please let me know, because..well..I'm curious.

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Postby Animator » Mon Apr 17, 2006 9:18 am

The main Sudoku article on Wikipedia has a link to: Mathematics of Sudoku.

It should contain more information about it. Also note that that last page has a See Also section with a link back to this forum. It links to a thread which contains 41 pages. I'm sure that is all the information you need.
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Postby SHuisman » Thu Apr 27, 2006 2:46 pm

As you might have noticed 27704267971 is a prime ! So i think it is very hard to calculate the number. Because when you calculate possibilities almost everytime you use 'products' and 'factorials'. And since it is a prime, it can't be the factorial or product of some numbers !
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