## # of different structures

Advanced methods and approaches for solving Sudoku puzzles

### # of different structures

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.

Thanks!

-Vinay
vinays84

Posts: 2
Joined: 16 April 2006

Vinay,

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

Look at:

http://en.wikipedia.org/wiki/Sudoku

Best wishes,

Keith
keith
2017 Supporter

Posts: 215
Joined: 03 April 2006

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.

-Vinay
vinays84

Posts: 2
Joined: 16 April 2006

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