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 DrSudoku
 Joined: 30 Oct 2005  Posts: 1  :   Items 

Posted: Sun Oct 30, 2005 12:17 pm Post subject: Number of "magic sudokus" (and random generation) 


Hi,
I am intereste in calculating how many "magic sudokus" it's possible to create. A "magic sudoku" is a normal sudoku with an extra constraint:
in each of the 9 3x3 squares the sum of each row and col must be the same (15).
I have read about the difficulty in calculating the number of regular sudokus but I reckon it's possible to calculate the numbers when it's a magic sudoku. The number of possible 3x3 squares where the sum of each row and col is 15 should be each to calculate.
I have written a simple program i c to generate random "magic sudokus" but I am interested in knowing how many it's possible to make. I have a hunch that it's not that many.
Here's some output examples from my program:
1 9 5  6 7 2  3 4 8
8 4 3  1 5 9  7 2 6
6 2 7  8 3 4  5 9 1

2 7 6  9 1 5  8 3 4
4 3 8  2 6 7  1 5 9
9 5 1  4 8 3  6 7 2

7 6 2  3 4 8  9 1 5
5 1 9  7 2 6  4 8 3
3 8 4  5 9 1  2 6 7
1 9 5  7 2 6  3 8 4
8 4 3  5 9 1  7 6 2
6 2 7  3 4 8  5 1 9

5 1 9  8 3 4  2 7 6
7 6 2  1 5 9  4 3 8
3 8 4  6 7 2  9 5 1

2 7 6  4 8 3  1 9 5
9 5 1  2 6 7  8 4 3
4 3 8  9 1 5  6 2 7
8 6 1  2 9 4  3 5 7
3 7 5  6 1 8  4 9 2
4 2 9  7 5 3  8 1 6

5 3 7  8 6 1  2 4 9
9 4 2  3 7 5  6 8 1
1 8 6  4 2 9  7 3 5

7 5 3  1 8 6  9 2 4
2 9 4  5 3 7  1 6 8
6 1 8  9 4 2  5 7 3
Thanks in advance. 

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 dukuso
 Joined: 14 Jul 2005  Posts: 454  :  Location: germany  Items 

Posted: Sun Oct 30, 2005 2:14 pm Post subject: 


I think it's
someone else please fill in the missing digits so to confirm it. 

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 mrcl
 Joined: 01 Dec 2005  Posts: 3  :   Items 

Posted: Thu Dec 01, 2005 12:54 am Post subject: 


dukuso wrote:  I think it's

maybe 5971968
besides transposition and reordering column or rows the only possible box of such a sudoku is
transposition divides the boxes into two classes. boxes of different classes cannot be in the same sudoku. there are 2*3!*3! posibilities to select a box 1: transposition (2) ,permuting rows (3!) or columns (3!).
for box2 there are 2!*3! possibilites: 2! for permuting the rows and 3! for permuting the columns. all in all there are the following possibilities to seleect boxes:
Code: 
2*3!*3! 3!*2! 3!*1!
2!*3! 2!*2! 2!*1!
1!*3! 1!*2! 1!*1!

this gives 2*2!^6*3!^6 possiblitis, that gives 5971968. _________________ guenter 

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