## Number of variants, rotation...

Everything about Sudoku that doesn't fit in one of the other sections

### Number of variants, rotation...

Hi,
Is someone knows howmany grids is't possible to do with a grid with swap, rotation, permutation, numbers mapping...

Papy
Papy Jhon

Posts: 6
Joined: 01 February 2006

The number of valid permutations (in case the grid isn't automorphic) should be 9!*6^8*2 = 1,218,998,108,160.

RW
RW
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Thanks
But why?

If your compute them the result is different

Here is the method

the theorical number is !9*!9*!9 corresponding to the permutation of tel colums, the roxs end the digit (!9 for each)

But the rows and the column cannot take 362880 value because uou have to preserve the boxe so each blkochs can only take !3 disposiutios . You have 3 bloch !3 afgain and at end the blocks can have also !6 combinaisons

so the niumber seams to be
6*6*6*6 = 1296 3row; 3 times, 3 blocs
1296*1296 = 1 679 616 (rows*colums)
1679616 * 362880 = 609 499 054 080 sib total * digits

So what is bad in my number.?

Papy
Papy Jhon

Posts: 6
Joined: 01 February 2006

Papy Jhon wrote:So what is bad in my number.?

Papy

You can also rotate the grid 90 degrees (rows become columns and columns become rows). That's what the "*2" at the end of my calculation stands for.

RW
RW
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I Think that it's false

Rotation is notr permutations it's just the way use to look.

You get them vby turning the peper not by permuting rox and column.
The rotation change the way to lokk not the grid!
Making colums with rows is not an isomorph I think..

Papy
Papy Jhon

Posts: 6
Joined: 01 February 2006

There for
If you compute the suare of my numùber you get

371 489 096 924 414 764 646 400
3.71e+23
Papy
Papy Jhon

Posts: 6
Joined: 01 February 2006

Papy Jhon wrote:I Think that it's false

Rotation is notr permutations it's just the way use to look.

Earlier when Papy asked his question he wrote:Is someone knows howmany grids is't possible to do with a grid with swap, rotation, permutation, numbers mapping...

Papy, all possible permutations only change the appearance of the puzzle. Rotation is no different from row swapping or digit substitution in this sence. The fact is that there always exists another grid with the exact same properties, only that the rows have been exchanged for columns and vice versa. If this is not an isomorph, then what is it? Rules for permutation is not something you can redefine based on your personal opinion. They have been discovered a long time ago and rotation is indeed a valid permutation.

Papy Jhon wrote:There for
If you compute the suare of my numùber you get

371 489 096 924 414 764 646 400

And the significanse of this number is...?

RW
RW
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Joined: 16 March 2006

when I speak about rotations, swap, permutation was;all techniques to modify the grid conserving the sudoku particularity

The problem: for me is to compute the number of latin square with differents size
If found the exact nmber unbtil trhe size 6
My calculation give the same resuts I conbtriol them by enumértion.
But I doesn,t find le way used to compute for the Sudoku
And ll the resulttaht i found do'esnot care of rotation.
So if i make e mistake sorry. For me a permutation is the inversion of to value: a cellulme, a row, a box or a digit
But three only are available for Sudoku:
Digit, Riw,Columns.

It's the number I'm looking for: hoaw many Soduko grid it's possible to create. And Idon't found how Bertram Felgenhauer compute them.

Papy
Papy Jhon

Posts: 6
Joined: 01 February 2006

For information on how Felgenhauer and Jarvis counted the total amount of grids, see here. For information about how Russell and Jarvis calculated the amount of essentially different grids, see here.

RW
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