## Unique Sudokus (Russell & Jarvis)

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

### Re: Unique Sudokus (Russell & Jarvis)

Mathimagics,

i had missed that last post. I knew that with gsf's program/grid collection you can list all automorph puzzle counts (and i told you so).

Thanks for your interesting summary. What i still don't clearly understand is, what happens to the multi-automorphism grids in Red Ed's/Jarvis table.
I think you should find the same grid in different classes, so isn't the sum more than all possible automorph grids ?

Ah, think i got it. This way they just reproduce the multi-automorph count correctly.
eleven

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Joined: 10 February 2008

### Re: Unique Sudokus (Russell & Jarvis)

eleven wrote:I knew that with gsf's program/grid collection you can list all automorph puzzle counts (and i told you so).

Surely you have noticed by now that I have to be told some things over and over and over again ...

eleven wrote:Ah, think i got it. This way they just reproduce the multi-automorph count correctly.

Cool, eh?

Mathimagics
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### Re: Unique Sudokus (Russell & Jarvis)

eleven

Posts: 2178
Joined: 10 February 2008

### Re: Unique Sudokus (Russell & Jarvis)

Hi Mathimagics,

Let's call :
Ne = 5,472,730,538 number of ed Sudoku solution grids
NT = 6,670,903,752,021,072,936,960 exact number of Sudoku solution grids
t = 2 x 6^8 = 362,880 size of the group of geometric transformations

What you call grid deficiency is
Gd = Ne.t.9! - NT = 344,420,270,386,053,120
D = Gd/9! = Ne.t - NT/9! = 949,129,933,824

In Russel & Jarvis' table, Class 1 contains only the identity. Therefore the number of invariants are all the sudoku grids (NT)
Before relabelling, their number is A(1) = NT/9! = 18,383,222,420,692,992

Then D = Ne.t - A(1)

Btw, there is a typo in your table: A(1) = 18,383,222,420,692,992

Yes, gsf calculated the number of automorphisms for each ed sudoku-grid independently of Russel & Jarvis.
The numbers were predicted 2 years before though here
His calculation confirmed both Ne and NT.

and yes, thre are only 560,151 ed sudoku-grids having # automorphisms greater or equal to 2.

JPF

edited a typo
Last edited by JPF on Mon Jan 22, 2018 7:22 am, edited 1 time in total.
JPF
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### Re: Unique Sudokus (Russell & Jarvis)

Thanks JPF!

I fixed the error, that last digit appears to have been lost in transit!

I did notice your handle appearing regularly as I waded through the mire of "About Red Ed's Sudoku Symmetry Group", and "Su-Doku's Maths", etc ..., looking for traces of Red Ed's automorphism enumerator.

Nice of you to chime in with that useful info ...

Cheers!

Mathimagics
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