## SudokuP - Analysis

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Re: SudokuP - Analysis

Hi Serg!

Serg wrote:53,666,689 PF-different SudokuP solution grids is the number of essentially different SudokuP solution grids.

We agree 100%!

And blue (bless his knickers) has produced a Canonical Form function that can be used to compare grids for P-equivalence and/or PF-equivalence.

The VPT group (S-equivalence) was not entirely a wasted exercise, however. blue's CF code only became available a day or two ago. Since I had already built my catalog of S-equivalence classes for SudokuP, I was able to verify that my orbit-connecting logic was correct by comparing results with CF function. So at the very least we have a reliable mechanism for orbit-connection should the need ever arise. Ok, that's probably unlikely, but we have learned much from the process. So no harm done!

And, by the way, your analysis above looks pretty fine to me in all respects. If the facts change, we simply need to change our minds (it happens to me on a regular basis! )

Mathimagics
2017 Supporter

Posts: 737
Joined: 27 May 2015

### Re: SudokuP - Analysis

Hi, Mathimagics!
Mathimagics wrote:
It seems true number of p-different SudokuP solution grids should be around 214,038,113/4 = 53,509,528 (approx.)

Very close! The actual number is 53,666,689

Burnside's Lemma method...

I confirm the number of PF-different SudokuP solution grids - 53,666,689.
My method was generation of all-different SudokuP solution grids for 11 Red Ed's equivalence classes and counting grids, not having isomorphs with lower metric. (10 hours of CPU time.)
Isomorphic transformation group contained 10368 transformations (including blue's F/G/E (etc.) transformations).

Serg
Serg
2018 Supporter

Posts: 607
Joined: 01 June 2010
Location: Russia

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