The New Sudoku Players' Forum

[m_b_metcalf]

.

Meanwhile, here is a grid in minlex form, which has rank 1, and which is composed of 64 x UA4's. It has 18,432 automorphisms, which is believed to be the maximum possible:

Grid with Most Automorphisms: Show

Code: Select all

+---------+---------+---------+---------+
| 0 1 2 3 | 4 5 6 7 | 8 9 A B | C D E F |
| 4 5 6 7 | 0 1 2 3 | C D E F | 8 9 A B |
| 8 9 A B | C D E F | 0 1 2 3 | 4 5 6 7 |
| C D E F | 8 9 A B | 4 5 6 7 | 0 1 2 3 |
+---------+---------+---------+---------+
| 1 0 3 2 | 5 4 7 6 | 9 8 B A | D C F E |
| 5 4 7 6 | 1 0 3 2 | D C F E | 9 8 B A |
| 9 8 B A | D C F E | 1 0 3 2 | 5 4 7 6 |
| D C F E | 9 8 B A | 5 4 7 6 | 1 0 3 2 |
+---------+---------+---------+---------+
| 2 3 0 1 | 6 7 4 5 | A B 8 9 | E F C D |
| 6 7 4 5 | 2 3 0 1 | E F C D | A B 8 9 |
| A B 8 9 | E F C D | 2 3 0 1 | 6 7 4 5 |
| E F C D | A B 8 9 | 6 7 4 5 | 2 3 0 1 |
+---------+---------+---------+---------+
| 3 2 1 0 | 7 6 5 4 | B A 9 8 | F E D C |
| 7 6 5 4 | 3 2 1 0 | F E D C | B A 9 8 |
| B A 9 8 | F E D C | 3 2 1 0 | 7 6 5 4 |
| F E D C | B A 9 8 | 7 6 5 4 | 3 2 1 0 |
+---------+---------+---------+---------+

Mathimagics, My program counts 256 UA4s. What's up? Regards,

Mike

[Mathimagics]

My program counts 256 UA4s. What's up?

My arithmetic, for a start!

[Mathimagics]

The current state of play :

Code: Select all

   Status         #Ranks
   ---------------------
   Grid exists     17812
   No band exists    327
   No grid exists      2   (*)
   
   Unknown (LBC)      33
   Unknown (HBC)     521
                   -----
                   18695


• (*) ranks 18601 and 18603 have been exhaustively searched (by BandKnit) and no grids found

• the missing ranks are divided into two categories, LBC for those ranks with low minlex band counts, and HBC for high minlex band counts.

Ranks greater than 18312 are LBC. These typically have 0 to 100 minlex bands. HBC ranks are 18312 and below, with band counts typically 100,000 and up.

The LBC missing ranks have all been tested for 1-ply grids, but full treatment with BandKnit is out of the question, for reasons given above. Proving rank 18601 had no grids took nearly 100 core-days.

BandKnit is essentially a permutation cruncher, and it just might be possible to parallelise the computations, so a GPU might be able to make more rank proofs possible. That's just a germ of an idea at this stage ...

[1to9only]

.
We now have software tools for producing canonical forms (minlex) for 16 x 16 Sudoku grids/puzzles in a very efficient manner.

I cannot find a download for this!! Did Mathimagics make this available to the public?
The code is based on holdout's minlex, does it also have the same 'bug'?

[Serg]

Hi, 1to9only!

.
We now have software tools for producing canonical forms (minlex) for 16 x 16 Sudoku grids/puzzles in a very efficient manner.

I cannot find a download for this!! Did Mathimagics make this available to the public?
The code is based on holdout's minlex, does it also have the same 'bug'?

Yes, Mathimagics tried to implement Michael Deverin's algorithm (9 x 9 Sudoku solution grids minlex canonicalization) to 16 x 16 Sudoku solution grids. This algorithm can process full solution grids only, not puzzles, and it works correctly, unlike Michael Deverin's algorithm for Sudoku puzzles canonicalization.

I have no Mathimagics code, but I still have my own code used in this thread for finding minlex forms of 16 x 16 Sudoku solution grids. Performance is at the level 20000 grids/sec (single core of very old notebook).

Serg

[1to9only]

Serg,
Thanks for info.
I have been coding my own minlexers for various sizes of unsolved sudoku puzzles, and I'm getting good enough speed!!
9x9 minlex of 49158 17-clues sudokus take 6792ms = 7237 grids per second.
16x16 minlex of tarek's tough 206 sudokus (posted here) take about 9.7s per grid!