Long whips SER 9.4, W31

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Re: Long whips SER 9.4, W31

Postby yzfwsf » Tue Dec 08, 2020 1:04 pm

ghfick wrote:Andrew Stuart's solver [sudokuwiki.org] detects the symmetry of givens. He refers to this technique as 'Gurth's Theorem'.
May I suggest that YZF_Sudoku should have this technique added?

Cenoman wrote:Andrew's solver detects this one, but if the puzzle is morphed a bit more (e.g; by circular swap of bands 1,2,3 to 2,3,1), it detects no longer the "symmetry", actually the automorphism, (nor would I have detected it manually). It doesn't detect the "stick symmetry" either (whether morphed or not).
What would be useful in a solver, would be detecting automorphic puzzles, for any automorphism.

As Cenoman said, to support automorphic puzzles, it is necessary to enumerate various isomorphisms of the puzzle, which will take a long time, and I am not sure if it is enumerating the various possible combinations of rows and columns,6^8=1679616 types in total.
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Re: Long whips SER 9.4, W31

Postby denis_berthier » Wed Dec 16, 2020 10:51 am

yzfwsf wrote:
ghfick wrote:Andrew Stuart's solver [sudokuwiki.org] detects the symmetry of givens. He refers to this technique as 'Gurth's Theorem'.
May I suggest that YZF_Sudoku should have this technique added?

Cenoman wrote:Andrew's solver detects this one, but if the puzzle is morphed a bit more (e.g; by circular swap of bands 1,2,3 to 2,3,1), it detects no longer the "symmetry", actually the automorphism, (nor would I have detected it manually). It doesn't detect the "stick symmetry" either (whether morphed or not).
What would be useful in a solver, would be detecting automorphic puzzles, for any automorphism.

As Cenoman said, to support automorphic puzzles, it is necessary to enumerate various isomorphisms of the puzzle, which will take a long time, and I am not sure if it is enumerating the various possible combinations of rows and columns,6^8=1679616 types in total.


And I'm not sure it would be a meaningful technique for a manual solver. If the puzzle's hidden symmetry is too far from being visible, no one will be able to notice it (unless warned in advance, which makes it useless: in this case, why not propose directly the morph of the puzzle that makes the symmetry visible?).
"Too far from being visible" leaves some room for "reasonable" automorphisms.

I don't remember exactly when Mauricio published the original form of the W31 puzzle of this thread, but I reported it in [PBCS1, 2012]. So, it took at least 8 years, some happy random morph I did (with no idea of symmetry in mind) and Cenoman's bright insight to notice the symmetry!
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