The New Sudoku Players' Forum

[denis_berthier]

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Resilience of the non-degenerate tridagon pattern

Following the last collection of T&E(2) puzzles published by Paquita:
http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1650.html

I had a few questions about it, because it had an unusually high proportion of puzzles in B6B.
I went back in time and checked his previous two collections:
http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1648.html
http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1644.html
They also have unusually high proportions of puzzles in B6B.

But what I had completely overlooked and what there's in common between the three collections is a very high proportion of puzzles with a non-degenerate tridagon (with guardians): 100%, 99.97% and 97.01% resp.

The result is, my questions in the "hardest" thread about the unusual BpB ratings were misguided by my idea that they could mainly result from the search for high SER.
Indeed, I now think they result mainly from the technique of vicinity search.

Starting from puzzles with a non-degenerate tridagon, "many" nearby ones will also have this non-degenerate pattern. Said otherwise, the non-degenerate tridagon pattern is very resilient to "small" changes of givens (even without counting all the trivial isomorphisms).

(For puzzles in T&E(3), this high resilience may also explain why so many puzzles with a non-degenerate tridagon have been found so fast after the first few ones.)

There remains to explain why the presence of a non-degenerate tridagon AND a high SER favours a high BpB, but at least this is easier to imagine than just a high value of the SER (because this explanation alone would contradict our previous vague correlation results).


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