Elimination of Candidates vs Sudoku Rating

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Elimination of Candidates vs Sudoku Rating

Postby AnotherLife » Thu Apr 14, 2022 5:31 pm

It seems obvious to most people that the rating of a puzzle becomes less or does not change if some of the candidates are eliminated because the puzzle becomes closer to its solution where each cell is filled with exactly one candidate. Is it always the case? Does anyone know a concrete puzzle that shows the opposite effect, that is, its rating increases when some candidates disappear (of course, the puzzle remains valid)?
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Re: Elimination of Candidates vs Sudoku Rating

Postby marek stefanik » Thu Apr 14, 2022 7:42 pm

Hi Bogdan,

Depending on the rating function used it might not be the case.

For example, take uniqueness-based techniques. This puzzle posted by mith is 4.5 skfr (solves with a UR and basics).
If one of the cells of the UR had a given in it (say 6r5c9), the UR logic would no longer apply and the rating would jump to 10.8.
Of course, if one of the UR's candidates got eliminated during the solve, making one of its solutions invalid, the UR still couldn't be part of the solution, as its solutions are equivalent.
Rating functions which don't distinguish between givens and solved cells (or simply don't have avoidable rectangle implemented) would still rate it as being very hard.

Marek
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Re: Elimination of Candidates vs Sudoku Rating

Postby AnotherLife » Thu Apr 14, 2022 8:57 pm

Hi Marek,

Thanks for your reply. I asked my question because I didn't know whether this issue had been discussed or not. Actually, I came across a similar UR situation when I was solving the below puzzle on a website.
Code: Select all
..5....62.63..9...........4.....67.3..67.5...1..8.....8.12..6........53..4....8..

It is rated SER/SKFR 4.5, but if you set r9c4=6, the puzzle becomes much harder for a human (I failed to spot the avoidable rectangle), and it is rated SER 7.2 / SKFR 7.1. It seems that these rating systems have not implemented The Avoidable Rectangle technique.
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Re: Elimination of Candidates vs Sudoku Rating

Postby denis_berthier » Fri Apr 15, 2022 8:10 am

.
This has been a well-known problem of the SER for years: problems related to uniqueness have been discussed ad nauseam.
That being said, the non-monotonicity problem appears only rarely in SER - which is not too surprising, as I've shown that rules for uniqueness very rarely change the W-rating (and SER is strongly correlated to W).

Whichever way one defines a rating, monotonicity should be a fundamental criterion of its validity.
Same remarks for stability under isomorphisms.
But a very different, practical criterion for a rating is its wide acceptance. On this point, SER is untouchable.

No rating is perfect.
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Re: Elimination of Candidates vs Sudoku Rating

Postby eleven » Fri Apr 15, 2022 1:49 pm

AnotherLife wrote:... I didn't know whether this issue had been discussed or not.

It was, in 2006, see here.
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Re: Elimination of Candidates vs Sudoku Rating

Postby AnotherLife » Fri Apr 15, 2022 8:12 pm

Ok, it seems that I've reinvented the wheel. Thanks.
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