Help to solve another hardest (WU#303)

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Help to solve another hardest (WU#303)

Postby Cenoman » Mon Jul 09, 2018 9:09 pm

Once again, I need help to start solving this Weekly Unsolvable (#303 from sudokuwiki.org)

Code: Select all
+-----------+
|..9|.4.|.3.|
|...|1..|..4|
|4..|..7|8..|
|-----------|
|92.|.6.|...|
|.5.|...[.6.|
|..6|3..|..2|
|-----------|
|.9.|4..|...|
|..2|.9.|.5.|
|...|..8|7.9|
+-----------+


..9.4..3....1....44....78..92..6.....5.....6...63....2.9.4.......2.9..5......87.9

My toolbox for hardest puzzles is really too empty.
Thanks to helpers !
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Re: Help to solve another hardest (WU#303)

Postby champagne » Tue Jul 10, 2018 7:58 am

short in time to-day for deeper investigations, but nothing easy found by my solver
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Re: Help to solve another hardest (WU#303)

Postby champagne » Tue Jul 17, 2018 11:14 am

still not found time to go deeper, but one remark

If no exotic pattern is found, a puzzle rated 11.1 by serate is a nightmare for a player, and if by chance something comes, it will be a good start to identify a possible new exotic pattern.
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Re: Help to solve another hardest (WU#303)

Postby SpAce » Wed Jul 18, 2018 5:34 pm

If no exotic pattern is found, I'd say guessing becomes a viable strategy as mentioned in the related thread. Right? If nothing else works, should we just call the puzzle unsolvable or what? I don't think so. Since guessing is sort of taboo here, as also mentioned in the other thread, there's little information available about such strategies. I just tried a naive t&e approach with this puzzle, which seems to work very quickly if you have a capable software solver helping to test the paths (I used SudokuWiki). However, since I do my real solving on pure p&p only, that approach wouldn't really work there (theoretically possible, but way too much work). How should one do the guessing when solving without any software help?

Anyway, my software-helped t&e approach here was a simple Ariadne's thread using random conjugate pairs and wishing for a conflict (or a solution), and if none found, then nesting them. I used zero thinking on picking the tested and nested pairs. Can someone show how this could be made smarter, more efficient, and doable on p&p (i.e. requiring simpler logic on the tested paths)?

1. (6|7)r8c4 -> no direct contradictions
1.1. (6)r8c4 & (2|9)r2c8 :
1.1.1. (6)r8c4 & (2)r2c8 -> contradiction
1.1.2. (6)r8c4 & (9)r2c8 -> no direct contradiction
1.1.2.1. (6)r8c4 & (9)r2c8 & (1|2)r3c8 -> contradiction with both 1 & 2 -> -6 r8c4 => 7r8c4

2. (2)r12c1 -> no direct contradictions
2.1. (2)r1c1 & (5|6)r1c6 -> contradiction with both 5 & 6 -> -2 r1c1 => 2r2c1

3. (7|9)r2c8 -> no direct contradictions
3.1. (7)r2c8 & (2)r1c6|7 :
3.1.1. (7)r2c8 & (2)r1c6 -> contradiction
3.1.2. (7)r2c8 & (2)r1c7 -> no direct contradiction
3.1.2.1. (7)r2c8 & (2)r1c7 & (5|6)r1c6 :
3.1.2.1.1. (7)r2c8 & (2)r1c7 & (5)r1c6 -> contradiction
3.1.2.1.2. (7)r2c8 & (2)r1c7 & (6)r1c6 -> SOLUTION => 7r2c8, 2r1c7, 6r1c6

=> => 7r8c4, 2r2c1, 7r2c8, 2r1c7, 6r1c6

Not at all elegant, but at least the solution was found very quickly. (By solution I mean that it was made solvable by the available SudokuWiki strategies, which approximate human capabilities on p&p).

(Btw, a JExocet was used in the test for (6)r1c6 in 2.1.)
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Re: Help to solve another hardest (WU#303)

Postby SpAce » Thu Jul 19, 2018 1:27 am

PS. In my very limited experience with the guessing game I've noticed one recurring tendency. When trying two conjugate options in a difficult puzzle, it almost always turns out that the option that would advance the puzzle more is the false one (unless it's a backdoor). I don't know if that observation has any real statistical backing, but if it does, I guess it might be useful if one were just trying to find a solution as quickly as possible by making a series of probabilistic guesses. Sure, sudoku is not a probability game but who says it couldn't be played like that, too?
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