Minimal x-sudokus: highest clue count

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Minimal x-sudokus: highest clue count

Postby m_b_metcalf » Sat Nov 28, 2020 11:22 am

IIRC, the highest clue count for a standard minimal sudoku is 40. Has the corresponding count for x-sudokus ever been investigated? On a quick test, I get up to only 23. Is there a searchable data base that contains a higher count?

Regards,

Mike

Code: Select all
 . 1 4 . 9 3 . 5 .
 . . . 6 . 8 . . .
 . . . . 4 5 . . .
 . . . . 8 . 1 6 2
 . 2 . 9 . . 5 . 3
 . . 6 . . . 8 . .
 . . . . . . . 3 .
 3 . . . . 9 . . .
 . 6 . . . . . . .  X-sudoku, 23 clues, minimal
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Re: Minimal x-sudokus: highest clue count

Postby dobrichev » Sat Nov 28, 2020 3:28 pm

Hi Mike,

Do you think that 200 GB zip files with 36+ minimal vanilla puzzles will be useful to you?
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Re: Minimal x-sudokus: highest clue count

Postby m_b_metcalf » Sun Nov 29, 2020 8:20 am

dobrichev wrote:Hi Mike,

Do you think that 200 GB zip files with 36+ minimal vanilla puzzles will be useful to you?

Mladen, Thanks for the offer, but more useful would be some hints on what strategy you used to get those high counts (other than mass production).

Thanks,

Mike

[Edit] Afterthought: could you post, say, 1000? I could check whether any of the solution grids have the X property. (A quick test on the 39s and 40s drew a blank.) Thanks.
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Re: Minimal x-sudokus: highest clue count

Postby m_b_metcalf » Sun Nov 29, 2020 12:23 pm

Code: Select all
 . . . . . . . . .
 . . . . . . . . .
 . . . . . . . . .
 . . . . . . . . .
 . . . . . 1 . 7 4
 . 1 6 . 7 . . 3 2
 . 8 . . 2 9 . 4 3
 4 . 3 . 1 7 9 . 8    X-sudoku, minimal.
 . 9 . . 4 3 2 6 .    24 clues, hard.
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Re: Minimal x-sudokus: highest clue count

Postby dobrichev » Sun Nov 29, 2020 1:50 pm

Hi Mike,

From Sudoku Puzzle Collections you can download 2M 38s as well as some symmetric 36+.

If you send me code to check whether a solution can be morphed to a X-grid, I can apply this filter locally.

In general exhaustive stripping of ~10 redundant clues is a painful process.
With the help of UA sets for vanilla sudoku once I managed to generate few 33s per hour by minimizing a given full solution grid. The code is here although I am not sure this version of the code wasn't broken after some experiment.

For 39s generation I used exhaustive vicinity search by stripping clues until 35 remain, and then, with help of UA sets, adding clues until redundancy or uniqueness, which came first. The code is here.
For several times I did more clues stripping on a small, subjectively determined as "more remote" or "more promising" subset of the puzzles to obtain new seed.
Information on other details of the method, like processes organization and cache data format, is spread in this forum.

Cheers,
M.
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Re: Minimal x-sudokus: highest clue count

Postby m_b_metcalf » Sun Nov 29, 2020 6:39 pm

Mladen,

Many thanks. In the first 1.2M of the 38s, I found 18 puzzles whose solutions are X-grids. I'll work on them tomorrow.

Regards,

Mike

Code: Select all
000000000000012034013405260001704820020080007087021043036107480078046300100008070
000000000001002034002034501004060708056708043807403056018207065060301007700006010
000000000001002034023054001006700000087425016204068075070006003140203067602507040
000000000001002034023054001006700400087025016204068075070006003140203067602507040
000000000001002034023054001006700400087425016200068075070006003140203067602507040
000000000001002034025036701002080000084025170153047802008004000046008310510063408
000000000001002034025036701002080040084025170153047802008004000046008310510063008
000000000001002034034150206007006805040208067086570342018020073070800400403700008
000000000001002034035064120000040070047005381053071040014007860076008003508036017
000000000001002034350461027006108052510240068800050000030004086060803200180620073
000000000001002034350461027006108052510240068800056000030004086060803200180020073
000000000001002034350461027006108052510240086800050000030004068060803200180620073
000000000001002034350461027006108052510240086800056000030004068060803200180020073
000000000001023045024051036007005000045130087310087054008302070072018063100070008
000000000001023045024500061007300026030005170610200053040000007076802014180704632
000000000001023045024506301000307800008050070047068153002030008080600507106085432
000000000001023045024510036007005010010060073408070650042057361076032094100000007
000000000001023045462070031027080504540207086608050000030700008076038400804062003
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25 clues

Postby m_b_metcalf » Sun Nov 29, 2020 8:16 pm

I couldn't wait:
Code: Select all
 . . . . . . . . .
 . . . . 1 2 . . 4
 . 1 3 4 . 5 . 6 .
 . . 1 . . . . . .
 . . . . . . . . 7
 . 8 7 . . . . 4 3
 . 3 . 1 . 7 4 8 .    Thanks to Mladen for his 38-clue standard puzzles!
 . 7 8 . 4 . . . .
 1 . . . . 8 . 7 .    X-sudoku, minimal, 25 clues, SE 9.0.
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Re: Minimal x-sudokus: highest clue count

Postby coloin » Sun Nov 29, 2020 8:37 pm

Excellent ..... it gets progressively more and more difficult to go up a max number of clues level ....
Removing clues from those 38C puzzles saved you a lot of time ...... hopefully a 26 will be found too ...
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Re: Minimal x-sudokus: highest clue count

Postby m_b_metcalf » Mon Nov 30, 2020 10:58 am

coloin wrote:Excellent ..... it gets progressively more and more difficult to go up a max number of clues level ....
Removing clues from those 38C puzzles saved you a lot of time ...... hopefully a 26 will be found too ...

No sooner said than done:
Code: Select all
 . . . . . . . . .
 . . . . 1 2 . 3 .
 . 1 . 4 . 5 2 . .
 . . 1 7 . 4 . 2 .
 . 2 . . . . . . 7
 . 8 . . . 1 . 4 .
 . 3 6 1 . 7 . 8 .
 . . 8 . 4 . . . .   X-sudoku, minimal, 26 clues.
 1 . . . . 8 . 7 .
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Re: Minimal x-sudokus: highest clue count

Postby m_b_metcalf » Mon Nov 30, 2020 4:29 pm

I ran a longer test retaining all 24+C puzzles. A 26C occurs about once per 200. Here's a sample, all hard for some reason:
Code: Select all
.............12.3..1.4.52....16.4.2..2......6.7...1.4..381.6.7...7.4....1....7.6.   ED=9.0/1.2/1.2   All 26-clue x-sudokus
.............1.....123.456...1..3.............78.5...2.2.1.837..87.362..1....7.8.   ED=9.0/1.5/1.5   
.............12.34.134.5.6...1....2..2......7.87..1.4..3.1.7.8..78......1....8.7.   ED=9.1/1.5/1.5   
.............12.3..1.4.52....1..462.........7.6..21.4..381.7.6..76.48........6...   ED=9.2/2.9/2.9   
.............1..23..23.456...17.3.5...........8...1....261.738...8..62..1....8.7.   ED=9.4/1.2/1.2   
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Re: Minimal x-sudokus: highest clue count

Postby m_b_metcalf » Mon Nov 30, 2020 6:43 pm

A longer run failed to turn up a 27C, but extended the narrow rating range of the 26Cs:
Code: Select all
.............12.34.1...526...17...2...........8..21.4..361.7.8..78.4....1....8.7.   ED=8.5/1.5/1.5   
.............12.3...34.526...1..4.2..2........78..1....361.847..8..4....1....7.8.   ED=8.9/1.2/1.2   
...........1..2....2..34..1..2.5......6..7...173.685.2..5..6....6.....1.71..43..5   ED=8.9/1.5/1.5   

.............1..23.12..4.5...16...7...........8..71.3..2.1.638..68.35...1....8.6.   ED=9.3/1.5/1.5   
.............12.34.134.5.....16.472..2........76.21.4..381.6.7..6............7...   ED=9.4/2.9/2.9   


THE END
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Re: Minimal x-sudokus: highest clue count

Postby coloin » Mon Nov 30, 2020 7:48 pm

m_b_metcalf wrote:THE END

awww ... the more 26C you find the more likely there will be a 27C wiithin {-1+2} ..... unless there just isnt one....
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Re: Minimal x-sudokus: highest clue count

Postby m_b_metcalf » Tue Dec 01, 2020 10:05 am

coloin wrote:
m_b_metcalf wrote:THE END

awww ... the more 26C you find the more likely there will be a 27C wiithin {-1+2} ..... unless there just isnt one....

Gasp ...
Code: Select all
 . . . . . . . . .
 . . . . 1 2 . 3 .
 . 1 . 4 . 5 2 . .
 . . 1 . . 4 . 2 .
 . 2 . . 6 . . . .
 . 6 7 . . 1 . 4 .
 . 3 8 1 . 7 4 6 .   X-sudoku, minimal, 27 clues
 . 7 . . 4 . . . .
 1 . . . . 6 . 7 .   ED=9.0/1.2/1.2
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Re: Minimal x-sudokus: highest clue count

Postby m_b_metcalf » Tue Dec 01, 2020 6:08 pm

Postscript: For human solvers, this puzzle becomes tractable when 5r1c8 is added.
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Re: Minimal x-sudokus: highest clue count

Postby coloin » Wed Dec 02, 2020 11:16 pm

m_b_metcalf wrote:Gasp ...
Code: Select all
 . . . . . . . . .
 . . . . 1 2 . 3 .
 . 1 . 4 . 5 2 . .
 . . 1 . . 4 . 2 .
 . 2 . . 6 . . . .
 . 6 7 . . 1 . 4 .
 . 3 8 1 . 7 4 6 .   X-sudoku, minimal, 27 clues
 . 7 . . 4 . . . .
 1 . . . . 6 . 7 .   ED=9.0/1.2/1.2


Yes ! Well done ... very satisfying ...
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