The hardest sudokus (new thread)

Everything about Sudoku that doesn't fit in one of the other sections

Re: The hardest sudokus (new thread)

Postby Paquita » Mon Jun 17, 2024 2:39 pm

Hi coloin,
Thank you, it works :)
Paquita
 
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Re: The hardest sudokus (new thread)

Postby hendrik_monard » Tue Jun 18, 2024 3:23 pm

Paquita wrote:(And Hendrik, you replied that the first was by mith (that is correct) and that the second and third are the same and by mith; they are not the same, different last 2 digits; I can't find those in miths collection, can you point out what they are, if duplicates?)

Hi Paquita,
I discovered your post today. The second and third puzzles were in fact posted by mith on January 16th 2022
see http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-975.html#p315542
last two in the batch
........1....23.....45...6...7...85..48....7.9.......2.8.6..7..3...91...4..7.....
........1....23.....45...6...7...85..48....7.9.......2.8.6..7..3...19...4..7.....
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Re: The hardest sudokus (new thread)

Postby Paquita » Wed Jun 19, 2024 4:50 pm

Hendrik,

You are right, those are the two. It seems that I still do not have all the puzzles provided by you and mith since ph2010. I did try to collect them by scraping this forum but turns out it is incomplete. As a result I may post puzzles as mine that were found before.
I would be very happy with an update of the database so I can do a full check.
Paquita
 
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Re: The hardest sudokus (new thread)

Postby Paquita » Sat Jun 22, 2024 5:34 pm

I have been collecting new NOT tridagon puzzles - at least I think they are new - can't be sure because I seem to be missing some of mith and hendriks files.
I did this because I was wondering if the tridagon puzzles are indeed the majority of existing puzzles, or was this a turn the investigations took by accident.


https://drive.google.com/file/d/1fSwyiC7L2WjwYkqOVUR0uMQz5q7Sbi6r/view?usp=sharing
These are the high rated ones

Code: Select all
98.76.5..7.5..8....46.59...89.....7.....4.3..........2.7.6.4.5....89.........5.6. ED=11.8/1.2/1.2
98.76.5..7.5.......46.59...89.....7.....8...3....4.2...7.6.4.5....89.........5.6. ED=11.8/1.2/1.2
98.76.5..7.5..9....46.58...89.....7.....4.3..........2.7.6.4.5....98.........5.6. ED=11.8/1.2/1.2
98.76.5..7.5.......46.58...89.....7.....9...3....4.2...7.6.4.5....98.........5.6. ED=11.8/1.2/1.2
9876........59.........4...83........927.68....6....2..7..3.9.8.2.....73......26. ED=11.8/1.2/1.2
987.........96.8.......5...84........93.72.8...2...3...7.4...98.3.2..7.4......23. ED=11.8/1.2/1.2
98.76....7.54......46..98..6......32.7............5.8..9.58..4....9.6.......47..8 ED=11.8/1.2/1.2
98.76.5..7.5....6...4......6..98....5.84.7....7..56..4.9..........8...39....9..2. ED=11.8/1.2/1.2
98.76.5..7.5.48....46..9....6.....3...4...62............74.6..8...95........87.9. ED=11.8/1.2/1.2
98.76.5..7.5.48....46..9....974.6.8.....87..9....5.....6......3..4...6.2......... ED=11.8/1.2/1.2
98.76.5..7.4.5..6..........6.794....5...87.....86.5.....9.....8....9432......64.. ED=11.8/1.2/1.2
98.76.5..7.4.5..6..........6.794....5...8......86.5.....9.....8....764.......432. ED=11.8/1.2/1.2
9876.........958.......4...8.32..69.2..3..7...76......7.9...26.32..6..87.6....3.. ED=11.8/1.2/1.2
9876.........958.......4...8.32..69.2..3.67...76......7.9...26.32.....87.6....3.. ED=11.8/1.2/1.2
9876.........958.......4...7.9...36..6....2...32....8767.......2.83..69...32.67.. ED=11.8/1.2/1.2
9876.........958.......4...7.9...36..6....2...32.6..8767.......2.83..69...32..7.. ED=11.8/1.2/1.2
9876.........958.......4...83.2..69.2..3..7....6......79....26.3.2.6..87.68...3.. ED=11.8/1.2/1.2
9876.........958.......4...83.2..69.2..3.67....6......79....26.3.2....87.68...3.. ED=11.8/1.2/1.2
9876.........958.......4...8.32..69.2..3..7.8.76......7.9...26.32..6...7.68...3.. ED=11.8/1.2/1.2
9876.........958.......4...83.2..69.2..3..7.8..6......79....26.3.2.6...7.68...3.. ED=11.8/1.2/1.2
98765.......4..........3...8..7..2...9....67..6.2...586...2.89.2...6.5.7.5....... ED=11.8/1.2/1.2
98765.......4..........3...8.62..75.7..8....2..9.....66...2..972...6.8.5..5...... ED=11.8/1.2/1.2
98765.......4..........3...8.6.2.97.2...6..58..5......7..8...2.6..2..5.7..9....6. ED=11.8/1.2/1.2
98765.......4..........3...8..7..2...9....67..6.2...586...2.5.72...6.89..5....... ED=11.8/1.2/1.2
98765.......4..........3...8.62..75.7..8....2..9.....66...2.8.52...6..97..5...... ED=11.8/1.2/1.2
987.........65.............8.493.2..27........932...8472...38.93....247..4......3 ED=11.8/1.2/1.2
987.........65.............8.493.2..72........932...843....247.2....38.9.4......3 ED=11.8/1.2/1.2
987.........65.............8.493.2..72........932...84.4.....23.....347......28.9 ED=11.8/1.2/1.2
987.........65.............8.493.2..72........932...842....347..4......3.....28.9 ED=11.8/1.2/1.2
9876.........958.......4...86....3...23....87..9...26.67.......3.82..69...23.67.. ED=11.8/1.2/1.2
9876.........958.......4...86....3...23.6..87..9...26.67.......3.82..69...23..7.. ED=11.8/1.2/1.2
98.76.5..7.5..8....64..9....4.....3...6...42....4.......76.4..8...95........87.9. ED=11.8/1.2/1.2
98.76.5..7.5.48....64..9....4.....3...6...42............76.4..8...95........87.9. ED=11.8/1.2/1.2
98.76.5..7.5..8....64..9....976.4.8.....87..9....5.....4......3..6...4.2...4..... ED=11.8/1.2/1.2
98.76.5..7.5.48....64..9....976.4.8.....87..9....5.....4......3..6...4.2......... ED=11.8/1.2/1.2
9876.........958.......4...8.32..69.2..3.67.8.76......7.9...26.32......7.68...3.. ED=11.8/1.2/1.2
9876.........958.......4...86....3...23....7...9...2.667.......3.82..6.9..23.678. ED=11.8/1.2/1.2
9876.........958.......4...86....3...23.6..7...9...2.667.......3.82..6.9..23..78. ED=11.8/1.2/1.2
9876.........958.......4...83.2..69.2..3.67.8..6......79....26.3.2.....7.68...3.. ED=11.8/1.2/1.2
9876.........958.......4...76....3...32....87..9...26.67.......2.83..69...32.67.. ED=11.8/1.2/1.2
9876.........958.......4...76....3...32.6..87..9...26.67.......2.83..69...32..7.. ED=11.8/1.2/1.2
9876.........958.......4...8.9...36..6....2...23....8767.......3.82..69...23.67.. ED=11.8/1.2/1.2
9876.........958.......4...8.9...36..6....2...23.6..8767.......3.82..69...23..7.. ED=11.8/1.2/1.2
9876.........958.......4...67....3...32....87..9...26.2.83..69..6.........32.67.. ED=11.8/1.2/1.2
9876.........958.......4...67....3...32.6..87..9...26.2.83..69..6.........32..7.. ED=11.8/1.2/1.2
98.76.5..7.5..9.6...4..8...6..9.....5..4.7.8..78.56..4.9..........8...39.......2. ED=11.8/1.2/1.2
98.76.5..5.7.48......5.9...6.5......49.....8..78..6.9..64....5......74.3........2 ED=11.8/1.2/1.2
98.76.5..7.45......56.948..8.5......64........79.8..6.4......5....97.4.........32 ED=11.8/1.2/1.2
98.76.5..7.4..96....58.4...6..94..7....5.6.......87...4.9...8.......8.5........32 ED=11.8/1.2/1.2
98.76.5..7.45......56.948..8.56......79.8..6..4.......4......5....97.4.........32 ED=11.8/1.2/1.2
98.76.5..7.5.......64..89...4.....3...6....2....4.......76.4..8...95........87.9. ED=11.8/1.2/1.2
98.76.5..7.5..9....64..89...976.4.8.....87..9....5.....4......3..6.....2...4..... ED=11.8/1.2/1.2
98.76.5..7.64.5.....4.896..8......324.7...8.........9.5...74.69...6.8.......9.... ED=11.8/1.2/1.2
98.76.5..7.64.5.....4.896..5...74.96...6.8.......9....4.7...8.....8....9.......32 ED=11.8/1.2/1.2
98.76.5..7.........46....7.6.9..5..447...6.8..58...96....32.4......7.........489. ED=11.8/1.2/1.2
98.76.5..7.........46....7.6.9..5..447...6.8..58...96...4.7.......32.........489. ED=11.8/1.2/1.2
9876.........958.......4...83.2...9.2..3..7....6......79....36.3.2.6..8..68...2.9 ED=11.8/1.2/1.2
98.76.5..5.7..98...465......7..85.....94.6......97..5..6....43...4....2......4... ED=11.8/1.2/1.2
98.76.5..7.5.489...46..9....7.4.6.....895........87.9..6.....3...4...62.......... ED=11.8/1.2/1.2
98.76.5..5.7.4..9..4.......67..94....5.8.7.....4.5...9.68...9.......632.......... ED=11.8/1.2/1.2
98.76.5..5.7.4..9..4.......67..94....598.7.....4.5.....68...9.......632.......... ED=11.8/1.2/1.2
9876.........958.......4...83.2...9.2..3.67....6......79....36.3.2....8..68...2.9 ED=11.8/1.2/1.2
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Re: The hardest sudokus (new thread)

Postby Paquita » Sat Jun 22, 2024 9:12 pm

It seems my attempt, as described before, failed.
Interesting in itself. I started with non-tridagon seed, and what I get is the above.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Sun Jun 23, 2024 3:55 am

Hi Paquita
Paquita wrote:I have been collecting new NOT tridagon puzzles - at least I think they are new - can't be sure because I seem to be missing some of mith and hendriks files.
I did this because I was wondering if the tridagon puzzles are indeed the majority of existing puzzles, or was this a turn the investigations took by accident.


Puzzles with a (non-degenerate) tridagin are definitely not the majority. There's none in the controlled-bias collection. As for the degenerate-cyclic case, there a a few (0.28%) but they have many guardians and are very far from a usable tridagon.

What happens is, when you already have a few tridagons in a collection and you apply divinity search, the probability is very high that the tridagon remains.

I quickly checked your new collection. They have a very large proportion of tridagons (18363 in 18439) and almost all have a degenerate-cyclic tridagon (18397 in 18439). Now the question is, what were your seeds? Did you say they didn't have a tridagon. You must have been mistaken. It's statistically impossible.
.
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Re: The hardest sudokus (new thread)

Postby Paquita » Sun Jun 23, 2024 10:03 am

Hi Denis

Yes my seeds were non tridagons. What I did was expand and then reduce to minimals. This created tridagons, as I see now when rechecking my moves. And after that, I used those as seed as well - I assumed all my puzzles were still non tridagons. And the tridagons result in much more new puzzles. Beside expansion I used a simple algorithm that replaces 1 digit or swaps 2 digits.
It is simply much harder to find new non-tridagons than tridagons. I think this raises the question if there really are more non-tridagon puzzles.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Sun Jun 23, 2024 1:49 pm

Paquita wrote:Yes my seeds were non tridagons. What I did was expand and then reduce to minimals. This created tridagons,

Could you post of few of the seeds that gave tridagons? And where they come from. The only possibility I see is if they were generated from tridagons by the same process and your search somehow reversed it.
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Re: The hardest sudokus (new thread)

Postby Paquita » Sun Jun 23, 2024 2:28 pm

Hi Denis

These were the seeds
Code: Select all
98.76....7.....9...54......6...3.8....5....2......4.1..7.38.......9..3.......1..2
98.7.....7..86......5..4...3..6..9....2.............51.7..8.3.......67.......1.42
98.76....75....9....6.......4.....3...8.5.7.....2....1..9.7.6.....3....2.....1.4.
98.7..6..5...9..4...3.....94...5...2.1...8.....5....3...2.4..9....1.6.........7..
98.7..6....5.9..4......8...8....79...4.....5...93....21.........6...91....8.2...3
98.76....75....9....6......8...4..3..2......1..95..8....86..5......1...4.....3.2.
98.7..6....5.9..4......3..93...7...2.4.2........3.1...2....7..1.6....5....4....8.
98.7.....6.....7....7....5.4......3...86..9......2...1..59..6......1...4.....3.2.
98.7..6....5.4.......9...8.79......3.3....8.7..2....1.3..6....8....5.........1.4.
98.7.....7..86......5..4...3..6..9....2.............51.7..8.3.......67.......1.24
98.7..6..5..........4.3....7..8...9.....23...........1.9.5...7..6....85......4..2
98.7.....7.....6....5.4....6..3..8...9.........4.2..1..3.9..7......7...5.....1..2
98.7.....6...5.8....4....3.5.....9.......2..1.......24.9.6..7....1..3......98....
98.7..6..5..........4.3..2.85...7......5.67......1...4.6...98.........1.........2
98.........76..5......4....4...3..9...2..6..7...1..2...3.....8...65....2.....71..
98.7..6..7..........5.4....83...9....9...68....2....1....9.73......1...5........2
98.7..6..7..........5.4....89...6....3...98....2....1....9.73......1...5........2
98.7..6..7..........5.4....89...6....3...89....2....1....8.73......1...5........2
98.7.....76..9.........5...8.....5...7.....8...4..3..2...92..6.....5.1.4.....12..
98.7.....7.....9....6.95...43........9.8..3....2....1....47.8.......2.6......1..2
98.7.....6...5.8....4....3..6.9.......2..4..1....8.7...5..9.6....6..1..3.......2.
98.7.....6...8.5....4..3...7..6..8......2..3.........4.9.5..6....1.7...2.....2.1.
98.7.....6...5.9....4....3.7..6..8....2.....4.....2.1..9...1..3...96.5......8....
98.7.....76..9......5..4...8.....4...9.....8...3..2..1...4..5.3....7..6......31..
98.7.....76..9......5..4...8.....5...7.....8...3..2..4...9...6.....5.1.3.....14..
98.7.....6...5.9....4....3.7..6..8....2.....4.....2.1....98........6.59......1..3
98.7..6..75..9......4..8...5...7.8.....3...42.....1....9..6.5.......2..3.......1.
98.7.....76..9.........5...8...5.4...9.....8...4..3..2...4..2.1....7..6......13..
98.7.....76..9.........5...8.....5...7..4..8...4..3..2...9...6.....5.1.3.....12..
98.7.....76..9.........5...8.....43..7....8....3..2..5...9..6......3..14.....1.5.
98.76......5..43.........9.5.4..2....7..1.......6.....4.....93.2....95.....1....6
98.7.....7..68......5..4...8...6.3.......2.5.........4.9..3.7....82..9....1....42
98.7..6..7......8...5.4...38..2...9..6....7.......4..1.9.6..2......5.........3...
98.7.....7.6..........5....8.....7...4...3.5.....2..41.3...1.2...89..6..........4
98.76....7..8..9....5..4...6...7.8...3............2.4..9..3.7....1.............25
98.7..6....5.4..3....9.....8.....9.226....7....1....4..2.6....7....13............
98.7.....7...9.6....5..4....9.6..3....2....1.........4.3.8..7......71.......3..52
98.7.....6...9.5....5....9.5...4.3...7...2..1..6....4...3.6.4.....1..........8..2
98.7.....7..........6.5....4..9..3...9....74......2..1.4.3..8....2..1.3.....6...5
98.7..6..76..9......5......4....3.2..3.........8.7.5....6.5.8.....1...4......2..1
98.7..6..5.4.6.........9...3....69....6....42....1.....7...83....5.....1....2..5.
98.7.....6...5......4..93..7......6..5.86......6..21....9....32....4.9.......3.1.
98.76....7..5..8....4.3....27....9...9.........1....62...2..5.8....4..3......3.1.
98.76....5.....9....4....8.3..5..6...4......2..8.....1...93.7.....6.1........2.19
98.7..6..75.....9...6......4.....3...2..4......96...5..9...32.1..85...6.....1.5..
98.76.5..7....4.....4.35...82........7....28...6.....1....1...5.....3..6......92.
98.76.5..7....4.....4.35...27.....9..9....2....6.....1....1...5.....3..6......82.
98.7.....7..86......5..4...83....6....26...4........2..9..7.3.......69.......1.54
98.7.....7..86......5..48...9..7..3...2.....5......4...3.6...8......7.6......15.2
98.76....5....8....4...38..7......2..15.....4..4...1.8...9.........2..6......53.1
98.76.5..7..........5.43....9.....8..7....29...6.....5...5..82.....3...1.....6..4
98.76....7....5.....5.43...87....2...2.....8...4.....6....3..61.....6..5......92.
98.7..6..7..........6.54....9.3...8..7....29...3.....6...6..82.....4...1.....3..5
98.76.5..7............43...82.....5..7....28...6.....1..8..4..3...5..92.....1....
98.7.....6...8......5..4...3..8..9...7....86.....4...2.9.6..3....1.5.........2..1
98.76.5..7............43...59.....8..7....29...6.........5..82.....3...1.....6..4
98.76....75....9....4......6..5..8.......3.2.........45...8......1..2......95.7.1
98.7.....7..96......5..4...8...7.3....9...8....2....51...39.6.......1..........14
98.7.....7..96......5..4...8...9.3....7...8....2....51...37.6.......1..........14
98.76....75....9....4......6...8.5.......3.2.........45..8.......1..2......59.7.1
98.76....75....9....4......8..5.......3..2......89.73.6...8.5.......1..2.......4.
98.7.....7...8......6..5...8.........54..3.....3...54..6.2....9....7...2.....165.
98.76....75....9....4......6...8.5.......3.2.........45..8.......1..2......95.7.1
98.7.....7..86......5..4...8.........53...2....4....3..2.6....9....7...6.....251.
98.7.....7...8......6..5....64...3....2...46.........9.5...3.4....8....1.....253.
98.7.....6..85......4..3....9..8.6....2.............32.5.6..7.......85.......1.24
98.7..6..5...8..4...4..3...85..9.....7..6.5....2.........97.8.......1..........12
98.7.....7.....6....5.4....6..8..3...7..6......4..2....3.9..7......1..2......5.1.
98.7..6..7......5...4.3...75..2..9...6.....8...7..3.....23....1....41.........5..
98.7..6..7...6......5.43....9.....2..7....9....6.3...4.....6..5.....4..1......28.
98.76....7.....9...54......6...3.8....5....2......1.4..7.38.......9..3.......2..4
98.76....7.....9...54......6...3.8....5....2......4..1.7.38.......9..3.......1..2
98.76.5..7....4.....6.35...27.....9..9....2....4.....1....1...6.....3..5......82.
98.76.5..7....4.....6.35...29........7....29...4.....1....1...5.....3..6......82.
98.76.5..7....4.....6.35...27.....9..9....2....4.....1....1...5.....3..6......82.
98.76.5..7....4.....4.35...87....2...2.....8...6.....1....1...5.....3..6......92.
98.76.5..7....4.....4.35...29........7....29...6.....1....1...5.....3..6......82.
98.7.....6..9..5....4.3....59....7....2....1.........4.7.8..6......9........1..23
98.7.....6..9..5....4.3....56....7....2....1.........4.7.8..9......9........1..32
98.7.....6...9.5....4..3...7..9..6....3..2.1.....7.....5.8..9......19..2........4
98.7.....6...9.5....4..3...7..9..6....3..2.1.....7.....5.8..9....9.....4....1...2
98.7..6..5..........4.3..2.8..6.7....5...97......4...1.9.8..5.........1.........2
98.7.....7.....8....6....7547........9.4..3....2.1......9..2..6...3..98.....6...1
98.7.....6..98......5..48...9..7..3......2..5......4...6..3..8...9....6...1...5.2
98.7.....7..86......5..4...3..6..9....2.............54.7..8.3.......67.......1.42
98.76....7...8......5..48...9..7..3...2.....5......4...3.6...8......7.6......15.2
98.7..6..7..69.....5...8...4.....93..2....4.5..5.....1...47.3......3.........1..2
98.7.......6.5.........4...8.....3...7.9...2...4..6..17......8..2.3..9......1...5
98.7.....7..68......5..47..8...6..3......2..4......5...9.3...7...8....9...1...4.2
98.7..6..7..96.....5...8...4.....93..2....4.5..5.....1...47.3......3.........1..2
98.7..6..7..96.....5...8...4.....73..2....4.5..5.....1...49.3......3.........1..2
98.76....7..9..8....6.5....84........7....4....3....2....1..9.4....2.15......5.3.
98.76....7..9..8....6.5....84........9....4....3....2....1..7.4....2.15......5.3.
98.76....7..5..8....6.4....83........7....3....2....1....9..5.3....1.94......4.2.
98.76....7..5..8....6.4....53........7....3....2....1....9..5.3....1.94......4.2.
98.76....7...8......5..48...9..7..3...4.....2......5...3.6...8......7.6......12.4
98.7.....7.....8....6....7549....3...7.4.......2.1......9..6..2...3..98.....2...1
98.76....7..9..8....6.5....43........7....3....2....1....8..4.3....1.95......5.2.
98.76....7..9..8....6.5....43........9....3....2....1....8..4.3....1.75......5.2.
98.76....7.6.......5...8...6.........48...3...3...4.2...51....9....7...1.....528.
98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.
98.7.....6.....87...7.....5.4..3.5....65...9......2..1..86...5.....1.3.......4..2
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98.7.....6.....8....5....7..4..3......89..5.......2..1..65..9......1..3......4..2
98.7.....6.....7....7.5.....4...5.3...68..5......2...1..95..8......1..4......3..2
98.76....5..........7..59..4....78.....3...2.....1...6.5...97....4.7...1...2...3.
98.7..6..7.....9....5....4.6...9.....3.86.......4.2....7..3.8....1....2......4..5
98.7..6.....9...7.....65...7.......443.....9...2...1...4.3...8...1.2.........65..
98.7.....6.....7....7.5.....6...4.3..2......1..95..8....68..5......1...4.....3.2.
987......65.........49..7..7..6..5......4..3......2..1.9.5..8......1..4......3..2
98.7.....7.....9....6.5.....4..3..2...74..8.......1..4..86..5......4..1......2..3
98.7.....6.....9....7....5..4..3...5..95..6.......2.1...86..5......1...3.....4.2.
98.76....54.........7..59..4....75.....3...2.....1...6.9...87....4....1....2....3
98.76....75....8....6.......4.....3...8.5.7.....2....1..9.7.6.....3....2.....1.4.
98.7.....6...5......4..93..5......6..7..8......9..24....1.....4....9.1.......1.32
987......65.........47..6..8..5..7......4..3......2..1.9.6..5......3..4......1..2
98.7.....7.6...8....5......8..6..4......5..3......2..1.7.4..9......1..2......3..5
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98.7.....7.6...8...5.......4..9..6......5..3......2..1..78..4......1..5......3..2
98.7.....6...5......4..93..5..8......7..9..6...9..42....1....3....9..1.......1.42
98.7.....7...6.9....5....4..9.3..8....2.....1.....4.5..3..7.6.....8...7......1..2
98.7.....6.....7....7.8..5.4....3..2..84..9......1..4...65..8......4..3......2..1
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98.7.....7.6...8....5......4..6..9......3..5......2..1.9.4..7......1..3......5..2
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98.7.....6...5......7..98..7....64....43...2.........1.7...46.....1....5....2..3.
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98.7.....6.....9....7....85.4..3......86..7.......2.1...95..8......4...2.....1.3.
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98.7.....6...9.5....4..3...5..9..7......8..3......2..1.7.6..8....1....4.........2
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98.7.....7.6...8....5......4..8..9......3..5......2..1.9.6..4......5...2.....1.3.
98.7.....6.....5....4......7..8..9......3..4......2..1.5.9..6......4..3......1..2
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98.76....75....9....6......8...4..3..2......1..95..8....86..5......3...4.....1.2.
98.7.....7.....9....6.95...47........3.4..7....2....1....84.3.......6..1.....2..6
98.7.....76..8......5......8..9..4....3....2......1..5...46.7......9.6.2.....2.34
98.........76..5......7..4.3....9....2......8..15...6...4.1.6.....7...1......2..3
98.7..6..7......5...4.3...75..2...8..6....9....7..3.....23....1....14.........5..
98.7.....6..89......5..4...7...3.9....6...7....2....51.6..8.3.......1.4.........2
98.7..6....5.6..7......4...4.....9...3.........6....25..1.7...6....5..17.....83..
98.7.....6..89......5..4...7...3.9....6...7....2....41.6..8.3.......1..5.......2.
98.7.....6..89......5..4...7...3.9....6...7....2....51.6..8.3.......1..4.......2.
98.7.....6..85......4..3...7...6.5....9...7....2....41.9..8.6.......1..3.......2.
98.7.....6..85......4..3...7...6.5....9...7....2....41.9..8.6.......1.3.........2
98.76....7.....9...54......6..3..2...4.....5...8..1......63.7......9...3.....8.1.
98.7.....6.....7....7....85.4..3......86..5.......2.1...68..9......1..2......4..3
98.7.....7.....6....5.4..7.5...9..8...4..32..........1.5..8..4....2....6.....13..
98.7.......6.5.4.........9.3..9..2...7..8...9..9..5.4.2..5....3..1.6..5......1...
98.7.......7.6.........57..4...3..2..1...6..3...9..8..2......4..3......1..86..5..
98.7.....6..8..9....5.4....73....6....2....1.........5.6.3..8......1...6.....8.24
98.7.....76....9....5.9.....4.....3...68..7.......2..1..76..5......3...2.....1.4.
98.7.....6..9..5....4.3....75....6....2....1.........3.6.8..7......1...2.....9.4.
98.7.....6...9.8....5....4..7.6..3......8.........2..1.6..3.9....1.....2.....4.5.
98.7.....6.....9....5....7.4...3......75..6.......2.1...96..8......1...2.....4.3.
98.7.....6.....7....7.5.....9...4.3...85..6......2...1.2...1.4...9..58......3...2
98.7..6....5.4.......9...8.73......6.9....3.8..2....1.3..6..8......2.........1.4.
9..8..7...8..6..5...4.....33..2....4.2...6.8...7.......1.6...2...9..1..8....5....
98.7.....6...5......4..93..7......2...1..2..3......41..5.6.......9..1.3.....8...9
98.7.....6.....7....7.5.....4...3.2...89.........4...1..98..6......1...4.....2.3.
98.7.....6..85......4..3...7..6..5....9...6....2....41.9..8.7.......1.2.........3
9..8..7...8..6......5....4.6...9.....3.7..9.......2..5.9..3.8....4.....1.....1.2.
98.7..6....5.4...........9.8..9...6..4..5...9..9..32..1.........7.1...8...8..2..3
9..8..7...8..6......5..4...8...3.9....4....2.........13..6......7..9.6....2..1..5
98.7.....6...5.8....4....3.7..9..5....3....4......2..1.6...1..2..9.........89.6..
98.7.....76....9....5.9.....4..5..3...78..5.......2..1..65..8......3...4.....1.2.
98.7.....7...6......5..87..5....69....43...6.....2...1.5...48.....6....3....1..2.
98.7.....6.....9....5....7..4..3..2...85..4.......4..1..69..5......2...3.....1.4.
98.7.....76....9....5......4...6..3...75..6.......2..1..86..5......1...2.....3.4.
98.7..6..5...9..4...3..6..94.......3.2.6..8....8....5..7..81......2.........671..
98.7.....7.6...8...5.......4..8..9......5..3......2..1..74..6......1..5......3..2
98.7..6..5...4......3..9.2.4...8.....7.........6..3..2..9..12.....5...39........1
98.7.....6.7...8...5.......4..6..9......5..3......2..1..94..7......3..5......1..2
98.7.....7.6...8....5......8..4..6......5..3......2..1.7.6..9......1..2......3..5
98.7.....7.6...8...5.......4..8..6......5..3......2..1..76..9......3...5.....1.2.
98.7.....7.....6...65......6..4..7......5..3......2..1.7.8..9......1..2......3..5
98.7.....6.....97...7.....54...3...9..86...5......21....68...9.....1.2.......4..3
98.7.....7.6...5....4......5..6..7......4..3......2..1.7.8..9......1..2......3..4
98.7.....6.....7....7.5..8..4..3...2..6...5.......1.4...89..6......4..1......2..3
98.7.....6.....7....7.5....5....4.3...89..5......2..1..3.....4...98..6......1...2
98.7.....6.7...8...5.......4..6..7......5..3......2..1..68..9......3..5......1..2
98.7.....6...5.8....4....3..9..8.7....2..1..4..........5..9.6.......5.13.....2...
98.7.....6...5.9....5....6.5...4..3..7...2..1..6...4....3.9..4....8..........1..2
98.7..6..7...8.....54..6...6...3.9....5....2......1..5.3..6.7.......2.1.........4
98.7.....7.6...9......5.....4.....3...78..5......2...1..85..6......1..2......3..4
98.7.......7.6.9.......9...8......5..4..3...2..16..7..5.......4.2..1..8...8..63..
98.7.....6.....9....7....5.4...3...2..64..5.......1.4...98..6......4...1.....2.3.
98.76....5.7..49....3....7.2....94....68........43....1.......9...2..1.......1.45
98.7.....76..5......4..87..6....98.....3...2.........1.4...76.....2...57....1...3
98.7..6..7.....9....5....4.67.9......9....3....2.1...9...3..8.6....5.........2.1.
98.7..6....5.4.......9...8.79......3.3....8.7..2....1.3..6....8....2..4......1...
98.7.....6...5.8....4....3..7.6..9.......4..2.......1..6.8..5....1..2..3....6....
98.7..6..7.........54.3....8.....92..1.........5.....1...2.8.6.....5...4.....627.
98.7..6....5.4.......9...8.73......9.9....8.3..2....1.3..6....8....2.........1.4.
98.7..6....5.4.......9...8.79......3.3....8.9..2....1.3..6....8....2.........1.4.
98.7..6..7.....8....5....4.87.6......6....3....2.1...6...3..9.8....5.........2.1.
98.7..6..7.....9....5....4.87.6......6....3....2.1...6...3..8.9....5.........2.1.
98.7..6....5.4.......9...8.79......3.3....8.7..2....1.3..6....8....2.........1.4.
98.7..6..5..........4.3..2.8..6....7.5....8.6.....1.3..7.5....9....1.........4...
98.7.....7...6.9....5..9.7.5....6.8...4.3.6.....2....1.5...7.4....6....3....1.2..
98.7.....6...9.5....4..3...7..9..6......7..42.....1....6.5..8....2.1...3.......1.
98.7.....7.....9....6....5.4..8..3...7.....2...1.2.....3.9..4......6..1......5..2
98.7.....7.6...5....4......8..6..9......4..3......2..1.7.8..6......1..2......3..4
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98.7.....76....8....5......4...5..3...96..5.......2..1..79..6......3..2......1..4
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98.7..6..5...9..4...3..2..92...3.....7.8..4.......5....6.....14...1...68......7..
98.76....75....9....6.......4.....3...5.8.7.....2....1..9.7.6.....3....2.....1.4.
98.7.....76....9....5......4...6..3...85..6.......2..1..76..5......3...4.....1.2.
98.7.....6...5.9....5....7.4...3...2..65..8.......4....1..2...3..98..5.........1.
98.7.....7.6...8....5......4..8..6......3..5......2..1.6.9..4......5...2.....1.3.
98.7.....7.....9....6.95...47........3.4..7....2....1....84.3.......6..1.....2.5.
98.7.....7..8..9....6.5....49....3...3.........2....41...4..73.....1...2.....6..5
98.7.....7.....9....6.95...47........3.4..7....2....1....84.3.......6.5......2..1
98.7.....6.....7....7.85....4..5..3...69..5.......2..1..85..6......1...4.....3.2.
98.7.......7.6........5.7..8....4.3..2......1..65..8..3.......2.1.....4...89..5..
98.7.....6.....8.........75.9.6..5......4..3......2..1.5.8..7....4..3.......1...2
98.7.....7.6...5...4.......5..6..9......4..3......2..1..79..8......1..2......3..4
98.7.....6...8.7....7..5...4...3......85..6.......2.43.1.........69..5.......1.26
98.7.....6..8..5....4.3....75....6....2....1.........4.9.5..8......1.........6.23
98.7.....7..6..8....5.4....37....6...6.........2....31...3..98.....1...2.....5..4
98.7.......6...5......4..9.7...8.....4.9...3......2..1.3.8...7...5.....6.....12..
98.........79..6......5....7..5..8....4.3..5......2..1.7.4..9....6.1...2.....5.3.
98.76....75....6....6....9..4.5....3..5.7.......2.4.1...8.5.9.....1...4......3..2
98.7..6....5.4.......9...8.83......9.7....8.3..2....1.3..6....8....5.........2.4.
98.7.....7..86......5..4...37....6....2....5.........1.9..8.3.......69.......1.24
98.7.....7..86......5..4...37....6....2....5.........1.9..8.3.......69.......1.42
98.7..6....5.4.......9...8.73......9.9....8.3..2....1.3..6....8....2..4......5...
98.7..6....5.4.......9...8.79......3.3....8.9..2....1.3..6....8....2..4......5...
98.7.....76..8......5......8...6.4....3....2......1..5...94.7.....6..9.2.....2.43
98.7.....6..9..5....4.3....75....6....9....4...2.....1.9.6..8......1.........9.32
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98.7.....7.....6....6.85....4.....3...56..9.......2..1..75..8......1..4......3..2
98.7.....6.....7....7.5.....9...4.3...85..9......2...1.2...1.4...9..56......3...2
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98.7.....6...5.8....4....3..7.8..6.......2..3.......1..6.9..5....1..4..2....8....
98.7.....6...5.8....4....3..9..7.6....2....4......3..1.7.9..5......8.........1..2
98.76....5..........4..58..4....97....73...2.........1.4...79.....1....6....2..3.
98.7.....6..5..9....4....3.5...8.6...9.........3..2..1...85.7.......1..4.......2.
98.7.....7...6......5..87..5....49....43...2.........1.5...94.....1....6....2..3.
98.7.......6.5........6.9..4......3..2......1..78..5...1.....2...86..7.......3..4
98.7.....6..85......4..3...7..9..5....6...9....2....31.6..8.7.......1.2.........4
98.7.....6.....7....7.5.....4..3..2...8..59.......1..4..95..6......4...1.....2.3.
98.7.....7.....9....6.5....43..........9.34......2..5..7.8..3....1.....2....6..1.
98.7.....6..85......4..3...7..9..5....6...9....2....31.6..8.7.......1..2.......4.
98.7.....7.....6....6.95....4.....3...76..5......2...1..85..9......1..4......3..2
98.7..6....5.4.......9...8.73......6.9....8.3..2....1.3..6....8....2.........5.4.
98.7.....6..85......4..3...7..6..5....9...6....2....41.9..7.8.......1.2.........3
98.7.....6..9..8....5.4....73....9....2....1.........3.6.8..3....8.5...2.....1..4
98.7.....6..9..8....5.4....73....9....6....3...2.....1.6.8..3......1..4......5.2.
98.7.....7.....6....6.5....4....3....9..2..1...59..8....96..5......4...2.....1.3.
98.7.....7...9.6....5..4...3..4..8...7.........4..2.1..6.3..9.......1.65.......2.
98.7.....6...8.7....7..5.8.4....3..2..96..8......2..4..9...1.3..1.........68..5..
98.7..6.....9.........5..4.73....8...6....9.3..2....5.3..6....8..1.4.........2...
98.7.......7.6.5.......4...5....9.3...2.7........1.2.63......8..4.....5...5...6.1
98.7..6....5.4.........9...79...8...3....69....2....5....8.73......1...2.......1.
98.7..6..5...9..4......8..74...3..9...5..62....2......1....93...5.....1..4..1...9
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98.7.....6..9..8....5.4....73....9....2....1.........3.6.8..3......1...2.....5.84
98.7.....6..8..9....5.4....73....8....2....1.........3.6.9..3......1...4.....5.92
98.7..6..5..........4.9..3.2..8..9...5.........9.6...3.2.....14..1.4.3.....1.7.9.
98.7.......6.5.9......6....4......3..2......1..79..8..3.......2..85..6.......1.4.
98.7..6....5.4.........9...3....87....2.............54.6.9.7....3.8..9......2...1
98.......7..9..8....6.5.....4.....3...75..9.......2..1..86..5......1...4.....3.2.
98.7..6..7..8.........54...39........7.3..9....2....1....68.3.......5.4......3..2
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98.7.....6...8.5....4..3...7......2..5..6.7....1.....6.9..7.8.....4....1.....2.3.
98.7.....6...9......5..69..5....98.....4...3.....2...7.6...81...5......4..1.3..2.
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98.7..6..75..4......3..9.7.8....7.5....4..2......1...63...2.....9...8.3....3....1
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98.7.....7...6......5..87..8....65....4.3..6....2....1.5...94.....6....3....1..2.
98.7.....6...5.8....5....7.4...3..2...89..6..........3.1..7...4..95..7.......2.1.
98.7.....6...9......5..69..4....78.....3...7.....2...1.6...95....4.7...3...1...2.
98.7.....6.....7....7.5.....4..8..3...95..8.......2..1..68..9......3..4......1..2
98.76....75....6....6......4......3..7...2..1..85..7....78..9......3..2......1..4
98.7.....7.6...5....4......8..5..6......4..3......2..1.7.6..9......3...2.....1.4.
98.7.....7.6...9...5.......4..6..8......5..3......2..1..78..4......1...5.....3.2.
98.7.....7.6...9...5.......4..6..8......5..3......2..1..78..4......3..5......1..2
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98.7.....6...8.7....7..5...4......3..6...2..4..89..5...1......2..65..8.......3.1.
98.7.....6.7...5....4......5..9..7......3..4......2..1.9.8..6......1...2.....4.3.
98.7..6..7..5.......4.8..7.3...9..8..4......2.....5..1.9..3..4...3.....6.....12..
98.7.....6.....87...7.5.....4..3.2....6....5......1..4..89...6.....4.1.......2..3
98.7.....7.6...8...5.......6..4..9......5..3......2..1..48..6......3..5......1..2
98.7.....6.7...8......5.....7.5..6......4..3......2..1.6.9..5....1.....2....3..4.
98.7..6..5...6......6..9.7.43.9.......5.7.9.......2.4...8.9.5.....1....2.....3.1.
98.7.....7...6......5..97..5....49....4.3..2....6....1.5...68.....1....6....2..3.
9876.....5.....8.........6..4..3......57..6.......2..1..98..5......1...2.....4.3.
98.7.....6...8.7....7..5...4......3...85..6......32..4.1.........69..5.......1.62
98.7.....6...9.7....7..5...4......3..9...2..4..65..9...1...3..2..98..5.........1.
9876.....65....7............4..3......97..5.......2.1...85..6......4...2.....1.3.
98.7.....6..85......4..3...7...6.8...5.9.......6..8.3..6......2..1..24.........13
98.7.....7.6...8...5.......4..6..9......5..3......2..1..94..7......3..5......1..2
98.7..6....5.9..7......4...6.......8.3....2....7..9.5.3...4......19...4.....51..2
98.7.....6...9.5....4..3.9.5..6......7..8......2..9.4...1.....2....3..1......14.9
98.7..6....5.4.......9...8.7.....8.336......9..2....1..3.6....8....2.........1.4.
9..8..7...8..6......5..4...7...9.5....3..2.1....6.....6..5..8...2.....4...1.....3
98.7..6..7.........54.3....8....9.2..1.........5.....4...8..26....2.7.9.....5...1
98.7.......6.5.........46..7......3..3......9..2..15..3..8....1..1.2.4.......5...
98.7..6..7.........54.3....8.....29..1.........5.....1...2.6.8.....5...4.....972.
98.7..6....5.9......4....9.3...5.....2.8..1.......2..7.1....8.6....3..4......6..2
9..8..7...8.....6...5.4....6..3..8...7.....9......5..23..6..9....1.2.........1..4
98.7.....7.6...9......5.....7.6..5....4..5.3.....2...1.6.5..8......3...4.....1.2.
98.7..6....56...4.....5...94...7...3.7.8..2.......3....1..87.....21....8.....61..
98.7..6..75..4......3..8...4...9.2...1.....5...5.....8...4..7.....26..9......1.3.
98.7..6..7.........54.3....8....9.2..1......4..5.........2.8.6.....5...1.....729.
9876.....65....7............4..3......87..5.......2.1...95..6......4...2.....1.3.
98.7..6..7...5......4..8.7.4....3.9..9.2..1....3.....6.4...7.8....3..5......1...2
9..8..7...8..6..5...4..3...8....93...6..3..2.........13.........1..2...5..8..74..
98.7.....6...9.7....7..5...4....3.2..6......4..85..9...1...2.....68..5.........13
98.7.....6.....7....7.85....7...4.3..2......1..98..5....85..6......3...4....1..2.
98.7.....6.....9....7....85.4..3......85..7.......2.1...96..8......4...2.....1.3.
98.7..6..7.....8....5....4.87.6......6....3....2.1...6...3..9.8....2.........5.1.
98.7..6..7.....9....5....4.87.6......6....3....2.1...6...3..8.9....2.........5.1.
98.7.....6.....7....7.6..5.4....3..2..86..4......4..1...98..5......1...3.....2.4.
98.7.....6...8......5..4...7..8..9...3....86.....4...2.9.6..3....1.2.........5..1
98.7..6..5..........4.3..2.8..6....7.5....8.6.....1.4..7.5....9....1.........3...
98.7.....6.....7....7.5.....6..4..3...86..5.......2.1..3..1..4...69..3.......3..2
98.7.....7...6.8....5..8.7.5....6.9...4.3.6.....2....1.5...7.4....6....3....1.2..
98.7.....6...8.5....4..3...7..8..9....9....2......1..4.9.5..6....2.1...3.......1.
98.7.....7.6...8...5.......4..9..6......5..3......2..1..78..9......3..5......1..2
98.7.....6.7...5....4......5..9..8......3..4......2..1.9.6..7......4...2.....1.3.
98.7.....6.7...5....4......5..6..8......3..4......2..1.6.9..7......4...2.....1.3.
98.7.....6.....5....4......5..8..6......4..3......2..1.7.9..8......3..4......1..2
98.7.....6.....9....5....7..4..3..2...98..4.......4..1..65..8......2...3.....1.4.
987......65.........49..8..5..8..7......3..4......2..1.6.7..5......4...3.....1.2.
98.7..6..5..........4.3..2.8..9.7....5...67......1...4.9...85.........12.........
9876.....65....9...........4......3...87..6......2...1..65..7......3..2......1..4
98.7..6..7.........54.3....8..9...2..15..............1...2.79......5...4.....826.
98.7.....6...9.7....7..5...4...5.....6...3.4...89..6...2..1...3..65..8.......2..1
98.7.....7..9..6....5.4....63....8...9..3......2....31...3..78......4..2.....1..4
98.7.....7..9..6....5.4....63....8...7..3......2....31...3..98......4..2.....1..4
98.7.....6..9..8....5.4....36........9....6....2....31...3..78.....2...4.....1..5
98.7.....6...5.8....5....7.4....5.....98..6......3..42.1...2.....65..7......1...3
98.7..6..7.........54.3....8....9.2..15..............1...8..26....2.79......5...4
98.7.....7..86......5..4...37....6....2....5.........4.9..8.3.......69.......1.42
98.7.....7..9..6....5.4....36....8...7.........2....31...3..98......4..5.....1..2
98.7.....7..9..6....5.4....36....8...9.........2....31...3..78......4..5.....1..2
98.7.....6...9.7....7..5...4...3......95..6.......2.43.1.........68..5.......1.26
98.7.....6...9.7....7..5...4...3......95..6.......2.43.1.........68..5.......1.62
98.7.....6...8.7....7..5...4......63..86..5.......4....2...3.1...95..8......1...2
98.7.....6...5.8....5....7.4.......3..89..7......32.4..1..9..2...95..6.......1...
98.7.....6...5.8....5....7.4....5.3...98..5......2..4..1..3...2..65..7.......1...
98.7..6..7...9......5..4....7..6.3....2....1......1..4.3..8.9.......6.52.........
98.........79..6......5....7..4..9....6.3..2......5..1.7.5..8....4.1..5......2..3
98.7.....7.6...5...4.......5..6..8......4..3......2..1..78..9......1..2......3..4
98.7.....7...9.6....5..4...6..3..7...7.........2....31.3.9..8......2..5......1..4
98.7.....7..9..6....5.4....63....8...7.........2....31...3..98.....1...5.....4..2
98.7.....7..8..6....5.4....63....9...7.........2....31...3..89.....2...5.....4..2
98.7.....7..86......5..4...37....6....2....4.........5.9..8.3.......69.......1.24
98.7..6....5.4.......9...8.73......8.6....3.9..2....1.3..6..8......5.........1.4.
98.7.....7..9..6....5.4....63....8...9.........2....31...3..78.....1...5.....4..2
98.7.......7.6.........59..4......3..2......1..86..5...3..7..4...68..7......1...2
98.7.....6...9.8....5....4..6..8.3....2..1..5...9......3.6..7.......2..........14
98.7..6....5.4.......9...8.6.....3.937......8..2....1..3.6..8......5.........1.4.
98.7.....6.....7....7.5.....4.....3...98..4......24..1..89..6......1...2.....3.4.
98.7.....6..89......5..4...7...3.9....6...7....2....41.6..8.3.......1.5.........2
98.7..6..7..69......5..8...4.....93..5......2.1....4.5...47.3......3.........2..1
98.7..6..7......5..45.3....8....2..9.14..................2.6..8....1..4......72.6
98.7..6..7.....9....5.4....83.6......7....8....2....1....8..3.9....5.........2.4.
98.7.....7..6..8....5.4....37....9...9.........2....31...3..68.....5...4.....2..5
98.7..6..7.........54.3....8.....29..1......5..5.........9..72....2.6.8.....4...1
98.7.....6...8.7....7..5...4...5..3...69..5.......2..4.1.........95..8.......3.12
98.7..6..75.....9...6......4.8.3...2..56...7......43...1.........79...8.....12...
98.7..6..7...8.....54......6...7.3....53...2......1..4.9..3.8.......2..5.......1.
98.7..6..7.........54.3....8.....29..1......5..5.........9.2.8....6..72.....4...1
98.7.....6..9..8....5.4....37........9....7....2....31...3..68.....5...2.....2..4
98.76....5.....9...4.....8.3..5..6...2......8.....4.1...9.7.3.....35.........1..2
98.7..6....5.4.........9...83...6....7...38....2....1....9.87......1...2.......5.
98.........76..5......9..4.3.........9..4..5...2..61....5..1..2...2..7......8..3.
98.7.....6...9.7....7..5...4......3..9...4..7..86..5...2..1......95..8.......3.21
98.7.....6..8..5....4.3....75....6....2....1.........2.9.6..8......5..43....1....
98.7..6....5.4.......9...3..6....8...3.....9...2.5...1..7..4......5.1..7....7.52.
98.7.....6...9.5....4..3...5..6..7...6.........3..2.1..7.9..8......1...2.....7..4
98.........76..5......9..4.6..3...7...3..2..6....5.3..4....1.8..1.........62..7..
98.7..6....5.4.........9.3.2....6..9.4..8......75.....1....39...7......3.......21
98.7..6..7..5.......4.9..7.4...7..9...3..52.7......1...4..3..8...7.....6...2....1
98.7.....7...8.6....5..4...3..4..8...9.....4...4..2..1.6.3..7.......1.2.........5
98.7.....6...9.7....7..5....4..3..2...8...5.......1..4..65..9......4..1......2..3
98.7.....6...8.7....7..5...4......63..86..5.......4....2...3..1..68..9......1..2.
98.7.....6.....7....7.6..5..4...3.2...65..4......4...1..86..9......2...3.....1.4.
98.7.....6...9.7....7..5...4......3...86..9......32..4.1.........69..5.......1.26
98.7.....7...6......5..97..5.....4....43...6.....24..1.5...79.....6....3....1..2.
98.7.....6...9.7....7..5....4..3..2...9...5.......1..4..65..8......4..1......2..3
98.7.....7...8.9....6..5...8..4..3....2....1......6..2.7.3......3....4.......1..5
98.7.....6..85......4..3...7..9..5....6...9....2....31.6..8.7.......1.4.........2
98.7.....6...9.7....7..5....4..3..2...8...5.......1..4..65..9......4...3.....2.1.
98.7.....6...8.7....7..5...4....3.2...96..8......2...4.1......3..68..5.......1.6.
98.7..6.....9.........5..4.83....9..6.....3.7..2....5..7.6....3..1.4.........2...
98.7.....6...5.8....4..3.2..9.6..5......7.........2..1.6..9.7....1....4.........3
98.7.....6.....7....7.5.....4...3.2...8..59......1...4..95..8......4..3......2..1
98.7..6..7.........54.3....6..8..2...1.....4...5.........2.7..8....1..5......89.2
98.7..6....54...7.......3..6...7.9...3..5...8..2..4.....7.4..1....1.2.........4.3
98.7.....6..85......4..3...7...9.5...42....1.......7...9..8.6....6..1.2.........3
98.7.....7...8.6....5..4...3..4..8...9.....4...4..2..1.6.3..7.......1..5.......2.
98.7.....7...9......6......54....8......8.5.......3.2..7..5.4....1..2.3......6..1
98.7..6....5.4.........9...6..9.7...3..8..7......2..1..3...89....2.............45
98.7..6..7.....8....5....4.37.6......6....3....2.1...6...3..9.8....2.........5.1.
98.7..6....5.9..7....4.....5...7..9..7....3....2..41...5..2..8...7.....6...1....3
98.7.....6..85......4..3....9..8.6....2....1.........4.5.6..7.......85.......1.32
98.7.....6.....9....5....7..4..3..8...98..6.......2..1..75..8......1..3......4..2
98.76....7.....9...54......6..3..2...4.....5...8..1......69...3....3.7.......8.1.
98.7.....6...9.7....7..5...4....3.2...65..9..........4.1...2..9..98..5.........13
98.7.....6...9.5....4..3...7..8..6...6.........3..2.1..5.9..8.......1.4.........2
98.7.....7...6......5..4...36....9......3.6.......2.1..7..8.3....4....5......1..2
98.7..6....5.4.........9...3....89....2.............54.6.9.7....3.8..7......2...1
98.7..6....5.4.........9...3....89....2.............54.6.9..7...3.8.7.......2...1
98.7..6....5.4.........9...6..9..7..3..8.7.......2..1..3...89....2.............45
98.7..6..5...4......3....7.4...6.8...9.........72....1.6..5.9.....1...3.........2
98.76....5....48....3....7.4...5.9....7.....3...2...1..6..9.5....51....2.........


They are mostly the highest rated puzzles from the ph2010 database.
I expanded them, then minimized them and collected the new puzzles

Code: Select all
98.76.5..7..45.....4...8.7.5.........76.8..5....5..36.2.....7...5.8...4...4.7.1.. ED=11.6/1.2/1.2
98.76.5..7.54......64......8..9........58.32......7..96.98.....57...4....48.9...6 ED=11.5/1.2/1.2
98.76.54.7....86....5.4....3.....9..2..........8..6....7..9.85....8.7.94....547.6 ED=11.5/1.2/1.2
98.76.5..7.54.9....64..8...87....32..5....8.........9.6.789.....48.75......6.4... ED=11.2/1.2/1.2
98.76.5..5.7...6...........85...4......32.8.....1...9.6....598.4....7.6..95...7.4 ED=11.7/1.2/1.2
98.76.5..5.7....9..4.......7.4.9...5.9..5...6.6.8.....6.8.....4....8632.....7.1.. ED=11.6/1.2/1.2
98.76.5..5.7...6...........85...4......32.8.....1...9.6....598.4.8..7.6..9....7.4 ED=11.7/1.2/1.2
98.76.5..5.7....9..4.......7.4.9...5.9..5...6..58.....6.8.....4....8632.....7.1.. ED=11.6/1.2/1.2
98.76.5..5....98...4...8...87.9...5...457...9.....6...7......3....84.6.........21 ED=11.6/1.2/1.2
98.7..6..7..5..4....5.86...8......3..9.....21...96.5..4......6..7...4....6.89...7 ED=11.7/1.2/1.2
98.76.5..5..4.......6.5.7..85...4.6..6.87...5..9......47....9......8...3.......21 ED=11.6/1.2/1.2
98.7..6..7..85.4....5..9...8.4...9.....5...3.....8..215.8.4...7.6..7.......6...4. ED=11.6/1.2/1.2
98.76.5..5....98...4.......7......3.4......21...84.6...7.9.4.5....57...9....86... ED=11.6/1.2/1.2
98.76....5..4.......3...76.2....4.17.1....42.......6.3..62....1..21..34......7... ED=11.7/1.2/1.2
98.76.5..5....98...4.......7......3....84.6.........21.7.9...5...457...9....86... ED=11.6/1.2/1.2
98.7..6..7.65..4....5.8....8......3..9.....21...96.5..4......6..7...4......89...7 ED=11.7/1.2/1.2
98.76.5..7.4.......56....8.8...9...44..5......678......49....57...6....9.....432. ED=11.6/1.2/1.2
98.76.5..7.4.......56....8.8...9...4.6784.......5......49....57...6....9.....432. ED=11.6/1.2/1.2
98.76.5..7.54..6....4.58...8.....93..9.....2......54.66......5..7........4.89...7 ED=11.7/1.2/1.2
98.76....7.....5...43....6.6....2..7...95.2.......68...2.58..7...8.2.9.5...6.9... ED=11.7/1.2/1.2
98.76.5..7.54..6....4..8...8.....93..9.....2......54.66.........7.5......4.89...7 ED=11.7/1.2/1.2
98.76....7.....5...43......6....2.7....95.26.......8...2.58...7..8.2.95....6.9... ED=11.7/1.2/1.2
987......65.94..........3..4......2....42...5....96..3..965.4.2..52...36....3..9. ED=11.6/1.2/1.2
987......65.94..........3..4......2....42...5....96..3..925.4.6..56...32....3..9. ED=11.6/1.2/1.2
98.76....7.5..8....64......6..57.9..4..9.68......84....97....3.....47..8.......21 ED=11.6/1.2/1.2
98.76....7.5.4.....64...9...9...748..4....5.6..8..4.79...32.......1.8.........6.8 ED=11.6/1.2/1.2
98.76.5..7.4.......56.4.7..69..5......789.......4.6...4.9....7....9.5..3.......21 ED=11.6/1.2/1.2
98.76.5..7.4.......56...7..69..5......789.......4.6...4.9....7....9.5..3.....4.21 ED=11.6/1.2/1.2
98.76....7.5..8....64......6..57.9..4..9.68......84....9.....3...6....21....47..8 ED=11.6/1.2/1.2
98.76....7.59......64...9...9...748..4....5.6..8..4.79...32.......1.8.........6.8 ED=11.6/1.2/1.2
98.76.5..7.4.......56.4.7..69..5......789.......4.6...4.9....7....6...32.....5..1 ED=11.6/1.2/1.2
98.76.5..7.4.......56...7..69..5......789.......4.6...4.9....7....6.4.32.....5..1 ED=11.6/1.2/1.2
98.76....7.5.......46...8..6..57..9.4..9.6.......84....97...3......47..8......2.1 ED=11.6/1.2/1.2
98.76....7.5...8...46......56.3........21........7.96...9....85..8..56.4......79. ED=11.7/1.2/1.2
98.76....7.5...6...4....8..6..57..9.4..9.6.......84....97...3......47..8......2.1 ED=11.6/1.2/1.2
98.76....5.7...9...46...8..8..94.......6.7.8.....85.7..65...3.2....9...........51 ED=11.7/1.2/1.2
98.76....5.74...........3...4..2.....3.1.7.......4361...4....61..1..64.7......23. ED=11.7/1.2/1.2
98.76....7.5.......468.....56.3........21........7.96...9....85..8..56.4......79. ED=11.7/1.2/1.2
98.76....5.74...........3..6..2.7....2..1........43.2...4....62..2..64.7......13. ED=11.7/1.2/1.2
98.76....7.5.......468.....8..32.....9.1.........7.96...9....85.....56.4......79. ED=11.7/1.2/1.2
98.76....5.74...........3..6....7....2..1........43.2...4....62..2..64.7....2.13. ED=11.7/1.2/1.2
98.76....5.74...........3..6....7....2.61........43.2...4....62..2...4.7....2.13. ED=11.7/1.2/1.2
98.76.5..7.5..8....46.59...89.....7.....4.3..........2.7.6.4.5....89.........5.6. ED=11.8/1.2/1.2
98.76.5..7.5.......46.59...89.....7.....8...3....4.2...7.6.4.5....89.........5.6. ED=11.8/1.2/1.2
98.76.5..7.5..9....46.58...89.....7.....4.3..........2.7.6.4.5....98.........5.6. ED=11.8/1.2/1.2
98.76.5..7.5.......46.58...89.....7.....9...3....4.2...7.6.4.5....98.........5.6. ED=11.8/1.2/1.2
9876........59.........4...83........927.68....6....2..7..3.9.8.2.....73......26. ED=11.8/1.2/1.2
987.........96.8.......5...84........93.72.8...2...3...7.4...98.3.2..7.4......23. ED=11.8/1.2/1.2
98.76....7.54......46..98..6......32.7............5.8..9.58..4....9.6.......47..8 ED=11.8/1.2/1.2
98.76.5..7.5....6...4......6..98....5.84.7....7..56..4.9..........8...39....9..2. ED=11.8/1.2/1.2
98.76.5..7.5.48....46..9....6.....3...4...62............74.6..8...95........87.9. ED=11.8/1.2/1.2
98.76.5..7.5.48....46..9....974.6.8.....87..9....5.....6......3..4...6.2......... ED=11.8/1.2/1.2
98.76.5..5.7...68..46..8...76.54.....598....4....9.......6...3.....7.82.........9 ED=11.7/1.2/1.2
98.76.5..7.4.5..6..........6.794....5...87.....86.5.....9.....8....9432......64.. ED=11.8/1.2/1.2
98.76.5..7.4.5..6..........6.794....5...8......86.5.....9.....8....764.......432. ED=11.8/1.2/1.2
9876.........958.......4...8.32..69.2..3..7...76......7.9...26.32..6..87.6....3.. ED=11.8/1.2/1.2
9876.........958.......4...8.32..69.2..3.67...76......7.9...26.32.....87.6....3.. ED=11.8/1.2/1.2
9876.........958.......4...7.9...36..6....2...32....8767.......2.83..69...32.67.. ED=11.8/1.2/1.2
9876.........958.......4...7.9...36..6....2...32.6..8767.......2.83..69...32..7.. ED=11.8/1.2/1.2
9876.........958.......4...83.2..69.2..3..7....6......79....26.3.2.6..87.68...3.. ED=11.8/1.2/1.2
9876.........958.......4...83.2..69.2..3.67....6......79....26.3.2....87.68...3.. ED=11.8/1.2/1.2
9876.........958.......4...8.32..69.2..3..7.8.76......7.9...26.32..6...7.68...3.. ED=11.8/1.2/1.2
9876.........958.......4...83.2..69.2..3..7.8..6......79....26.3.2.6...7.68...3.. ED=11.8/1.2/1.2
98765.......4..........3...8..7..2...9....67..6.2...586...2.89.2...6.5.7.5....... ED=11.8/1.2/1.2
98765.......4..........3...8.62..75.7..8....2..9.....66...2..972...6.8.5..5...... ED=11.8/1.2/1.2
98765.......4..........3...8.6.2.97.2...6..58..5......7..8...2.6..2..5.7..9....6. ED=11.8/1.2/1.2
98765.......4..........3...8..7..2...9....67..6.2...586...2.5.72...6.89..5....... ED=11.8/1.2/1.2
98765.......4..........3...8.62..75.7..8....2..9.....66...2.8.52...6..97..5...... ED=11.8/1.2/1.2
987.........65.............8.493.2..27........932...8472...38.93....247..4......3 ED=11.8/1.2/1.2
987.........65.............8.493.2..72........932...843....247.2....38.9.4......3 ED=11.8/1.2/1.2
987.........65.............8.493.2..72........932...84.4.....23.....347......28.9 ED=11.8/1.2/1.2
987.........65.............8.493.2..72........932...842....347..4......3.....28.9 ED=11.8/1.2/1.2
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Re: The hardest sudokus (new thread)

Postby Paquita » Sun Jun 23, 2024 3:25 pm

The other restraint to found puzzles is the rating. Maybe there are plenty non tridagon puzzles, but few are high rated.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Sun Jun 23, 2024 3:54 pm

.
I started from your 414 seeds (none of which has a tridagon) and I applied expansion by Singles.
Then I searched for the minimals. I found only 415 (414 of which must be the original ones.
The only new puzzle is
Code: Select all
.2...6...4...8.2...89.........6...5...4.2.9.......1..73..7...6...8.6.3...4...5..1

it has 3 degenerate-cyclic tridagons, but no non-degenerate tridagon.
.
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Re: The hardest sudokus (new thread)

Postby Paquita » Sun Jun 23, 2024 9:06 pm

Hi Denis
From what I documented I got that the resulting file is made by expanding. The seed is not the file I presented, as you pointed out. I have to look into it.
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Re: The hardest sudokus (new thread)

Postby Paquita » Tue Jun 25, 2024 10:39 am

Hi Denis

The puzzles were contaminated by an older batch. I was trying to limit my search to non-tridagon, some tridagon puzzles were mixed with them. I understand that if a puzzle is tridagon, it will produce tridagon puzzles when used as seed. Likewise, a non-tridagon puzzle will most probably produce non-tridagon puzzles. Now I had a mix of both types as seed and the result is almost all puzzles are tridagon. If they are equally likely the result should have been that about half the puzzles are non-tridagon. This is a rough estimate as there are many other factors.
I am going to try once again with a clean non-tridagon batch, to see if I can produce large amounts of that type. But the previous results, contaminated and all, make it probable that it will be hard to find many more non-tridagon with a high rating.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Tue Jun 25, 2024 2:55 pm

.
I you use only expansion by singles and/or vicinity search, starting from the high SERs in ph2010, I don't think you'll find many new high SER puzzles.
One thing you could try is Singles+1 expansion: after expansion by Singles, add 1 clue from the solution. I've had some interesting results this way, but I wasn't trying to increase the SER. The problem is, it multiplies the number of puzzles to search for minimals.
.
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Re: The hardest sudokus (new thread)

Postby Paquita » Wed Jun 26, 2024 8:36 pm

Thank you for the suggestion. The first results are very few new puzzles with a high SER (I look for 11.0 and above). Of course, a tridagon puzzle has a high rate, almost by definition. Whereas most non tridagon puzzles have a low rate, the ones with complex patterns are relatively rare. It is amazing that there are so many possible tridagons. I assume there are many many more non-tridagons, but they are usually lower rated.
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