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 coloin » Mon Aug 19, 2024 1:24 pm

If it helps ... only these ones are new ... and could be used as furthur seeds i guess
Hidden Text: Show
Code: Select all
1.3.56....567.....78.1.3..5.35..7...61...83..8.73...1..68.........8..9.6......2..
1.3.56....5678....78.1.3..5.35..7...61....3..8.73...1..68.........8..9.6......2..
1.3.56....5678....78.1.3..5.35..7...61...83..8.73...1..68............9.6......2..
1.3.56....5678....78.1.3..5.35..1...67...83..8.13...7..68............9.6......2..
1.3.5...9.5.1....669.73...5.......43......8..7.......1.7.6......6139....9.5..1...
1.3.5...9.5.1....669.73...5.......43......8..7.......1.7.6.5....6139....9....1...
1.3.5...9.5.1....669.73...5.......43......8..7.......137.6......6139......5..1...
1...567....718....68.3.75.........4.36....8.7........251..3....7.8.65....368.1..5
1...567...5.18....68.3.75.........4.36....8.7........251..3....7.8.65....368.1..5
....567....718....68.3.75.........4.361...8.7........251..3....7.8.65....368....5
....567...5.18....68.3.75.........4.361...8.7........251..3....7.8.65....368....5
.234..7..4.7..9.3.69.......26....3......6.85...........7.24.....46.93...9..6.7..3
.234..7..4.7..9.3.69.......26....3......6.85..........37.24.....46.93...9..6.7...
.234.67..4.7..9.3..9.......26....3......6.85...........7.24.....46.93...9....7..3
.234.67..4.7..9.3..9.......26....3......6.85..........37.24.....46.93...9....7...
1.3.56....567.....78.1.3..5.35..1...67...83..8.13...7..68.........8..9.6......2..
1.3.56....5678....78.1.3..5.35..1...67....3..8.13...7..68.........8..9.6......2..

It tends to be the11.7 which have the high BxB however....
the first 4 are bxb=6
The next ones seem to be higher !
coloin
 
Posts: 2494
Joined: 05 May 2005
Location: Devon

Re: The hardest sudokus (new thread)

Postby Paquita » Mon Aug 19, 2024 1:47 pm

Hi coloin

I wonder where the ones that were known to you are published? Because it seems I am missing some files in my collection....and I marked those as new.
Paquita
 
Posts: 132
Joined: 11 November 2018

Re: The hardest sudokus (new thread)

Postby coloin » Mon Aug 19, 2024 2:08 pm

The first 3 have got 22 clues or so so should be in the original big file by champagne....
the others I would have to dig deeper
Hidden Text: Show
Code: Select all
.2.4....9..7....3.6...7.1...4......87.....5....5.1..6.3...6..5......8..2...9.....## 21  ED=11.8/11.8/10.7
.2.4.........89......23.6....5....9..3..4.2..7.......1..1....5..6.3..8..9.......7## 21  ED=11.8/11.8/10.4
...4....9....8.2..6....3.1..7...5.6....9..8......2...45.8......76...1....3.....7.## 21  ED=11.8/11.8/11.1
....567.....1.9...6...7......4.....13...6.9...8.....2.5....73....2.....8.1.....4.## 21  ED=11.8/11.8/11.2
.2.4..7....6.....17...3......5....6..4.2..9.......5..8..1..8....9..7.......92.3..## 21  ED=11.8/11.8/9.8 
1......8......92....6.3...52....8.....5.7.....6.5....4..47...........91..3..6...7## 21  ED=11.8/11.8/2.6 
1.......9.5....2....87...4.2...3......48.5....8.6...7...6..4.5.........1....9.3..## 21  ED=11.8/11.8/7.9 
....56......1....6.8.3.7....6...3..75......2...4...9...1.7....8..2....4.9.....5..## 21  ED=11.8/11.8/10.4
.2.....8....7...23......5.6..4.1.....6.3....29....5....7.8...6.5....4.....1.9....## 21  ED=11.8/11.8/10.8
.....678........327.....5....1.4.....9.2.....6....7.5.3....58....29......4..1....## 21  ED=11.8/11.8/3.4 
1......89.....91.3.......6...7.4....3....1..5.6.2.....5....89...4..7......26.....## 21  ED=11.8/11.8/3.4 
1.......9..67...2..8....4......75.3...5..2....6.3......9....8..6...4...1..25...6.## 22  ED=11.8/11.8/11.6
..3.5.7..4....9...6..2.......5...8.3.9.....6.8..........8.1...75....4.2.....3.5.8## 22  ED=11.8/11.8/2.6 
...4...8......92..6...7...5...8...9......24...3..1...7316......57.........2.6...3## 22  ED=11.8/11.8/11.7
.2...67..4...8......93........9..57..1...7..2......61.3...4..6...8.......6...5.2.## 22  ED=11.8/11.8/11.5
.2.4....9..7.8.2..6.....1.........93.....5.2..9.2..4..5....7....1.3...4...8.6....## 22  ED=11.8/11.8/9.4 
.2.....894......3...9.7.5......6.9..3.......2.8...2.4...16......7..1..9....5..1..## 22  ED=11.8/11.8/2.6 
..345........89......23.5...1......7..4..28..9......6...2..84..6......9..7......1## 22  ED=11.8/11.8/11.4
...4.6.....6..9.2.7...1.....1..3.4....96...5.8.......7.3......8..2..49.....5...4.## 22  ED=11.8/11.8/10.6
......7.9...1...3..8...74...9....5.4.....5..75.6....2...1.6......23.....94...8...## 22  ED=11.8/11.8/2.6 
.2...6......1...3...9.7...5..8....57.3.....1.7...4.8....4.9.5...6.2.....9.......8## 22  ED=11.8/11.8/10.0
..34...8.......1.37........2...9.......5..8...6...7.4...51....8.7...5...9...62.5.## 22  ED=11.8/11.8/2.6 
1....6.8....7..1........5.6..9.4.....7.2...3.8....76..3....1..5.4.9.......2.7....## 22  ED=11.8/11.8/11.6
...4....9.....9.327...3.5..2......6...1.....8.3....25...41.8...6.........1.9.4...## 22  ED=11.8/11.8/2.6 
.2...6..94.7....3..9.....5..6...85..3..........1.7.......9..8.2...8.2..5....1..4.## 22  ED=11.8/11.8/2.6 
1....6....5...9.6.8..23.....9....54.3.......2.15...6..........7...37......1..4.5.## 22  ED=11.8/11.8/2.6 
1..4.......6.8...278...3....3..6...7..7..2...9......5....1..4..5......9..7...8..3## 22  ED=11.8/11.8/10.5
.2.4....9..7......6....2.5....91.....3...4..1...3..8....5....7..1..4...28.2...6..## 22  ED=11.8/11.8/11.4
.....67.....1...3...9.2...4.4..9......5..2...89......5.3.....6...8.4...29....71..## 22  ED=11.7/11.7/3.4 
.2......94...8.1....9.....6....483....16...97....1..6.3....1...5....4....72......## 22  ED=11.8/11.8/2.6 
...4...8...7..92......3...526...1.....19......7....1..5......4..1.8....3..6..29..## 22  ED=11.8/11.8/9.9 
.....6..94...8.2.....7...1.2.9...8....4.3.9...6.....5.3.8.4.....4.5......7...1...## 22  ED=11.8/11.8/3.4 
1....6.......8.2...9.7....5.7.3...5.....716....4....73..59....48...2.....3.......## 22  ED=11.8/11.8/9.8 
....5...9...7...3..8...1......3...7...8..24..6...9...5..2....548....42...14......## 22  ED=11.8/11.8/9.7 
..3..6.8....1......9..7...4...8..6..3...4...2.....5.1...2.9...373.......94....5..## 22  ED=11.8/11.8/3.4 
..3.....94...8.2...6.7...1.2...9...8..4...3.......1.5.3.8.4.....4.6......7...5...## 22  ED=11.6/11.6/2.6 
..3..6......1...3.9...7...42.....84..4..9...7..5....6........1..7..2...88.....4.2## 22  ED=11.8/11.8/10.0
...4....9....8.2..6....3.1..36..1...7.........15....7.3....5.6..6.39.8....42.....## 23  ED=11.8/11.8/8.3 
1.....7.9..6...12........4.2.7.6.....3...8.7..8.5........8.4.5.....2.9.......5.34## 23  ED=11.8/11.8/2.6 
...4....9..6....2.7...3.5......48...8..5..3...15.73.....2.....65....48...9.....1.## 23  ED=11.8/11.8/11.5
1.....78...6.8...278.....5..1.9...7...4..2.......6.......5....7....24..3.9.8..5..## 23  ED=11.8/11.8/2.6 
.....6...4...89.....823.........7.56....2.9.....6.5.1.3.9...4...7...3..1.1......5## 23  ED=11.3/11.3/2.6 
1.....78..5......6......41..3.5.......69.3...9...74.......481....23.....8...9..7.## 23  ED=11.8/11.8/2.6 
1......89........3..8...56..7..4...66.91......4...2......5...9......43.2....23..7## 23  ED=11.8/11.8/2.6 
........94....92......7..45..1.3.....7.6..9..8....7..2.3.7..8....6.1....9....5.2.## 23  ED=11.8/11.8/10.5
......7..4......23..8...5.4.1..9....3.5..8....6.1..3.....97.6......1.97......2..5## 23  ED=11.8/11.8/2.6 
..3....894.....2...89.....1.3...1..57..52.....9...3......7..6.2........8....6.54.## 23  ED=11.8/11.8/2.6 
...4...89..7..92......3...526...1.....19.....7.....1..5...9..4...6..29.....8....3## 23  ED=11.8/11.8/10.7
......7.9...1...3..8...74...9....8.5..8..5..75.6....2...2.6......13.....94...8...## 23  ED=11.8/11.8/2.6 
1...56.....71......9....1.......3..87..5..9......2..4..7..45.2...2..8..36.....5..## 23  ED=11.8/11.8/11.3
.2....78.4.7.....6.9..7..1....5....3.....1.......9.12..7..1.8..5....4.....67.3...## 23  ED=11.8/11.8/2.6 
.2.....8..56.....17...3.5.......49....5.9....9..3.7...5...7.4.....8...52.1.....6.## 23  ED=11.8/11.8/11.3
1...5.7....7.....6.8...7.4....9..3...6...4..7..8....2.5..3.....8...9.1....2..8.7.## 23  ED=11.8/11.8/2.6 
....5...9..71.9.3.6..2.3...2..6...7..4....8......9...53.2....1.....2.....8...14..## 23  ED=11.8/11.8/2.6 
.23.5...9.571.....8....3.....97....5......8......654..3....4.6..1.5....2....1....## 23  ED=11.8/11.8/2.6 
.....6.8..5.1....3..9....4.2.......553..7......8...4......64...71.23...4...7....2## 23  ED=11.8/11.8/2.6 
..34.........8...668..7.1.....5....1.9..1.6.......2..4..5.....28.....96.97.....1.## 23  ED=11.8/11.8/2.6 
.2...6..9..6...1....8.3..4.2....7..8....4.5.....1...3...2..8..78..57....97.......## 23  ED=11.6/11.6/2.6 
..34......5..89...78...2...2....5..7...62.41....9....5.......6.8...9...2..1...3..## 23  ED=11.8/11.8/2.6 
.....6.8....1..2...9..7...5..5.4...734.7.8...97.........9...6..7...3...4...2...1.## 23  ED=11.8/11.8/11.3
.2...67..4...8......9.......3.....7.5.8...34..1.3....2....9..5....6.1..3...2..6.7## 23  ED=11.8/11.8/2.6 
...45.....5...9.3.6...2...52..8.......4.6...8.3...5.1.3..5...7......79...7......1## 23  ED=11.6/11.6/7.6 
....5..8....1.9..6...3..1.4.3...14..5......2...8.......9..1.....6.9..3..8.2.73...## 23  ED=11.8/11.8/7.6 
.23.5.7...56.....37....3...2...3...63...7...5.4.9.....5...2.6.7..2....1......8...## 24  ED=11.8/11.8/10.6
.2.4..7...57..9.3.6...7......5..8.9.7...2.....4.6..3.......1..85......1...1...9.3## 24  ED=11.8/11.8/11.2
..34.67..45..8............42...6..9...1..3..6...1.......46....7.8...5.4.9...4.2..## 24  ED=11.8/11.8/10.5
...4..78.....8.26......2..5.7.3..8..5.......2..9..1..7.65...47..4.6.....9.1......## 24  ED=11.8/11.8/2.6 
coloin
 
Posts: 2494
Joined: 05 May 2005
Location: Devon

Re: The hardest sudokus (new thread)

Postby Paquita » Mon Aug 19, 2024 2:31 pm

coloin, well yes

1.3.5...9.5.1....669.73...5.......43......8..7.......1.7.6......6139....9.5..1... is B10B
I am checking them now so maybe more.
Probably these are B10B too
1.3.5...9.5.1....669.73...5.......43......8..7.......1.7.6.5....6139....9....1...
1.3.5...9.5.1....669.73...5.......43......8..7.......137.6......6139......5..1...

See my B10B files in the BxB thread : are they not new either?

I wonder if you have a collection of unpublished puzzles that you checked against my puzzles?
I do check against T&E(2), the following :

ph2010
files posted by mith or hendrik before september 2023
files posted by me in the fall of 2023
hendriks new 11.8 file
your 11.9 study
the high BxB file collection - that one is a bit unclear what the latest updates are


tell me what I am missing?
Paquita
 
Posts: 132
Joined: 11 November 2018

Re: The hardest sudokus (new thread)

Postby Paquita » Mon Aug 19, 2024 2:41 pm

Yes this is the 11.8 part of min-expands from ph2010 plus the puzzles T&E(2) published before september 2023
One thing is that if one minimal of a min-expand is published, there may still be more (unpublished) minimals.
These are also interesting to use as seed. My just-pubblished list is of unpublished MINIMALs, not the corresponding MIN-EXPANDs


Code: Select all
1...567.9...1.926.6..27..51...91...5.1.5.792.....62.17.34............5...6.7..... ED=11.8/11.8/9.3
1.3.56....5718..3.68.7.3....618.53.73.5......87.3....15.6.........5..96.......4.. ED=11.8/11.8/3.4
1.3.56....5718....68.7.3....618.53.73.5......87.3....15.6.........5..96.......4.. ED=11.8/11.1/3.4
...4...8......92..6...7...5...8...9......24...3..1...7316......57.........2.6...3 ED=11.8/11.8/11.7
1....6.8....7..1........5.6..9.4.....7.2...3.8....76..3....1..5.4.9.......2.7.... ED=11.8/11.8/11.6
1.......9..67...2..8....4......75.3...5..2....6.3......9....8..6...4...1..25...6. ED=11.8/11.8/11.6
...4....9..6....2.7...3.5......48...8..5..3...15.73.....2.....65....48...9.....1. ED=11.8/11.8/11.5
.2...67..4...8......93........9..57..1...7..2......61.3...4..6...8.......6...5.2. ED=11.8/11.8/11.5
.2.4....9..7......6....2.5....91.....3...4..1...3..8....5....7..1..4...28.2...6.. ED=11.8/11.8/11.4
..345........89......23.5...1......7..4..28..9......6...2..84..6......9..7......1 ED=11.8/11.8/11.4
....567.....1.9...6...7......4.....13...6.9...8.....2.5....73....2.....8.1.....4. ED=11.8/11.8/11.2
...4....9....8.2..6....3.1..7...5.6....9..8......2...45.8......76...1....3.....7. ED=11.8/11.8/11.1
.2.....8....7...23......5.6..4.1.....6.3....29....5....7.8...6.5....4.....1.9.... ED=11.8/11.8/10.8
...4...89..7..92......3...526...1.....19.....7.....1..5...9..4...6..29.....8....3 ED=11.8/11.8/10.7
...4.6.....6..9.2.7...1.....1..3.4....96...5.8.......7.3......8..2..49.....5...4. ED=11.8/11.8/10.6
........94....92......7..45..1.3.....7.6..9..8....7..2.3.7..8....6.1....9....5.2. ED=11.8/11.8/10.5
1..4.......6.8...278...3....3..6...7..7..2...9......5....1..4..5......9..7...8..3 ED=11.8/11.8/10.5
.2.4.........89......23.6....5....9..3..4.2..7.......1..1....5..6.3..8..9.......7 ED=11.8/11.8/10.4
....56......1....6.8.3.7....6...3..75......2...4...9...1.7....8..2....4.9.....5.. ED=11.8/11.8/10.4
.2...6......1...3...9.7...5..8....57.3.....1.7...4.8....4.9.5...6.2.....9.......8 ED=11.8/11.8/10.0
...4...8...7..92......3...526...1.....19......7....1..5......4..1.8....3..6..29.. ED=11.8/11.8/9.9
.2.4..7....6.....17...3......5....6..4.2..9.......5..8..1..8....9..7.......92.3.. ED=11.8/11.8/9.8
.2.4....9..7.8.2..6.....1.........93.....5.2..9.2..4..5....7....1.3...4...8.6.... ED=11.8/11.8/9.4
...4....9....8.2..6....3.1..36..1...7.........15....7.3....5.6..6.39.8....42..... ED=11.8/11.8/8.3
1.......9.5....2....87...4.2...3......48.5....8.6...7...6..4.5.........1....9.3.. ED=11.8/11.8/7.9
1......89.....91.3.......6...7.4....3....1..5.6.2.....5....89...4..7......26..... ED=11.8/11.8/3.4
.....678........327.....5....1.4.....9.2.....6....7.5.3....58....29......4..1.... ED=11.8/11.8/3.4
.....6.....718........2...5..85....13.....9...6.....4...2.7...8.4.....6.9.....3.. ED=11.8/11.8/3.4
1....6....5...9.6.8..23.....9....54.3.......2.15...6..........7...37......1..4.5. ED=11.8/11.8/2.6
1.....78..5......6......41..3.5.......69.3...9...74.......481....23.....8...9..7. ED=11.8/11.8/2.6
1......8......92....6.3...52....8.....5.7.....6.5....4..47...........91..3..6...7 ED=11.8/11.8/2.6
..34...8.......1.37........2...9.......5..8...6...7.4...51....8.7...5...9...62.5. ED=11.8/11.8/2.6
......7.9...1...3..8...74...9....5.4.....5..75.6....2...1.6......23.....94...8... ED=11.8/11.8/2.6
..3.5.7..4....9...6..2.......5...8.3.9.....6.8..........8.1...75....4.2.....3.5.8 ED=11.8/11.8/2.6
.2...6..94.7....3..9.....5..6...85..3..........1.7.......9..8.2...8.2..5....1..4. ED=11.8/11.8/2.6
......7.9...1...3..8...74...9....8.5..8..5..75.6....2...2.6......13.....94...8... ED=11.8/11.8/2.6
..34......5..89...78...2...2....5..7...62.41....9....5.......6.8...9...2..1...3.. ED=11.8/11.8/2.6
...4..78.....8.26......2..5.7.3..8..5.......2..9..1..7.65...47..4.6.....9.1...... ED=11.8/11.8/2.6
..34.67..45..8............42...6..9...1..3..6...1.......46....7.8...5.4.9...4.2.. ED=11.8/11.8/10.5
.23.5.7...56.....37....3...2...3...63...7...5.4.9.....5...2.6.7..2....1......8... ED=11.8/11.8/10.6
....5.7.9.5.....2.7..2..6.52.5.7..9.68.92..5...15.8...........45...9..7....3..... ED=11.8/11.2/3.4
1...56.....71......9....1.......3..87..5..9......2..4..7..45.2...2..8..36.....5.. ED=11.8/11.8/11.3
.2....78.4.7.....6.9..7..1....5....3.....1.......9.12..7..1.8..5....4.....67.3... ED=11.8/11.8/2.6
.....6.8....1..2...9..7...5..5.4...734.7.8...97.........9...6..7...3...4...2...1. ED=11.8/11.8/11.3
.....6..94...8.2.....7...1.2.9...8....4.3.9...6.....5.3.8.4.....4.5......7...1... ED=11.8/11.8/3.4
1....6.......8.2...9.7....5.7.3...5.....716....4....73..59....48...2.....3....... ED=11.8/11.8/9.8
..3..6.8....1......9..7...4...8..6..3...4...2.....5.1...2.9...373.......94....5.. ED=11.8/11.8/3.4
.2.4..7...57..9.3.6...7......5..8.9.7...2.....4.6..3.......1..85......1...1...9.3 ED=11.8/11.8/11.2
..34.........8...668..7.1.....5....1.9..1.6.......2..4..5.....28.....96.97.....1. ED=11.8/11.8/2.6
.2.....8..56.....17...3.5.......49....5.9....9..3.7...5...7.4.....8...52.1.....6. ED=11.8/11.8/11.3
....5...9...7...3..8...1......3...7...8..24..6...9...5..2....548....42...14...... ED=11.8/11.8/9.7
.2...67..4...8......9.......3.....7.5.8...34..1.3....2....9..5....6.1..3...2..6.7 ED=11.8/11.8/2.6
1...5.7....7.....6.8...7.4....9..3...6...4..7..8....2.5..3.....8...9.1....2..8.7. ED=11.8/11.8/2.6
.2.4....9..7....3.6...7.1...4......87.....5....5.1..6.3...6..5......8..2...9..... ED=11.8/11.8/10.7
...4....9.....9.327...3.5..2......6...1.....8.3....25...41.8...6.........1.9.4... ED=11.8/11.8/2.6
....5..8....1.9..6...3..1.4.3...14..5......2...8.......9..1.....6.9..3..8.2.73... ED=11.8/11.8/7.6
.2.4.6.89...1..2.6.6...214.....61..4...9.8.12...24..6.57......8.......919..8.4... ED=11.8/11.1/3.4
..3.567.9..71.9.63...73.15..3.51.69.....93......6.73.........1..7..6....84....5.. ED=11.8/11.8/3.4
1.3...7.9.57..9.3669....51.....4.....3..21.........1.336.....51.7.5..96.9.5...3.7 ED=11.8/11.8/9.3
..3..6.894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267.... ED=11.8/11.1/3.4
..3..6.894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267...1 ED=11.8/10.9/3.4
..3..6.894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267...1 ED=11.8/10.9/3.4
..3....894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267...1 ED=11.8/11.0/3.4
1...567.9...1.926.6..27..51...91...5.1.5.792.....62.17.34....7.......5...6....... ED=11.8/11.8/9.3
....5678....78.1.3...1.3.65...3.8.515...1.8.68..56.37........17.7..3....9.2....3. ED=11.8/11.8/10.5
1.3.56....5718....68.3.75.........9..3....12.....31...37.81....8.5.63....6.7.5..8 ED=11.8/11.8/9.6
....5678....78.1.3...1.3.65...3.8.515...1.8.68..56.37........17.7.......9.2...... ED=11.8/11.0/10.5
....5678....78.1.3...1.3.65...3.8.515...1.8.68..56.37........17.7.......9.2....3. ED=11.8/10.6/10.4
12..56....571.9..66.927...127.69.....917.5.....6.12.9.......8.2...5...........3.5 ED=11.8/11.8/2.6
1.3..678..57....3686...71.5.......5...86........92....6.1...5.773....8...857...13 ED=11.8/11.8/9.6
12..56....571.9..66.927...127.69.....9.7.5.....6.12.9.......8.2...5...........3.5 ED=11.8/2.0/2.0
12..56....571.9..66.927...127..9.....917.5.....6.12.9.......8.2...5...........3.5 ED=11.8/8.4/2.6
1...5678....18..36...3.75.1...8.1.75.7..35.6...576.8..34....6.....6.3....9....... ED=11.8/11.8/6.6
1..4.678.4..18..36....371.4........7.1...8....95...4.....86..7.....1364..6.7.4..3 ED=11.8/11.8/6.6
12..56....5718.2..6.87.21..2.5.17....7.6.5.2...682.........8.1.7......93.6....... ED=11.8/11.8/6.6
.2345....45.7.9...7.9.32.....5...8.6374...........5.7.53...42...4259....9.72.3... ED=11.8/11.8/2.6
..3.........1.9.3....7..4.5..5.6..787.6...3.48...7.56.36.....575.46..8.3.8....64. ED=11.8/11.8/7.1
1..4.678.4..18..36....374.1........7.4...8....95...1.....86..7.....4361..6.7.1..3 ED=11.8/11.8/6.6
12.4.6...4.6.89....9821....2.4.6...1.89.21...61.8.4.......4.9...4.....57962...... ED=11.8/11.8/2.6
12..56....571.92..6.972.1..2.5.71....7.56...2..69.2.......9...17......38.6....... ED=11.8/11.8/6.6
12.4.6...4.6.89....9821....2.4.6...1.89.21...61.8.4.........9...4.....57962...... ED=11.8/11.1/2.6
..3.........1.9.3....7..4.5..5.7..687.6...3.48...6.57.36.....575.46..8.3.8....64. ED=11.8/11.8/7.1
.2345....45.7.9...7.9.32.........8.6374.............7.53...42...4259....9.72.3... ED=11.8/11.0/2.6
.2345....45.7.9...7.9.32.....5...8.6374.............7.53...42...4259....9.72.3... ED=11.8/11.1/2.6
..3.......5.1.9.3....7..4.5..5.6...87.6...3.48...7.56.36.....575.46..8.3.8....64. ED=11.8/7.1/7.1
...4.6.....7....36.......5.24.6.7...7.8.14..2.6182......274.1...14.68...87.2.1... ED=11.8/11.8/9.3
12.4.6...4.6.89....9821....2.4.6...1.89.21...61.8.4.........9.........57962...... ED=11.8/11.0/2.6
1..........6........8....4..1.59.3.7.7.3.1.94.3..4751.....759.....9.4.73...13.45. ED=11.8/10.2/2.6
1..........6........8....4..1.59.3.7.753.1.94.3..4751.....759.....9.4.73...13.45. ED=11.8/11.8/2.6
...4.....4...89..6......14523....46..65....13..4.6.5.23.6....5451....62..42...3.1 ED=11.8/11.8/2.6
...4..7..4.......2.......46.3.1.5....41.97...9.534....3.497..5159..14.7..175.3... ED=11.8/11.8/10.4
...4.....4...89.36......14523....46..65....13..4.6.5.23.6....5451....62..42...3.1 ED=11.8/11.8/2.6
............1.9.3....37.5.4.6......75.4...6.887..6.3..34.....657.56..8.3.865..47. ED=11.8/7.2/3.4
..........5.1.9......37.5.4.6......75.4...6.887..6.3..34.....657.56..8.3.865..47. ED=11.8/10.5/3.4
...4.....4...89.........14523....46..65....13..4.6.5.23.6....5451....62..42...3.1 ED=11.8/11.0/2.6
12..56....571.9...6.972....2.169.....95.17...76...2.9.572..............5......34. ED=11.8/10.4/2.6
...4.....4...89.3.......14523....46..65....13..4.6.5.23.6....5451....62..42...3.1 ED=11.8/11.0/2.6
12..56....571.9...6.972....2.169.....95.17...76...2.9.572..............5.1....34. ED=11.8/11.8/2.6
...4.....4...89.........51423....64...4.6..53.65...1.23.2...4.151....36..46....25 ED=11.8/11.0/2.6
...4.....4...89..6......51423....64...4.6..53.65...1.23.2...4.151....36..46....25 ED=11.8/11.8/2.6
...4.....4...89.3.......51423....64...4.6..53.65...1.23.2...4.151....36..46....25 ED=11.8/11.0/2.6
...4.....4...89.36......51423....64...4.6..53.65...1.23.2...4.151....36..46....25 ED=11.8/11.8/2.6
1..4.........8.......2......1..3..5636....87.5.7...1.36.13..5.883...5.67.75..831. ED=11.8/11.0/10.5
1..4.........8.......2......1..3..5636....87.5.7...1.36.13..5.883...5.67.756.831. ED=11.8/11.1/10.4
1..4.........8.......2......1..6..5336....87.5.7...1.66.13..5.883...5.67.756.831. ED=11.8/11.1/10.4
1..4.........8.......2......1..6..5336....87.5.7.3.1.66.13..5.883...5.67.756.831. ED=11.8/11.8/10.6
..3..6......1...3.9...7...42.....84..4..9...7..5....6........1..7..2...88.....4.2 ED=11.8/11.8/10.0
.2.....894......3...9.7.5......6.9..3.......2.8...2.4...16......7..1..9....5..1.. ED=11.8/11.8/2.6
.2......94...8.1....9.....6....483....16...97....1..6.3....1...5....4....72...... ED=11.8/11.8/2.6
.....6.8..5.1....3..9....4.2.......553..7......8...4......64...71.23...4...7....2 ED=11.8/11.8/2.6
......7..4......23..8...5.4.1..9....3.5..8....6.1..3.....97.6......1.97......2..5 ED=11.8/11.8/2.6
..3....894.....2...89.....1.3...1..57..52.....9...3......7..6.2........8....6.54. ED=11.8/11.8/2.6
1......89........3..8...56..7..4...66.91......4...2......5...9......43.2....23..7 ED=11.8/11.8/2.6
1.....7.9..6...12........4.2.7.6.....3...8.7..8.5........8.4.5.....2.9.......5.34 ED=11.8/11.8/2.6
.23.5...9.571.....8....3.....97....5......8......654..3....4.6..1.5....2....1.... ED=11.8/11.8/2.6
1.....78...6.8...278.....5..1.9...7...4..2.......6.......5....7....24..3.9.8..5.. ED=11.8/11.8/2.6
12..56..9.571.9..66.927...52.....3........8.........5..7259......16.7...96..12... ED=11.8/10.2/2.6
12..567.9.571.9..66.927...52.....3........8.........5..7259......16.7...96..12... ED=11.8/11.8/2.6
...45.7.9..71.92....9.72.51.1.5.79.474.29.51.9...41.723..........4......89.....2. ED=11.8/11.8/10.5
.234..7.94..............154...51.87.....479.5...9.8.41...87.49.....95.17.7...45.8 ED=11.8/11.8/2.6
..34.6.8.4.7.89...68.73.....68.4397.73.69.84.9.48.76..........8.......2..7.....5. ED=11.8/11.8/2.6
..34.678...718..638.6.371.4.8..143.6...76.81....3.8.4.5.......1.7.......9........ ED=11.8/11.8/2.6
..34.6...4.7.89...68.73..4..68.439..73.69.8.49.48.76.........9.........2.7......5 ED=11.8/11.8/2.6
..34.6...4.7.89...68.73.....68.439..73.69.8.49.48.76.........9.........2.7......5 ED=11.8/11.8/2.6
..34.678...718..638.6.371.4....143.6...76.81....3.8.4.5.......1.7.......9........ ED=11.8/11.8/2.6
..34.678...718..63..6.371.4....143.6...76.81....3.8.4.5.......1.7.......9........ ED=11.8/10.2/2.6
..34.6...4.7.89...68.73.....68.439..73.69.8..9.48.76.........9.........2.7......5 ED=11.8/10.2/2.6
..34.6.8.4.7.89...68.73.....68.439..73.69.84.9.48.76..........8.......2..7.....5. ED=11.8/10.4/2.6
.234....94..............154...51.87.....479.5...9.8.41...87.49.....95.17.7...45.8 ED=11.8/10.4/2.6
.23......4..............451...54.87.....179.5...9.8.14...87.19.....95.47.7...15.8 ED=11.8/10.2/2.6
.23.....94..............451...54.87.....179.5...9.8.14...87.19.....95.47.7...15.8 ED=11.8/11.8/2.6
...45.7.9..71.92....9.72.51.1.7.59.474.29.51.....41.723..........4......8......2. ED=11.8/11.7/10.6
...4..7..4.......2.......46.17.94.5.3.4....9159.1.3....3..15....419.7...9.534.... ED=11.8/11.8/2.6
...4..7..4.......2.......46.17.94.5.3.457..9159.1.3....3..1.....419.7...9.534.... ED=11.8/2.0/2.0
....5.......1.9.3....37.5.4.6......75.4...6.887....3..34.....657.6...8.3.8.6..47. ED=11.8/10.6/3.4
....5.......1.9......37.5.4.6......75.4...6.887..6.3..34.....657.6...8.3.8.6..47. ED=11.8/11.1/3.4
.23.....94....9.........451...54.87.....179.5...9.8.14...87.19.....95.47.7...15.8 ED=11.8/11.8/2.6
............1.9.3....37.5.4.6......75.4...6.887..6.3..34.....657.65..8.3.856..47. ED=11.8/7.2/3.4
1.3.567...5718..3.68.3.7................78.61...6..42.51..6...37.8.35....3...1... ED=11.8/7.2/3.4
1.3.567...5718..3.68.3.7................78.61.7....42.51..6...37.8.35....3...1... ED=11.8/10.6/3.4
..........5.1.9......37.5.4.6......75.4...6.887..6.3..34.....657.65..8.3.856..47. ED=11.8/10.5/3.4
1.3.56....5718..3.68.3.7................78.61.7....42.51.76...37.8.35....3.8.1... ED=11.8/10.6/8.8
..........5.1.9......37.5.4.6.....575.4...6.887..6.34.34.....657.6...8.3.856..47. ED=11.8/10.6/8.8
1.3.56....5718..3.68.3.7.................8.61.7.6..42.51.76...37.8.35....3.8.1... ED=11.8/11.0/10.3
..........5.1.9.3....37...4.6.....575.4...6.887..6.34.34.....657.6...8.3.856..47. ED=11.8/10.6/10.3
............1.9.3....37.5.4.6.....575.4...6.887..6.34.34.....657.6...8.3.856..47. ED=11.8/7.2/7.2
1.3.56....5718..3.68.3.7................78.61...6..42.51.76...37.8.35....3.8.1... ED=11.8/7.2/7.2
....5.....5.1.9.3....37.5.4.6.....575.4...6.887....34.34.....657.6...8.3.856..47. ED=11.8/10.5/9.4
....5.....5.1.9......37.5.4.6.....575.4...6.887..6.34.34.....657.6...8.3.856..47. ED=11.8/10.6/8.8
....5.......1.9.3....37.5.4.6.....575.4...6.887....34.34.....657.6...8.3.8.6..47. ED=11.8/10.6/9.4
....5.......1.9......37.5.4.6.....575.4...6.887..6.34.34.....657.6...8.3.8.6..47. ED=11.8/11.0/9.0
1.3.56.8..5718..3.68.3.7................78.61.7....42.51..6...37.8.35....3...1... ED=11.8/10.5/3.4
..........5.1.9......37.5.4.6......75.4...6.887..6.3..34.....657.6..48.3.856..47. ED=11.8/10.6/3.4
1.3.56.8..571...3.6..3.7................78.61...6..42.51..6...37.8.35....3...1... ED=11.8/7.2/2.6
............1.9.3....37.5.4.6......75.4...6.887..6.3..3......657.6..48.3.856...7. ED=11.8/7.2/2.6
..........5.1.9.3....37.5.4.6......75.4...6.887..6.3..3......657.6..48.3.856...7. ED=11.8/7.2/2.6
1.3.56.8..571...3.6..3.7................78.61.7.6..42.51..6...37.8.35....3...1... ED=11.8/7.2/2.6
..34.6.8.4.7.89...68.73.....68.4397.73.89.64.9.46.78..........8.......2..7.....5. ED=11.8/11.8/2.6
..34.6.8.4.7.89...68.73.....68.439..73.89.64.9.46.78..........8.......2..7.....5. ED=11.8/10.4/2.6
...4.678....18.2.6....72.14.19...6......21.....5..........68...7..2.48....271.46. ED=11.8/11.8/3.4
..34.6...4.7.89...68.73.....68.439..73.89.6..9.46.78.........9.........2.7......5 ED=11.8/10.2/2.6
..34.6...4.7.89...68.73.....68.439..73.89.6.49.46.78.........9.........2.7......5 ED=11.8/11.8/2.6
..34.6...4.7.89...68.73.....68.479..73.89.6.49.46.38.........9.........2.7......5 ED=11.8/11.8/2.6
..34.6...4.7.89...68.73..4..68.439..73.89.6.49.46.78.........9.........2.7......5 ED=11.8/11.8/2.6
..34.6...4.7.89...68.73.....68.479..73.89.6..9.46.38.........9.........2.7......5 ED=11.8/10.2/2.6
..34.6...4.7.89...68.73..4..68.479..73.89.6.49.46.38.........9.........2.7......5 ED=11.8/11.8/2.6
12..5..........2.66...3....2.....8.7.8.....24.7....16.76..24...8.4..16.2.12..847. ED=11.8/11.8/2.6
.2345...945...92.36.9......2..6.5.9...592....9.6.34.2.364.......9....1.8......... ED=11.8/11.8/2.6
...4.6...4...8923.9.832...4.8.6.49.3.....284..4.8...625.1.4................963... ED=11.8/11.8/2.6
.....6.8...6...1.2...2....4.3...75..5...9......85...1...28...4..7..3....9....5... ED=11.8/11.8/11.3
1......89....8.12.......5..2...9...8.7...4.....53.......4..7....3.5.....9...1..6. ED=11.8/11.8/10.8
....567.9.5.78..3.7..1.......5.4....3.8....4..4....2.....9..6........3.1.3..2..5. ED=11.8/11.8/10.0
...4....9....8...6.....215.2....7.1...9.4....71.......53.....7..7...3.....6...3.8 ED=11.8/11.8/2.6
..3....894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267.... ED=11.8/11.1/3.4
.2.4.6.89...1..2.6.6....14.....61..4...9.8.12...24..6.57.....28.......919..8.4... ED=11.8/10.5/3.4
.2.4.6.89...1..2.6.6...214.2...61..4...9.8.12...24..6.57......8.......919..8.4... ED=11.8/11.0/3.4
.2.4.6.89...1..2.6.6...214.....61..4...9.8.12...24..6.57.6....8.......919..8.4... ED=11.8/11.1/3.4
.2.4.6.89...1..2.6.6...214.2...61..4...9.8.12...24..6.57.6....8.......919..8.4... ED=11.8/10.9/3.4
.2.4.6.89...1..2.6.6....14.....61..4...9.8.12...24..6.57.6...28.......919..8.4... ED=11.8/10.4/3.4
.2.4.6.89...1..2.6.6...214.2...61..4...9.8.12...24..6.57.....28.......919..8.4... ED=11.8/11.0/3.4
1..4.........8.......2......3.....565.7...1.361....87.3.16.75.886...5.17.75..836. ED=11.8/11.8/2.6
.2.4.6.89...1..2.6.6...214.2...61..4...9.8.12...24..6.57.6...28.......919..8.4... ED=11.8/11.6/3.4
1..4.........8.......2......3.....565.7...1.361....87.3.1..75.886...5.17.75..836. ED=11.8/10.2/2.6
1.3....894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267...1 ED=11.8/11.0/3.4
1.3....894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267.... ED=11.8/11.1/3.4
1.3..6.894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267.... ED=11.8/11.2/3.4
1.3..6.894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267...1 ED=11.8/11.6/3.4
12....7.9.56...12.7.9....65...3.8.9........17.9..7.....1.5..6.256.2..97.9.2....51 ED=11.8/11.8/10.2
12....7.9.56...12.7.9....65...3.8.9........17....7.....1.5..6.256.2..97.9.2....51 ED=11.8/10.6/10.4
12....7.9.56...12.7.9....65...3.8..........17....7.....1.5..6.256.2..97.9.2....51 ED=11.8/10.6/10.5
......7.....1.9.36....3.4.52.6.......193.2...73.6......7..61.2..629.3.7...172.... ED=11.8/2.0/2.0
..3...7.....1.9.36....3.4.52.........193.2...73.6......7..61.2..629.3.7...172.... ED=11.8/9.1/3.4
....567..4..........932.....74..59.886.....759.....46..4.....97....9.8.4.98...65. ED=11.8/3.4/3.4
..3.........1.9.36...7..4.5..5.6..787.6...3.48...7.56.36.....575.46..8.3.8....64. ED=11.8/11.8/7.1
....567.94..........932.....74..59.886.....759.....46..4.....97....9.8.4.98...65. ED=11.8/3.4/3.4
...4.6.....7....36.......5.24...7.1.7.8.14..2.6182...4..274.1...14.68...87.....4. ED=11.8/7.1/7.1
..3.........1.9.36...7..4.5..5.7..687.6...3.48...6.57.36.....575.46..8.3.8....64. ED=11.8/11.8/7.1
..3.......5.1.9.3....7..4.5..5.7..687.6...3.48...6.57.36.....575.46..8.3.8....64. ED=11.8/11.8/7.1
...4.6.....7....36.......5.24...7.1.7.8.14..2.6182......274.1...14.68...87.....4. ED=11.8/7.1/7.1
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Re: The hardest sudokus (new thread)

Postby Paquita » Mon Aug 19, 2024 4:10 pm

Yes and these are also B10B, at least the first 3 - still calculating

1...567....718....68.3.75.........4.36....8.7........251..3....7.8.65....368.1..5
1...567...5.18....68.3.75.........4.36....8.7........251..3....7.8.65....368.1..5
....567....718....68.3.75.........4.361...8.7........251..3....7.8.65....368....5
....567...5.18....68.3.75.........4.361...8.7........251..3....7.8.65....368....5

when it is done I will post an update in het BxB thread
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Re: The hardest sudokus (new thread)

Postby m_b_metcalf » Mon Aug 19, 2024 7:24 pm

Note that two of your puzzles can be morphed into anti-diagonal symmetrical patterns. They would have been ideal for the ill-fated Patterns Game!

Code: Select all
 . . 8 5 . . . . 1
 3 . . . . . 9 . .
 . 6 . . . . . 4 .
 . . . . . 6 . . .
 . . 7 1 8 . . . .
 . . . . 2 . . . 5
 . . 2 . 7 . . . 8
 9 . . . . . 3 . .
 . 4 . . . . . 6 .

 . 2 . 4 . . . . 9
 6 . . . 7 . 1 . .
 . . 7 . . . . 3 .
 . . . 9 . . . . .
 3 . . . 6 . . 5 .
 . . . . . 8 . . 2
 7 . . . . . 5 . .
 . 4 . . . . . . 8
 . . 5 . 1 . . 6 .


Regards,

Mike
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Re: The hardest sudokus (new thread)

Postby m_b_metcalf » Tue Aug 20, 2024 12:10 pm

m_b_metcalf wrote:Note that two of your puzzles can be morphed into anti-diagonal symmetrical patterns. They would have been ideal for the ill-fated Patterns Game!

It turns out that first of these patterns did appear in the Patterns Game, #169.

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Re: The hardest sudokus (new thread)

Postby Paquita » Thu Aug 22, 2024 7:36 pm

Nice!

Sorry I don't have records of the Patterns Game puzzles.
More and more a proper database of what puzzles are known, is missed - at least by me.
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Re: The hardest sudokus (new thread)

Postby eleven » Fri Aug 23, 2024 8:39 pm

If a solver knows the tridagon pattern, the list contains trivial puzzles like this one
Code: Select all
..3..6.894.7..........23..427..6..1.3.4.12.6..16..7...6..2.1...7.1.34.....267....

and extremely hard ones like the two shown by Mike.
Same old story.

[Added:] Note: if the only givens of 2 digits are in the same box - and one is missing, check for a tridagon in the opposite boxes (those not in the same band/stack).
In the sample:
Code: Select all
+-------+-------+-------+
 | . . 3 | . . 6 | . 8 9 |
 | 4 . 7 | . . . | . . . |
 | . . . | . 2 3 | . . 4 |
 +-------+-------+-------+
 | 2 7 * | . 6 ° | . 1 . |
 | 3 * 4 | ° 1 2 | . 6 . |
 | * 1 6 | . x 7 | . . . |
 +-------+-------+-------+
 | 6 . ° | 2 * 1 | . . . |
 | 7 ° 1 | * 3 4 | . . . |
 | ° . 2 | 6 7 * | . . . |
 +-------+-------+-------+

5 not given, 8 and 9 are only given once in box 3. Now look at boxes 4578:
You immediately have 589 candidates in boxes 48, and also in the diagonal cells of box 7. In box 5 in r4c6 and r5c4 (all seeing 123467). These cells have (only) one rectangle (r58c24). So r6c5 cannot be 589 and must be 4.
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Re: The hardest sudokus (new thread)

Postby mith » Thu Oct 10, 2024 3:47 pm

eleven wrote:[Added:] Note: if the only givens of 2 digits are in the same box - and one is missing, check for a tridagon in the opposite boxes (those not in the same band/stack).


I have a script which does this (for the T&E(3) database), it would be easy enough to run this on the high SER puzzles to filter them like this.

@Paquita (or anyone else), do you have a full list of puzzles posted here (since ph2010, or since my last file postings, or whenever). Hoping to *finally* get some scripts running again and would like to make sure I'm not missing anything, if that list already exists that would be great (if not I'll get back to work on my scraper).
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Re: The hardest sudokus (new thread)

Postby ag24ag24 » Thu Oct 17, 2024 6:19 pm

I decided I was duty-bound to work my way through all 119 pages of this thread before bothering the group with any more questions, which I've now done. My main one is: I'm interested to understand why the focus here regarding T&E, BpB etc is all on Singles as the resolution theory. Has this group ever explored (perhaps in a different thread that I haven't found) using a richer resolution theory - "basics", or perhaps basics plus X-wings and fishes so as to preserve isomorphism? If so, what has been found? - for example, what proportion of puzzles that are in T&E(Singles,2) are in T&E(T,1) for such richer T's? My main reason for asking is that I've developed a reasonably concise resolution theory that I think may be of interest because of its power given its simplicity, and which I'm in the process of developing into a reasonably efficient solver.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Fri Oct 18, 2024 3:11 am

ag24ag24 wrote:I decided I was duty-bound to work my way through all 119 pages of this thread before bothering the group with any more questions, which I've now done. My main one is: I'm interested to understand why the focus here regarding T&E, BpB etc is all on Singles as the resolution theory. Has this group ever explored (perhaps in a different thread that I haven't found) using a richer resolution theory - "basics", or perhaps basics plus X-wings and fishes so as to preserve isomorphism? If so, what has been found? - for example, what proportion of puzzles that are in T&E(Singles,2) are in T&E(T,1) for such richer T's? My main reason for asking is that I've developed a reasonably concise resolution theory that I think may be of interest because of its power given its simplicity, and which I'm in the process of developing into a reasonably efficient solver.

Hi ag24ag24
Welcome on this forum
You are asking interesting questions, but what you are suggesting has not been done on a large scale or in a systematic way. About proportions, we have no unbiased collection for T&E(2) puzzles, so any stats based on the existing collections will be biased.
We do have unbiased stats for all the puzzles (based on the controlled-bias collection (https://github.com/denis-berthier/Controlled-bias_Sudoku_generator_and_collection).One point to remember is, statistically, adding specific patterns such as whips[1], Subsets...., to the Singles used in the basic B rating doesn't change much the results.

T&E(Singles, n) is canonical in some obvious way. There's no particular reason to choose any other T (with the confluence property) and to use T&E(T, n) instead. As for BxB, it's meaningful only within T&E(Singles, 2). Of course, one could introduce a B'xB' sub-classification of T&E(T, 2), but I can't see any advantage to it.
One case that might be of interest is T=W1. This would lead to the gT&E(n) and the gBxB classifications.

Even if they are not classified as you'd like, you can always use the existing puzzle collections to explore your questions. SudoRules allows to do any T&E(T, n) computations, so that you can compare with the results of your software.
.
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Re: The hardest sudokus (new thread)

Postby ag24ag24 » Fri Oct 18, 2024 7:34 pm

Hello Denis - many thanks for your reply. My real name is Aubrey de Grey, by the way.

I had not known that SudoRules can work with any resolution theory. That's terrific. Does Cordoliani's SHC also have that ability? - I have read the documentation at your github page and it doesn't seem to say. If it doesn't, what is currently the best place to download SudoRules?

I don't really agree that there's no particular reason to study any other T. My logic is as follows.

- Since there are finitely many pencil-marked grids (PMGs), resolution theories (RTs) exist that are "omnipotent", i.e. with respect to which all PMGs are in T&E(0).

- The most simplistic omnipotent RT (ORT) is one that simply maps every possible PMG separately to the elimination of some candidate that is not in its solution. But since that would be rather unwieldy, a noble goal is to find a maximally concise ORT. I view this as the Holy Grail of Sudoku research (though I of course appreciate that the field has plenty of other noble goals!).

- Every partial, i.e. non-omnipotent, RT (PRT) corresponds to an ORT that is more concise than the simple-mapping ORT, since it reduces the number of cases to the number of PMGs that the PRT cannot derive any elimination from. I say that such a PMG "resists" the PRT, and that a PMG from which the PRT can derive an elimination is one that "yields" to that PRT. Let us define the power of a PRT T as the proportion of all possible PMGs that yield to T (i.e., its conciseness) minus some natural measure of T's own complexity. One can then view the hardness of a PMG as the greatest power of a PRT that it resists.

- We then have two (alternating) challenges in the (possibly endless!) quest for the Holy Grail: to identify increasingly powerful PRTs, and to identify PMGs that resist them.

- My claim is that, independently of being inherently distasteful as a solving strategy, T&E actively hinders these efforts, and thus that there is value in studying PRTs that minimise the need for T&E (which means more powerful PRTs). Essentially, a puzzle that is in T&E(T,2) for some PRT T is equivalent to a pair of PMGs that both resist T and that happen to be ordered by inclusion (i.e. each cell of the second PMG has only candidates that are also in the same cell of the first PMG). I don't see that this constitutes a reason to expect such a puzzle to be more informative than one that is in T&E(T,1) and thus leads to only one T-resisting PMG. As far as I can see, all that really matters is which PMGs are T-resistant and which are not. I think the tridagon saga circumstantially supports this claim: the fact that tridagons took so many years to be discovered tells me that searching for hard sudokus needs some new ideas.

- If that claim is true, we face the question of what metric to use for vicinity search (hill-climbing) to identify PMGs that are "informative", i.e. that give hints about the possible nature of more powerful PRTs. I suspect that the best such metrics will actually be RT-agnostic in some fundamental sense, but will highlight the boundary between resistance and yielding for any given RT T. For example, one might rank T-yielders by how "close" they are to being T-resistant - in how many alternative ways one can add a single candidate and thereby make the PMG T-resistant but still valid (so the reverse of T&E, in a sense) - and focus the design of more powerful PRTs on ones to which a lot of such derived PMGs yield.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Sat Oct 19, 2024 3:22 am

ag24ag24 wrote:I had not known that SudoRules can work with any resolution theory. That's terrific. Does Cordoliani's SHC also have that ability? - I have read the documentation at your github page and it doesn't seem to say. If it doesn't, what is currently the best place to download SudoRules?

The only place to download CSP-Rules is on GitHub:https://github.com/denis-berthier/CSP-Rules-V2.1. SudoRules is a part of it. Be aware that CSP-Rules was not designed to deal with procedural techniques such as T&E and it is very slow for them, especially T&E(T, n) for large n or complex T.
SHC deals only with T&E(Singles). Its only goal is to compute the T&E-depth, and the B, BxB and BxBB classifications. It's mainly used as a tool in the search for the hardest puzzles.

ag24ag24 wrote:I don't really agree that there's no particular reason to study any other T.

Actually, I've also studied T&E(T) when T is a braid resolution theory. This leads to the BxB sub-classification of T&E(2).
All the puzzles in T&E(1) can be solved by braids, all the puzzles in T&E(2) can be solved by B-braids. Beyond, one can define much more complex chains but they will be illegible. These results are universal (for any finite CSP).
All the details are in [PBCS]: https://www.researchgate.net/publication/356313228_Pattern-Based_Constraint_Satisfaction_and_Logic_Puzzles_Third_Edition

I don't see how any "omnipotent" theory could bypass the (now standard) T&E-depth question.
.
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