# 1 to 12 and 15, 16 are in T&E(3)
# 13 and 14 are in B5B
the rest is in B6B
The hardest sudokus (new thread)
Re: The hardest sudokus (new thread)
by denis_berthier » Thu Nov 16, 2023 4:34 am
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Re: The hardest sudokus (new thread)
by P.O. » Thu Nov 16, 2023 9:30 am
the template classification for these puzzles, in parentheses is the number of time the highest combination has been done
- Code: Select all
from GP/champagne dry to eleven/Imam_bayildi : 5(3) 5(2) 5(3) 5(3) 5(2) 5(2) 4(4) 5(1) 5(3)
from 26c mith/Loki to new twin max-expand : 4(1) 4(1) 3(4) 3(4) 4(1) 4(1) 4(1) 4(1) 4(1) 4(1) 4(1)
all the others are <= 4-template
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Re: The hardest sudokus (new thread)
by Paquita » Sat Nov 25, 2023 1:35 pm
A bit late but Mith, I wish you a good recovery
I have posted a new file of T&E(2) puzzles here https://drive.google.com/file/d/1NfHZByy-v9oNB64b4CzocztH_eRw3d0H/view?usp=sharing
I have posted a new file of T&E(2) puzzles here https://drive.google.com/file/d/1NfHZByy-v9oNB64b4CzocztH_eRw3d0H/view?usp=sharing
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Re: The hardest sudokus (new thread)
by Paquita » Sat Nov 25, 2023 9:58 pm
Coloin
of your list of 34 I count 28 different puzzzles (6 doubles a you can see after maxlexing them)
of your list of 34 I count 28 different puzzzles (6 doubles a you can see after maxlexing them)
- Code: Select all
98.76.5..7.4.5......6......5.8..7.4..79.45.6..6.98.......8.........9.3.2......4..
98.76.5..7.4.5......6......5.8..7.4..7..45.6..6.98.....9....4.....8.........9.3.2
98.76.5..7.5.498...465......984.6.7...795........8.....6.........4....32.......5.
98.76.5..7.5..98...465......984.6.7...795........8.....6.........4....32.....4.5.
98.76.54.7.5.......6.9..7..89....6..5.6....87.47...95.4.8..........384......2....
98.76.54.7.5.......6.9..7..89....6..5......87.47..695.4.8..........384......2....
98.76.5..7.59.4....46.859..56.......4.78.6.5..98.........6.7......4...32.......9.
98.76.5..7.59.4.....6.859..56.......4.78.6.5..98........4....9....6.7......4...32
98.76.54.7.5.......6.8..7..8.....6..5.6....97.47...85.4.9..........394......2....
98.76.54.7.5.......6.8..7..8.....6..5......97.47..685.4.9..........394......2....
98.76.5..7.54.98...64..5....96.......4.....32.......8..79.46.5....95.......8.7...
98.76.5..7.5..98...64..5....96.......4.....32.....4.8..79.46.5....95.......8.7...
98.76.5..7.5..9....64.58...8.....4.....9...........32.6.8..5..4.7.64.....498.7..5
98.76.5..7.5.496....45.8...64.......5.869.....798.4.6..9.....5......7..........32
98.76.5..7.4.5......6......6..89....5.8..7.4..79.45.6....9.........8.3.2......4..
98.76.5..7.5.498...648......9..87....574.6.9.....5.....4.....32..6.............8.
98.76.5..7.5.84.....69.....8.7.5..6.46..79.8..5........94..........9.4.3........2
98.76.5..7.5..8....649......9748..6..5.6.9.8.....5.....7....4.3....74...........2
98.76.5..7.6..49...458......784.6.9...95.........98....64...........7.5........32
98.76.5..7.5.......465.....8..9.6.5..7.48......9.75.4.6.....4.....89..........3.2
98.76.54.7.58..6...6.......5.6...79.47....8.5..8....64.49..........394......2....
98.76.54.7.58..6...64......5.6...79..7....8.5..8....64.49..........394......2....
98.76.54.7.58..6...46......5.9...76..7....8.5.68....94.94..........394......2....
98.76.5..7.5.946....45.8...64.......5.96......784.9.6..9.....5....8.7..........32
98.76.54.7.54..9...4.......69.5.7....54.86.....794.....68.........6...38.......2.
98.76.5..7.54..9...4.......69.5.7.4..54.86.....794.....68.........6...83........2
98.76.54.7.54..9...46......8.794.....9.5.7....54.86....68.........6...38.......2.
98.76.5..7.58.49...64.5.....76.48.9...957.......9.6....48...........7.5........32
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Re: The hardest sudokus (new thread)
by Paquita » Sat Nov 25, 2023 10:00 pm
Congrats for finding some new 11.9
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Re: The hardest sudokus (new thread)
by coloin » Sun Nov 26, 2023 1:00 am
Paquita wrote:of your list of 34 I count 28 different puzzzles
Thanks - You are correct and I have corrected the post
I included a duplicate of one of the max-expands.
But checking the other puzzles I realized thati had missed some other max-expands
However I dont think that they are truely "new" puzzles in the solving/rating sense. Although some twin max-expands do minimize differently.
I think all the puzzles originating from a max-expand have the same solving state [pencil mark grid of the max-expand]
And all the twin max expands have this solving state. see here
I have looked through many of the posts in this thread files for all the true 11.8s that I could find.
A true 11.8 perhaps may be considered if the puzzle rates by SE or PGExplainer as 11.8 either in the minlex puzzle [sic] or the minlex solution grid. [concordence for both is over 95 %]
I only found 274 different max-expand puzzles [expanded up to pearl SE 11.8/11.8/*.*] [ I realize this is different from expanding to a similar T&E level]
The first 67 max-expands 11.8s have 24 clues or less and are different beasts - not having the Thor's hammer pattern prominent.
On looking at the remaining 11.8 max-expand puzzles its clear that there are twin puzzles in this list - and these were all found .
These 207 max-expands have between 27-34 clues and all rate 11.8 [ though some new twins strangely get downgraded to a 11.7].
In total there over 1750 different minimal puzzles - all potentially 11.8 although i have notiiced a few which degenerate to 11.7
Will publish when rating has been completed.
These twin puzzles occur because there are UAs in the clues of the puzzle - as noted by 999_springs and others.
A partial max-expand up to SE *.*/*.*/2.6 can be accomplished easily with gsf's program [-E] funtion [ sudoku64 -E file.txt > fileexpand.txt]
The problem with a neighbourhood search is that we walk through the minimal puzzles of
1. the same solution grid or 2. a neighbouring twin puzzle solution grid.
With the number of clues of these puzzles above 25 a {-1+1} is doable but a {-2+2} is swamped !!!
The use of T&E2/T&E3 filtering is I am sure ongoing - but finding actual new 11.8 puzzles is extremely difficult. !!!!
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Twin puzzle 11.9 with 5 max expands
by coloin » Tue Nov 28, 2023 3:23 pm
I Thought I should expand more on the finding of these probably new 11.9s
They are a long distance away from the initial puzzle - and so they wernt going to be found with a neighbourhood search
the converse puzzle is
and it has 5 solutions
manual extraction gives these puzzles - all with the same pattern.
PM grid of #1 and #4 [identical pencil marks]
the 348 cant go into r5c9 - so it has to be 6@r5c9. All 5 puzzles have this PM grid and hence the same initial step and should have the same rating.
They are a long distance away from the initial puzzle - and so they wernt going to be found with a neighbourhood search
- Code: Select all
1...567.9...1.926.6..27..51...91...5.1.5.792.....62.17.34............5...6.7.....## ED=11.9/11.9/9.3 Penta1 max-expand
the converse puzzle is
- Code: Select all
.234...8.457.8...3.89..34..276..834.3.8.4...69453..8..5..891672791624.388.2.35194
and it has 5 solutions
- Code: Select all
123456789457189263689273451276918345318547926945362817534891672791624538862735194
123456987457189263689273415276518349318942756945367821534891672791624538862735194
123467985457189263689253417276518349318942756945376821534891672791624538862735194
123476985457189263689253417276518349318942756945367821534891672791624538862735194
623459781457186923189273465276518349318947256945362817534891672791624538862735194
x...xxx.x...x.xxx.x..xx..xx...xx...x.x.x.xxx.....xx.xx.xx............x...x.x.....
manual extraction gives these puzzles - all with the same pattern.
- Code: Select all
1...567.9...1.926.6..27..51...91...5.1.5.792.....62.17.34............5...6.7.....#1 Penta1 max-expand
1...569.7...1.926.6..27..15...51...9.1.9.275.....67.21.34............5...6.7.....#4 Penta4 max-expand
1...679.5...1.926.6..25..17...51...9.1.9.275.....76.21.34............5...6.7.....#2 Penta2 max-expand
1...769.5...1.926.6..25..17...51...9.1.9.275.....67.21.34............5...6.7.....#5 Penta5 max-expand
6...597.1...1.692.1..27..65...51...9.1.9.725.....62.17.34............5...6.7.....#3 Penta3 max-expand
PM grid of #1 and #4 [identical pencil marks]
- Code: Select all
+----------------------+----------------------+----------------------+
| 1 248 238 | 348 5 6 | 7 348 9 |
| 34578 4578 3578 | 1 348 9 | 2 6 348 |
| 6 489 389 | 2 7 348 | 348 5 1 |
+----------------------+----------------------+----------------------+
| 23478 2478 23678 | 9 1 348 | 3468 348 5 |
| 348 1 368 | 5 348 7 | 9 2 3468 |
| 34589 4589 3589 | 348 6 2 | 348 1 7 |
+----------------------+----------------------+----------------------+
| 25789 3 4 | 68 289 158 | 168 789 268 |
| 2789 2789 12789 | 3468 23489 1348 | 5 34789 23468 |
| 2589 6 12589 | 7 23489 13458 | 1348 3489 2348 |
+----------------------+----------------------+----------------------+ #1
+----------------------+----------------------+----------------------+
| 1 248 238 | 348 5 6 | 9 348 7 |
| 34578 4578 3578 | 1 348 9 | 2 6 348 |
| 6 489 389 | 2 7 348 | 348 1 5 |
+----------------------+----------------------+----------------------+
| 23478 2478 23678 | 5 1 348 | 3468 348 9 |
| 348 1 368 | 9 348 2 | 7 5 3468 |
| 34589 4589 3589 | 348 6 7 | 348 2 1 |
+----------------------+----------------------+----------------------+
| 25789 3 4 | 68 289 158 | 168 789 268 |
| 2789 2789 12789 | 3468 23489 1348 | 5 34789 23468 |
| 2589 6 12589 | 7 23489 13458 | 1348 3489 2348 |
+----------------------+----------------------+----------------------+ #4
the 348 cant go into r5c9 - so it has to be 6@r5c9. All 5 puzzles have this PM grid and hence the same initial step and should have the same rating.
Hidden Text: Show
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Re: The hardest sudokus (new thread)
by afkcodes » Thu Nov 30, 2023 1:45 pm
Paquita wrote:A bit late but Mith, I wish you a good recovery
I have posted a new file of T&E(2) puzzles here https://drive.google.com/file/d/1NfHZByy-v9oNB64b4CzocztH_eRw3d0H/view?usp=sharing
can you help me with generation, which software are you using, i am trying with sudoku/sukaku explainer. please share the command to batch generate the sudokus
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Re: The hardest sudokus (new thread)
by Paquita » Sun Dec 03, 2023 9:55 pm
Hi afkcodes
You can read about generating puzzles with Sudoku Explainer here https://sourceforge.net/projects/sudoku-explainer/.
I do not use that, I use puzzle strings and shuffle the digits around to generate new puzzles (so called vicinity search)
You can read about generating puzzles with Sudoku Explainer here https://sourceforge.net/projects/sudoku-explainer/.
I do not use that, I use puzzle strings and shuffle the digits around to generate new puzzles (so called vicinity search)
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- Joined: 11 November 2018
Re: The hardest sudokus (new thread)
by Paquita » Tue Dec 19, 2023 9:47 pm
This is another batch with T&E(2) puzzles https://drive.google.com/file/d/1CpXjo-2LS3rhPtvPk92Jy73uhcZgMmbZ/view?usp=sharing
I am going to stop generating puzzles for now. Time to do some other things.
This is the complete file of what I generated since september 2023 https://drive.google.com/file/d/1twLA_GsfVh_n-qz7Q39WH7bhmb7eyqE-/view?usp=sharing. So I about doubled the database for high rated T&E(2) - after Mith and Hendrik exploded the small collection it was at the moment of the ph2010 database.
I think there a more puzzles out there still, but I notice 11.8 is getting rarer and rarer.
One more think about high rated T&E(2). Quite a few have an (almost) SK Loop. I don't know how to generate those, maybe someone else can.
Still the T&E(3) database is larger and that one is I think almost exhaustive, I found just a handful of other T&E(3) puzzles in all my searches :
I am going to stop generating puzzles for now. Time to do some other things.
This is the complete file of what I generated since september 2023 https://drive.google.com/file/d/1twLA_GsfVh_n-qz7Q39WH7bhmb7eyqE-/view?usp=sharing. So I about doubled the database for high rated T&E(2) - after Mith and Hendrik exploded the small collection it was at the moment of the ph2010 database.
I think there a more puzzles out there still, but I notice 11.8 is getting rarer and rarer.
One more think about high rated T&E(2). Quite a few have an (almost) SK Loop. I don't know how to generate those, maybe someone else can.
Still the T&E(3) database is larger and that one is I think almost exhaustive, I found just a handful of other T&E(3) puzzles in all my searches :
- Code: Select all
98.76.5..7.58.4....64..9...4...76....78....6...95.8....4......3...94...........21 ED=11.6/1.2/1.2
987......6..8...........5...4.35.21....1.8..5....243.8..12.38.......54.3.......21 ED=11.7/1.2/1.2
98.76....7.54..8....6.5.9..5...9....49.8.7....67..5.8...4...........6.3........21 ED=11.6/1.2/1.2
9876.....5..8...........6...4.3..21....18...6....423.8..123........6.4.3.....8.21 ED=11.7/1.2/1.2
9876.....5..8...........6...4.3..21....18...6....423.8..123.8......6.4.3.......21 ED=11.7/1.2/1.2
98.76.5..7.5.94....4...87..8........6.795.....948...75.6..........4....3.......21 ED=11.6/1.2/1.2
987......6..8...........5...4.38..21.2.1.543.............41.38....2.3.5.......1.2 ED=11.7/1.2/1.2
98.76.5..7.5....6...4......6..9.7...5...8...4.7845...6.9..........8...3....69.21. ED=11.6/1.2/1.2
987......6...........85....4.352.1..1.2.843.......3....4.3.521....2...58....1.4.3 ED=11.7/1.2/1.2
987......6..8...........5..4.32..81.1..4..3.5.......2..1..524.3...3.81.....14..82 ED=11.6/1.2/1.2
98.76....7.54..8...64.5.9..8.6.95...45.........78.4....7............6.32......61. ED=11.7/1.2/1.2
9876.....5..43..........5..85..7.92...2...8.1.......5727...1.851....72.9.9....... ED=11.7/1.2/1.2
9876.....5..43..........5..85..7.92.7.2...8.1.......572....1.851....72.9.9....... ED=11.7/1.2/1.2
9876.....5..43.......8..5..7.5...92..2....7.1.......582.8..1.751....82.9..9...... ED=11.7/1.2/1.2
9876.....5..43.......8..5..82....71.7.5...9.2.......852....1.571....829...9...... ED=11.7/1.2/1.2
98.76.5..7.5..4....64..98..64.5...9.5.89.........86......47..........7.3.......21 ED=11.6/1.2/1.2
98.76.5..7.5..4....64..98..64.5...985..9.........86......47..........7.3.......21 ED=11.6/1.2/1.2
98.76.5..5.7..4....4....8..87.64....6.59.......4.5.....69....8.....9..32....7...1 ED=11.7/1.2/1.2
98.76.5..5.7..4....4...98..87.64....6.59.......4.5.....69....8.....7...3.......21 ED=11.7/1.2/1.2
9876.........958.......4...87.......3.62......923.876.7......3..3..6..2..2....9.8 ED=11.7/1.2/1.2
987......6..8...........5...4.38..2..1.2.543.....1.......42.18......3.5.......2.3 ED=11.7/1.2/1.2
987......6..8...........5...4.38..2..1.2.543.....1.......43.18......2.5.......3.2 ED=11.7/1.2/1.2
98.76.54.7.5.......64......8.695.....794.........87..6.97.....8....9532.......1.. ED=11.6/1.2/1.2
98.76.5..5.7.......46......8.....97..59...6.4.....4.85.95..8......32..97...1..... ED=11.6/1.2/1.2
9876.....5...8.....4....3..6.2.1.43.......1.2.......86.1.84........63.41.....28.3 ED=11.7/1.2/1.2
987......6...........5.....43.72.1..21..534.............42..31....34..75....172.4 ED=11.7/1.2/1.2
987......6...........5.....43..5271.12..4..3............14...23...21.5.7....3714. ED=11.7/1.2/1.2
987......6...........85....4.35.21..1.248.3............1..4523....3..4.1...12..85 ED=11.7/1.2/1.2
987......6..8...........5..4.328..512.13...4...........2.1.34.....42..38....5.12. ED=11.7/1.2/1.2
987......6...........85....4.35.21..1.238.4............1..3524....4..3.1...12..85 ED=11.7/1.2/1.2
987......6...........5.....43..5271.12..3..4............13...24...21.5.7....4713. ED=11.7/1.2/1.2
987......6..8...........5..4.328..512.14...3...........2.1.43.....32..48....5.12. ED=11.7/1.2/1.2
987......6...........5.....43.72.1..12..534.............42..31....34..75....172.4 ED=11.7/1.2/1.2
98.76.54.7.5.......6.9..7..49....65..57....8...6..59.7.48.........32........1.4.. ED=11.7/1.2/1.2
987......6...........5.....43..5271..2..4..3....1.3.....14...23...31.5.7....2714. ED=11.7/1.2/1.2
987......6..8...........5..4.328..51..13...4.......2.3.2.1.34.....42..18....5.32. ED=11.7/1.2/1.2
98.76.5..7.5..98...46..8...5...74.9....9.6..5...58....4......32.7......1....4.... ED=11.7/1.2/1.2
98.76.5..7.5...6....4.5....8.....4.....9.........8.32.6...95..4.7.84.....496.7..5 ED=11.7/1.2/1.2
987......6..8...........5...4.32.81..2.1.4.35....5.2.4...2.148.....8.1.3....3..5. ED=11.7/1.2/1.2
987......6..8...........5...4.32.81..2.1.4.35....582.4...2.148.....3..5.......1.3 ED=11.7/1.2/1.2
987......6...........5......4.83.21..2..15.34...2.45.8...48..23...3.18......5.1.. ED=11.7/11.1/2.6
987......6..8...........5...4.32.81..2.1.4.35....5.2.4...2.348.....8.3.1....1..5. ED=11.7/1.2/1.2
987......6..8...........5...4.32.81..2.1.4.35....582.4...2.348.....1..5.......3.1 ED=11.7/1.2/1.2
987......6...........5......4.83.21..2..15.34...2.45.8...48..21...1.38......5.3.. ED=11.7/11.1/2.6
987......65..........6.....4..93.2..1...26.3....1.4.9....4...12...2.396.....9.4.3 ED=11.7/1.2/1.2
987......6...........5......4.32.51..3..41.28...8........28..31...1.48......5.24. ED=11.7/1.2/1.2
98.76.5..7.45..6....5......6.7.9.....5.87..96..8..4.7..4..........98...3...4...21 ED=11.7/1.2/1.2
98.76.54.7.58..9...4.......6..9....4.97.46.....857....57.....3....68..........21. ED=11.6/1.2/1.2
98.76.5..7.58.49...4.......6..9...4..97.46.....857....57......3...68..........2.1 ED=11.6/1.2/1.2
98.76.5..7.59.48...64.5....8...46...4.75.9.....68......4.....3.....97..........21 ED=11.6/1.2/1.2
9876.........958.......4...76.......3.92..7...283..6..2.6....97.73...2.8......36. ED=11.7/1.2/1.2
9876.........958.......4...76.......3.92..7...283..6..2.6....97.9....36...3...2.8 ED=11.7/1.2/1.2
987......6...........85....4.352.1..1.2..43.......3....4.3..21....2...58....184.3 ED=11.7/1.2/1.2
98.76.5..7.45......6..48...6...57...54.89..6..7........9....83....98.4.6.......21 ED=11.7/1.2/1.2
98.76.5..7.45..6...6..48...6...57...54.89.....7........9....83....98.4.6.......21 ED=11.7/1.2/1.2
98.76.54.7.5....68..4......84...9.765....7.9..9......56..9.4......32..8.....18... ED=11.7/1.2/1.2
98.76.5..7.4...68........9.6.7..54.95....68....8.....5...32.......1.4.......5974. ED=11.7/1.2/1.2
98.76.5..7.4...6....5.48...6...57...54.89.....7........9....83....98.4.6.......21 ED=11.7/1.2/1.2
98.76.5..7.5.4.....64..8...4.9...8........93........21..8.94.....765.......8.7.6. ED=11.7/1.2/1.2
98.76.5..7.54..8...46......5.8.94...46.8......795......9....4.....6...3......7.21 ED=11.7/1.2/1.2
98.76.5..7.54..8...46......5.8.74...46.89.......5......97...4.....6...3......7.21 ED=11.7/1.2/1.2
98765....64........32......7...6985....8...1.....1.7....8.7.9.1...9.5......18.56. ED=11.7/1.2/1.2
987......6...........5......4.32.51..3..1..28...8....4...48..31...1.28......5.2.. ED=11.7/1.2/1.2
987......6...........5......4.32.51..3..1..28...8....4...48..32...2.18......5.1.. ED=11.7/1.2/1.2
987......6...........5......4.32.51..3..14.28...8..3.....48..31...1.28......5.24. ED=11.7/1.2/1.2
987......6...........5......4.32.51..3..14.28...8..3.....48..32...2.18......5.14. ED=11.7/1.2/1.2
987......6..8.......5...4..3.258..41..12...3.........5...32..1....1.53.8....4852. ED=11.7/1.2/1.2
987......6..5......4.......36..2.1..12..53.7......6......61..57...2.73.6....3.21. ED=11.7/1.2/1.2
98.76.5..7....48...4...5...67.4...9..5.8.........9...5.67...4.....6....3....7..21 ED=11.7/1.2/1.2
98.76.5..7....48...4...5...67.4...9..5..8.......9....5.67...4.....6....3....7..21 ED=11.7/1.2/1.2
98.76.5..7.59.4....64.8.9..6...7....4..8.6....985......4.....3....4.7..........21 ED=11.7/1.2/1.2
98.76.5..7.59.4....64.8.9..6...7.....9854.......8.6....4.....3....4.7..........21 ED=11.7/1.2/1.2
98.76.5..7.59.4....64.8.9..8...7....4..6.8....965......4.....3....4.7..........21 ED=11.7/1.2/1.2
98.76.5..7.59.4....64.8.9..8...7.....9654.......6.8....4.....3....4.7..........21 ED=11.7/1.2/1.2
987......65.9...........6..4...3.92.1....2.36......1.4...3.14.....24..9.....963.2 ED=11.7/1.2/1.2
987......6..8...........5..4.328.15.2.13....4........3...42..38...1..4......5321. ED=11.6/1.2/1.2
987......6..8...........5..4.32...1.1..48.3.5.......2..1..524.3...3..1.....14..82 ED=11.6/1.2/1.2
987......6..8...........5..4.32..15.2.13....4........3...42..38...1.84......5321. ED=11.6/1.2/1.2
98.76.5..7.58.49...........6..57....45.9.8....79.......64.........6...32.......51 ED=11.6/1.2/1.2
98.76.5..7.5.849...64..9...6.84.7.9....69........58...4.6.....3..7....21...8..... ED=11.7/1.2/1.2
98.76.5..7.54.8.....6.95...8.4..........4..3........2157.......4.9.7...6.68.5..97 ED=11.6/1.2/1.2
98.76.54.75.8...9.......8..32.......1..6............64..75.8..9...97.65.....4..78 ED=11.7/1.2/1.2
987......6...........85....4.35.21....248.3......13....1..4523....2..4.1...13..85 ED=11.7/1.2/1.2
987......6...........5.....43..521...2.74.3.....1.3.....14..23....31..75....274.1 ED=11.7/1.2/1.2
987......6...........5.....43..5271.12..4..3......3.....14...23...31.5.7....2714. ED=11.7/1.2/1.2
987......6..8...........5..4.328..512.13...4.........3.2.1.34.....42..18....5.32. ED=11.7/1.2/1.2
987......6...........5.....43.72.1..21..534.......1.....42..31....14..75....372.4 ED=11.7/1.2/1.2
987......6...........85....4.35.21..1.248.3.......3....1..4523....2..4.1...13..85 ED=11.7/1.2/1.2
9876.....65.9..............4...3.2.....4.2.93...19.6...1326.9.4......32........16 ED=11.6/1.2/1.2
9876.....65.9..............4...632.....42..93...1.96...132..9.4......32........16 ED=11.6/1.2/1.2
987......65.9...........6..4...63.2....42.9.3...1.9.6..132...94......23.......1.6 ED=11.6/1.2/1.2
9876.....65.9..............4...3.2.....4.2.63...16.9...1329.6.4......32........19 ED=11.6/1.2/1.2
9876.....65.9..............4...932.....42..63...1.69...132..6.4......32........19 ED=11.6/1.2/1.2
9876.....65.............9..4...93.2....42.6.3...1.6.9..132...64......23.......1.9 ED=11.6/1.2/1.2
9876.....65.9..............4...3.2.....4.2.63...16.9...1329.6.4...3...19.......2. ED=11.6/1.2/1.2
9876.....65.9..............4...932.....42..63...1.69...132..6.4...3...19.......2. ED=11.6/1.2/1.2
98.76.54.7.5.......46......6.4....7..7...69.4.5....68...8.7.......32..9....1...5. ED=11.6/1.2/1.2
9876.....65.............9..4...93.2....42.6.3...1.6.9..132...64...3..1.9......2.. ED=11.6/1.2/1.2
9876.....65.9..............4...632.....42..93...1.96...132..9.4...3...16.......2. ED=11.6/1.2/1.2
987......65.9...........6..4...63.2....42.9.3...1.9.6..132...94...3..1.6......2.. ED=11.6/1.2/1.2
98.76.54.7.5.......46......6.4....7..7....9.4.5...768...86........32..9.....1..5. ED=11.6/1.2/1.2
9876.....65.9..............4...3.2.....4.2.93...19.6...1326.9.4...3...16.......2. ED=11.6/1.2/1.2
98.76.5..7.4...9...6...4...5......32..7....1....67.4...5.98.......4.6..8....57... ED=11.7/1.2/1.2
98.76.5..7.5.......64......6.859..4..79.4..5..5.8.7......9...83...68.2.1......... ED=11.6/1.2/1.2
98.76.5..7.5.......64......6.859..4.4..8.7....79.4..5....9...83...68.2.1......... ED=11.6/1.2/1.2
98.76.5..75...89.......9...43........2....1.....61......85..79.....918.5....7..16 ED=11.7/1.2/1.2
98.76.5..7.5.......64.5....8...........9...3....68.21.6...9...44..8.7....79.4...5 ED=11.6/1.2/1.2
98.76.5..7.45......6.......6.84...5.5...96....7.8...4..9..........97.3.2....8...1 ED=11.6/1.2/1.2
98765....64........32......7...6985....8...1....51.7....8.769.1...9........18.56. ED=11.7/1.2/1.2
98.76.5..7.5..4....64.598..64...7.9.5.89.........86......47..........7.3.......21 ED=11.6/1.2/1.2
98.76.5..7.5..4....64.598..64...7.985..9.........86......47..........7.3.......21 ED=11.6/1.2/1.2
98.76.5..7.58.4....64..98..65.......4...76.9...95.8....47............4.3.......21 ED=11.7/1.2/1.2
9876.....54....3..2.3.......9.83.71....9.16.3.....7.....837.9.6...1.68.......9..1 ED=11.7/1.2/1.2
9876.....54....3..2.3.......9.83.71....9.16.3....67.....837.9.6...1..8.......9..1 ED=11.7/1.2/1.2
9876.....5.....94..3.......2..95.......2.149.....64..5.61..9.54......6.9......12. ED=11.7/1.2/1.2
9876.....5...8.....4....3..6.2...43.......1.2.......86.1.84.......1.28.3....63.4. ED=11.7/1.2/1.2
98.76.5..7.5.......64......8.6....9....6....3.....42.16.8.5..4..9748.......9.6.7. ED=11.6/1.2/1.2
98.76.5..7.5..4....64...8..6...47.9....98.......5.6....5.....32..6.....1...67.4.. ED=11.7/1.2/1.2
98.76.5..7.4.5.6...564.....8..69......7..4.5......5..8..9.....3....874.........21 ED=11.6/1.2/1.2
987......6..8...........5...4.35..21...2.84.5.....183...31..28...24...53......1.4 ED=11.6/1.2/1.2
98.76.5..7....98...46..8...5...74.9....9.6..5...58....45.....32.7......1....4.... ED=11.7/1.2/1.2
98.76.5..7.4.8.....569.4....4.....3...7....21....79......6........59..78....48.5. ED=11.7/1.2/1.2
98.76.5..7.5..98...46..8...45.....32.7.....1.....4.......9.6.5....58........74..9 ED=11.7/1.2/1.2
98.76.54.7.5....6..4.......6.4....75.7....9.4.....768.5.86........32..9.....1.... ED=11.6/1.2/1.2
987......6..8...........5...5.48..3..2.5.3.41....218....431..82...2..45.......1.3 ED=11.7/1.2/1.2
987......6..8...........5...5.48.32..3.5.2.41.....18....421..83...3..45.......1.2 ED=11.7/1.2/1.2
98.76.5..7.58.49...64.5....6.9.47...5..98......8......4.7...65.......4.3.......21 ED=11.7/1.2/1.2
98.76.5..7.58.49...64......67.58....5.9.47.....89...5.4.6............63........21 ED=11.7/1.2/1.2
98.76.5..7.58.49...64......67.58....5.9..7....489...5.4.6.........4..63........21 ED=11.7/1.2/1.2
98.76.5..7.58.49...64......67.98....5.9.47.....85...9.4.6............63........21 ED=11.7/1.2/1.2
98.76.5..7.58.49...........6..57....4..9.8....97..6.8..64.............53.......21 ED=9.5/1.2/1.2
98.76.5..7.58.49...64......4..9.8....97..6.8....57.....46.............53.......21 ED=9.5/1.2/1.2
98.76.5..7.58.49....6......4..9.8....97..6.8....57.....64.............53.......21 ED=9.5/1.2/1.2
98.76.5..7.58.49...64......67.98....5.9..7....485...9.4.6.........4..63........21 ED=11.7/1.2/1.2
987......6..8...........5...5.43.82..3.5.2.41....813....421..83...3..45.......1.2 ED=11.7/1.2/1.2
987......65.9...........6..4...3.92.1....2.36....961.4...3.146....24..9.......3.2 ED=11.6/1.2/1.2
987......65..........6.....4..93.2..1...26.3....1.496....46..12...2.3.9.....9.4.3 ED=11.6/1.2/1.2
98.76.5..7.54.8....4..957..8.4....5.6...74.....985.......9.6.7........32........1 ED=11.6/1.2/1.2
987......65.9...........6..4..39..6.2....6.1....2.19.4.3.1...92...4..3.6......1.. ED=11.6/1.2/1.2
9876.....65.9......4.......4..39.6..2...461.....2.1.9..3.1..9.2......41........36 ED=11.6/1.2/1.2
9876.....65.9..............4..39.6..2....61.....2.1.94.3.1..9.2...4...36.......1. ED=11.6/1.2/1.2
98.76.54.7.5.......46......6.4....75.7....9.4.....768.5.86........32..9.....1.... ED=11.6/1.2/1.2
98.76.54.7.....6...5.......6.5...7...7.....95.4...786.4.86........32.9......1.... ED=11.6/1.2/1.2
9876.....65.9..............4..36.9..2....91.....2.1.64.3.1..6.2...4...39.......1. ED=11.6/1.2/1.2
9876.....65.9..............4..36.9..2.....1.....2.1.64.3.19.6.2...4...39.......1. ED=11.6/1.2/1.2
98.76.54.7.....6...5.......6.5...7...7...6.95.4....86.4.8.7.......32.9.....1..... ED=11.6/1.2/1.2
9876.....65.9......4.......4..36.9..2...491.....2.1.6..3.1..6.2......41........39 ED=11.6/1.2/1.2
9876.....5.....84...3......2.51..6.4......58........21.2..61..5...5.821....42.... ED=11.6/1.2/1.2
98.76.5..7.4.......56......5...87.4..475.6......94..5..69...4.....8..3.2........1 ED=11.6/1.2/1.2
98.76.54.7.5.9.8...4.......87..5...46..98.....594.7....9.....3...7...21....6..4.. ED=11.6/1.2/1.2
98765....43.2.1......9.....57........93.4.87...4.9.5.3..8....37......95.......4.8 ED=11.6/1.2/1.2
98.76.5..7.4.......5..489..8.5....3267....41...........6.8.7..9...49........56... ED=11.6/1.2/1.2
98.76.5....5...79...4....8.86....4.....6...3.......21.7...86...5..9.4....9.57...4 ED=11.6/1.2/1.2
98.76.5..7.4.......5...89..8.5....3267....41......4....6.8.7..9...49........56... ED=11.6/1.2/1.2
987......6..85......4......3.2..1...1..52.83...5..6....6.2..31.....3.5.8....1..26 ED=11.6/1.2/1.2
987......6..85......4......3.2.81...1..52.3....5..6....6.2..13.....3..58....1.2.6 ED=11.6/1.2/1.2
98.76.5..7.59.46...64.5....8......3.49.....2.....8....5..89...7...6.5.......47... ED=11.6/1.2/1.2
98.76.5..7.59.46...64.5....8......3.49.....2.....8....5..89...7.7.6.5.......4.... ED=11.6/1.2/1.2
98.76.5..7.59.46...64.5....8......3.47.....2.....8....5..87...9...6.5.......49... ED=11.6/1.2/1.2
98.76.5..7.59.46...64.5....8......3.47.....2.....8....5..87...9.9.6.5.......4.... ED=11.6/1.2/1.2
98.76.5..7.6.45.....49.....6...74.9.57.8.9......65....4.......3....8...........21 ED=11.6/1.2/1.2
987......6...........85....4.3.2.1....23.54.....14.....1.4.235....51.2.8....83..4 ED=11.7/1.2/1.2
987......6...........85....4.3.2.1....23.5.8....14.....1.4.235....51.2.8....83..4 ED=11.7/1.2/1.2
98.76.5..7.6.45.....49.....6...74.9557.8.9......6.....4.......3....8...........21 ED=11.6/1.2/1.2
987......6..8...........5..4.32..81.1..4..3.5.......2..1..524.3...3.81.....14..82 ED=11.7/1.2/1.2
98.76.5..7.5.......64......6.895..4..794...5..4..87....9..........8....3...69.2.1 ED=11.6/1.2/1.2
9876.....5..43.......8..5..7.5...92..2....7.1.......582.8..1.751....82.9..9...... ED=11.7/1.2/1.2
9876.....5..43.......8..5..82....71.7.5...9.2.......852....1.571....829...9...... ED=11.7/1.2/1.2
98.76.5..7.59.46...64.5....8......3.49.....2.....8....5..89...7.7.6.5.......4.... ED=11.6/1.2/1.2
98.76.5..7.59.46...64.5....8......3.47.....2.....8....5..87...9...6.5.......49... ED=11.6/1.2/1.2
98.76.5..7.59.46...64.5....8......3.47.....2.....8....5..87...9.9.6.5.......4.... ED=11.6/1.2/1.2
98.76.5..7.6.45.....49.....6...74.9557.8.9......6.....4.......3....8...........21 ED=11.6/1.2/1.2
9876.....5..43.......8..5..7.5...92..2....7.1.......582.8..1.751....82.9..9...... ED=11.7/1.2/1.2
9876.....5..43.......8..5..82....71.7.5...9.2.......852....1.571....829...9...... ED=11.7/1.2/1.2
- Paquita
- Posts: 132
- Joined: 11 November 2018
Re: The hardest sudokus (new thread)
by coloin » Wed Dec 20, 2023 1:58 am
On the back of your post...
I searched in all of yours and Hendrik's puzzle lists and found a few perhaps un-attributed 11.8s and also a few new ones by searching the edges of the 11.7s..
The disparity caused by SE and isomorph handling meant that some of the 11.7s were upgraded when in minlex solution grid puzzle and/or minlex format.
Previously I suggested that if they were 11.8 in minlex or minlex solution grid then that was a good definiton.
The concordance rate appeared to be high - but this was a biased sample as they are only in the sample if they rate 11.8 !
Probably SE has an individual false negative [-ie 11.7 instead of 11.8] rate of 30%.
I dont know the workings of SE and whether it is the borderline chain length puzzles or whether its unrelated.
The new max expand puzzles formed by the twinning process have the same solving status so should really have the same rating .... but they do have the potential to minimize differently.
Twinned 11.7s give new seeds for the 4 squares with the Thor's hammer pattern.
Conversely expanding the puzzles reduces significantly the number of puzzles to rate.
Here is a selection of would be 11.8s, some related to published 11.7s and some new ones.
Each one has around 4 other minimal puzzles from the same max expand. The max expands are 11.8
Each max expand has a couple of twin solution grids.
The more clues the max expand has [ 11.7/11.7 or 11.8/11.8] potentially there are more twins and more minimal puzzles !! .
Minlex puzzles
Same puzzles in min lex solution grid puzzle ...
Will post a link to the list of the posted and potential 11.8s that I have found....
It would be interesting to see the SE rating of these puzzles in max lex puzzle format too.
I searched in all of yours and Hendrik's puzzle lists and found a few perhaps un-attributed 11.8s and also a few new ones by searching the edges of the 11.7s..
The disparity caused by SE and isomorph handling meant that some of the 11.7s were upgraded when in minlex solution grid puzzle and/or minlex format.
Previously I suggested that if they were 11.8 in minlex or minlex solution grid then that was a good definiton.
The concordance rate appeared to be high - but this was a biased sample as they are only in the sample if they rate 11.8 !
Probably SE has an individual false negative [-ie 11.7 instead of 11.8] rate of 30%.
I dont know the workings of SE and whether it is the borderline chain length puzzles or whether its unrelated.
The new max expand puzzles formed by the twinning process have the same solving status so should really have the same rating .... but they do have the potential to minimize differently.
Twinned 11.7s give new seeds for the 4 squares with the Thor's hammer pattern.
Conversely expanding the puzzles reduces significantly the number of puzzles to rate.
Here is a selection of would be 11.8s, some related to published 11.7s and some new ones.
Each one has around 4 other minimal puzzles from the same max expand. The max expands are 11.8
Each max expand has a couple of twin solution grids.
The more clues the max expand has [ 11.7/11.7 or 11.8/11.8] potentially there are more twins and more minimal puzzles !! .
Minlex puzzles
- Code: Select all
BnB
........1.......2.....34..5..6.78....743.26..83.6..2....74.....4.3.67.8.62.8.3... ED=11.7/1.2/1.2 #01# #5 #
........1....23.4....5.1.62...2......24.16.5..653.41...47......35.......618....35 ED=11.8/1.2/1.2 #02# #6 #
........1.......2......3..4..2.356...367.28..57.68.2...875.....26...7...3.5.68... ED=11.8/1.2/1.2 #03# #6 #
........1.......23...245........6.....647.8...54.286.7.68.54...4.76.....52.78.... ED=11.8/1.2/1.2 #04# #TE3#
..............1.23...45.1.6..1.74....876.5...54.81...7.15.87....6.......4.8..67.. ED=11.8/1.2/1.2 #05# #6 #
........1.....2.34.23.......3..56....5728....8.6..75...8572....3..6.....6.2.35.78 ED=11.8/1.2/1.2 #06# #6 #
........1.....2.34...56.2.......7....256.8.1.76.1......82..67..51.2.....6.78.5... ED=11.8/1.2/1.2 #07# #TE3#
........1.....2.3...4....25....6.7...4..38....6...7..4.2.3......367.4.8.8.7.26... ED=11.7/1.2/1.2 #08# #6 #
........1.....2.3...1...456...27.....1.4.67..4...186...76..4..814.......2.87..... ED=11.8/1.2/1.2 #09# #6 #
........1.....2.34....56.....7.25....286.17..65..8.1...86......2.5.67..871....... ED=11.8/1.2/1.2 #10# #TE3#
.......12......3.4....15.6...56.7.8..1683..7.8...5......8.7.6...671.3...53....... ED=11.7/1.2/1.2 #11# #6 #
..............1.23..4.56.........23..3.7...4828....1.7.73.....214.....8.8.2.17... ED=11.8/1.2/1.2 #12# #6 #
........1.....2.34.23..........35.6...2.7...865.2.8.7...6..78...75.2....38..56... ED=11.8/1.2/1.2 #13# #6 #
........1.....2.34...56.27...1.578....762.1...5.1.8....6528....1.27.....87....... ED=11.8/1.2/1.2 #14# #6 #
..............1.23...45.1.6..1.47....578.6...48.51...7.14.75....6..8....5.86.47.. ED=11.8/1.2/1.2 #15# #6 #
........1.....2.3...4...2.5....67.....63.4.8..4782..63.2..83....784.6...6.3.7.... ED=11.8/1.2/1.2 #16# #TE3#
........1.......23....245......67.....65..8...742.8..5.6847....4.58.2...72..56... ED=11.8/1.2/1.2 #17# #TE3#
........1.......23....24.....5.67....7.5..8..64.8.2....874.6.5.2.6..8...45..7.... ED=11.8/1.2/1.2 #18# #5 #
Same puzzles in min lex solution grid puzzle ...
- Code: Select all
12......9.56...12.7......65...3.8..........17.9..7.....1.5..6..56.2..97.9.2....51 ED=11.8/1.2/1.2 #01# #5 #
12..56...4.6.8.........1.........9.8....42351.......42.6.......5.1.2.8.684.1..2.5 ED=11.7/1.2/1.2 #02# #6 #
1..4.........8.......2......3.....565.7...1.36.....87.3.1..7..886...5.17.75..836. ED=11.8/1.2/1.2 #03# #6 #
12...6....5...........37.....87.3..4..4.653.8..5.4.67......85.7......84.....74.63 ED=11.8/1.2/1.2 #04# #TE3#
....5.......18.2.66..2.7..5.94.....8.........8.5...17....62..51...8..6.7..6.7182. ED=11.8/1.2/1.2 #05# #6 #
12.....8..5.1..2.66.9...51.......89.....7.....9..48.....2.....881..659.29.5...16. ED=11.8/1.2/1.2 #06# #6 #
.234.6.8...7.......8.27....26......4......8....4...19..4.86......23.4..7.36.27... ED=11.8/1.2/1.2 #07# #TE3#
....567..4..........932.....74..59.886......5......46.........7....9.8.4.98...65. ED=11.8/1.2/1.2 #08# #6 #
1.3......4.....2.668..7......5.4.6.7.......28...2..45....5.8..4....248..8..76.... ED=11.7/1.2/1.2 #09# #6 #
........94.7......6......15..874.9..7.6..3...94.6.83..3.4.67..8...8.4......93.... ED=11.8/1.2/1.2 #10# #TE3#
12....7.9.5....23...9....1.29....5..7....13...31..5..7...86........3...297.5.2... ED=11.7/1.2/1.2 #11# #6 #
....567...5.18....68.7.3....15......7.68...5.83...5.6.3............3.91.....1.4.. ED=11.6/1.2/1.2 #12# #6 #
.2..........1.9....89...1.....39.45.3....46.....6.5.1..3...1.6...4...59...654.3.1 ED=11.8/1.2/1.2 #13# #6 #
......7.....1.9.36....3.4.52.6.......193.2...73.6......7..61.2..6.9.3.7...172.... ED=11.8/1.2/1.2 #14# #6 #
............1.9.3....73.5.4.85.6..4734....65.7.....8..56.....788.46..3.5.3....46. ED=11.8/1.2/1.2 #15# #6 #
.2.........71.9...86...7..........9..3.9.417......34.2....92.41..234.9.7...7.13.. ED=11.8/1.2/1.2 #16# #TE3#
12...6.89.5..8...6......51....9.4........7.......6.92..62....9858....1.29.1...65. ED=11.6/1.2/1.2 #17# #TE3#
12....7...57..926.6.9.....52.6...17..9....5.2..57...9.....41.......3..........6.1 ED=11.8/1.2/1.2 #18# #5 #
Will post a link to the list of the posted and potential 11.8s that I have found....
It would be interesting to see the SE rating of these puzzles in max lex puzzle format too.
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Re: The hardest sudokus (new thread)
by denis_berthier » Wed Dec 20, 2023 7:27 am
coloin wrote:I searched in all of yours and Hendrik's puzzle lists and found a few perhaps un-attributed 11.8s and also a few new ones by searching the edges of the 11.7s..
The disparity caused by SE and isomorph handling meant that some of the 11.7s were upgraded when in minlex solution grid puzzle and/or minlex format.
Previously I suggested that if they were 11.8 in minlex or minlex solution grid then that was a good definiton.
The concordance rate appeared to be high - but this was a biased sample as they are only in the sample if they rate 11.8 !
Probably SE has an individual false negative [-ie 11.7 instead of 11.8] rate of 30%.
I dont know the workings of SE and whether it is the borderline chain length puzzles or whether its unrelated.
I think you are taking it the wrong way. If SE rates a puzzle 11.8 and some iso 11.7, the 11.8 means it misses a 11.7 elimination in its 11.8 resolution path. So, the "right" SE rating shouldn't be defined as the max of all the possible ratings of isos, but as the min.
Anyway, due to all the artbitrary thresholds in SE and to the mixing of rules of very different kinds in such thresholds, a difference of 0.1 is totally meaningless.
My opinion is, forget about SE and use PGX instead. This will eliminate most of the problems due to isomorphism dependency (and it will be faster if you use the version that includes all the changes to SE:https://github.com/denis-berthier/Controlled-bias_Sudoku_generator_and_collection/tree/master/PROGRAMS/FPGX
I've recently rated almost 6M controlled-bias puzzles with it, so there's no reason one couldn't completely re-rate the ph2010 database with it.
More radically, forget about SE and use BpB instead. This will eliminate ALL the problems.
.
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Re: The hardest sudokus (new thread)
by eleven » Thu Dec 21, 2023 12:59 am
denis_berthier wrote:More radically, forget about SE and use BpB instead. This will eliminate ALL the problems..
More properly, forget about SE, PGX and BpB for high ratings, as long as they have not integrated Thor's Hammer (tridagons) as an easy (advanced) solving technique.
It's still ridiculous, that puzzles with highest ratings are presented, which can be solved on paper in 15 minutes (seems, that i have to repeat that all half years).
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Re: The hardest sudokus (new thread)
by denis_berthier » Thu Dec 21, 2023 5:18 am
eleven wrote:denis_berthier wrote:More radically, forget about SE and use BpB instead. This will eliminate ALL the problems..
More properly, forget about SE, PGX and BpB for high ratings, as long as they have not integrated Thor's Hammer (tridagons) as an easy (advanced) solving technique.
It's still ridiculous, that puzzles with highest ratings are presented, which can be solved on paper in 15 minutes (seems, that i have to repeat that all half years).
The only merit of SER (or its PGX variant) is being an old reference for almost everybody interested in Sudoku. It relies on no widely used rules, it has a totally void theoretical background, it has arbitrary thresholds and it is inconsistent wrt isomorphisms. Changing its set of rules would destroy its only merit.
Moreover, the change you propose is indeed undefined (as I've already said every time you've suggested it). Having a tridagon pattern doesn't imply being easily solvable. On the contrary, I've shown that it may require very complex ORk-chain rules.
And then, why add tridagon but not sk-loops, Exocets or whatever pattern will appear tomorrow - turning SER into a weathercock that changes its results with the slightest blow of wind.
That being said, there is indeed a big problem related to the tridagon pattern - and it cannot be solved by changing the SER.
The problem is a consequence of what I've mentioned here: http://forum.enjoysudoku.com/the-tridagon-rule-t39859-120.html, i.e. the stability of the non-degenerate tridagon under small changes of givens, which also means its stability by the techniques of vicinity search, and which may ultimately make it appear as an unwanted virus.
After Loki has been found by mith and after I found that it was in T&E(3), the search for the "hardest" puzzles has turned for some time into the search for T&E(3) puzzles. Hundreds of thousands of such puzzles have been found (mainly by mith). I've shown that all these puzzles have a non-degenerate tridagon pattern. (The question whether this is true of all the T&E(3) puzzles remains open.)
And then a few other people have started to use the puzzles in the T&E(3) database as seeds for re-launching a SER-hardest search. Unsurprisingly, considering the stability of tridagon by vicinity search, most of the puzzles thus found have a non-degenerate tridagon, whether they are in T&E(2) or T&E(3).
It is of course interesting to have T&E(2) puzzles with a tridagon (mith must have millions of them, but he hasn't puiblished any). In particular, it allowed to find puzzles in T&E(2) beyond B7B.
But the result is also a totally biased view of T&E(2).
This was already the case for the ph2010 database, because most of it was the result of searching for specific patterns (sk-loops) or pseudo-patterns (exocet). But it has reached a new dimension with tridagon.
And now, we're back to the real question about the search for the hardest puzzles (setting aside the search for puzzles in T&E(3) - which has a perfectly defined goal). Should we continue to search wrt a rating (SER) that has no theoretical background and that doesn't allow to ask any structural question? What's the goal? What's the purpose of having thousands or millions of new puzzles that will not teach us anything about T&E(2)?
.
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Are these new?
by m_b_metcalf » Fri Dec 22, 2023 10:58 am
Following an exchange on this thread, I came across these three whopping, minimal pearls, here in minlex form. I have no way of checking whether they are already known.
Merry Xmas to all,
Mike
- Code: Select all
........1.....2.34..3...25...4..6.2..1..7....8..9.......6..53...9..8....7..1..... ED=11.8/11.8/11.2
........1.....2.34..3...25...4..53...6..1....7..8.......9..4.2..8..7....1..6..... ED=11.7/11.7/11.2
........1.....2.34..3...56...4..3.2..1..7....8..9.......5..63...9..8....7..1..... ED=11.7/11.7/10.8
Merry Xmas to all,
Mike
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