## The hardest sudokus (new thread)

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

### Re:

Please include one additional detail in the second post. The command line that was used to create the output, if appropriate (understanding the options available on the gsf command line can be challenging). You specify converting to the row-normal Minlex line format and providing questions 1 and 2, but you don't specify how to construct them.
jemsnixon

Posts: 1
Joined: 10 January 2023

### Re: The hardest sudokus (new thread)

I believe it is the case that all MSLS has a corresponding SET partition

msls use a balance of naked{which includes givens} and hidden sets in a sector for 9 digits in 9 cells exactly as set does...
how is that not a given they are equivalent, exactly the same concepts just using different words

phistomefel-s-theorem-t38410.html?hilit=phistomefel#p297553

might be the same as Naked SK-loop but can it find the Hidden SK loop that co-sides with it?
as there is 2 types of Sk loops. Naked set & Hidden set

hidden SK loop
Code: Select all
`+-------------------------+--------------------------+-------------------------+| 5       17(3)     1467  | 23468   234678    378    | 12     46(8)     9      || 46(3)   2         46(9) | 1       -46(389)  (3589) | 46(5)  7         46(8)  || 1467    17(9)     8     | 24569   24679     579    | 3      46(5)     12     |+-------------------------+--------------------------+-------------------------+| 13678   4         15679 | 389     1389      2      | 5679   -6(3589)  3678   || 123678  -17(389)  12679 | 3489    5         1389   | 24679  -46(389)  234678 || 238     (3589)    259   | 7       3489      6      | 2459   1         2348   |+-------------------------+--------------------------+-------------------------+| 24      17(5)     3     | 2569    12679     1579   | 8      46(9)     1467   || 17(8)   6         17(5) | (3589)  -17(389)  4      | 17(9)  2         17(3)  || 9       17(8)     24    | 2368    123678    1378   | 1467   46(3)     5      |+-------------------------+--------------------------+-------------------------+`

normal naked sk loop
Code: Select all
`+-----------------------+---------------------+-----------------------+| 5       (137)   1467  | 23468  234678  378  | 12     (468)   9      || (346)   2       (469) | 1      389-46  3589 | (456)  7       (468)  || 1467    (179)   8     | 24569  24679   579  | 3      (456)   12     |+-----------------------+---------------------+-----------------------+| 13678   4       15679 | 389    1389    2    | 5679   3589-6  3678   || 123678  389-17  12679 | 3489   5       1389 | 24679  389-46  234678 || 238     3589    259   | 7      3489    6    | 2459   1       2348   |+-----------------------+---------------------+-----------------------+| 24      (157)   3     | 2569   12679   1579 | 8      (469)   1467   || (178)   6       (157) | 3589   389-17  4    | (179)  2       (137)  || 9       (178)   24    | 2368   123678  1378 | 1467   (346)   5      |+-----------------------+---------------------+-----------------------+`

it is pretty easy to issomorphically change the naked sk-loop into a phistomefel-ring directly showing that they are similar constructs

these two sets types should given you enough to formalize a proof on how msls is a balance of 9 digits in 9 cells per sector IE set
{as msls uses both of these in constructs}

my 2 cents
Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1427
Joined: 05 September 2006

### Re: The hardest sudokus (new thread)

On the sudoku puzzles group on facebook a new member proposed this as a new extreme sudoku he has created.
SE 11.6
Can this be checked against the database. I think it's one of the existing list instead of a self created puzzle.
Code: Select all
`.8.....4...53....16.....2...4....8..2......6...9.1...7.....6.....39.5......17...5`
urhegyi

Posts: 746
Joined: 13 April 2020

Code: Select all
`.8.....4...53....16.....2...4....8..2......6...9.1...7.....6.....39.5......17...5 ED=11.6/11.6/10.8`

It is an isomorph of the Easter-Monster, found in champagne's ph_2010 list.
Code: Select all
`1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1 ED=11.6/11.6/10.8 017 tax;Easter-Monster;78;21;`

1to9only

Posts: 4176
Joined: 04 April 2018

### Re: The hardest sudokus (new thread)

It is an isomorph of the Easter-Monster

created 16 years ago!
see here

JPF
JPF
2017 Supporter

Posts: 6132
Joined: 06 December 2005
Location: Paris, France

### Re: The hardest sudokus (new thread)

With some help of '1to9only' I was able to get gsf's sudoku-64.exe write a minlex file in the the Microsoft Windows Script Host environment. Therefore I am now planning a big switch of my maxlex based system to minlex. But before doing so, I prepared a new batch of all the maxlex puzzles produced the previous months.
This new batch contains 33596 minimal puzzles in the SER(ating) range 11.6 to 11.8. The SERs in the present list correspond with the puzzles as listed. My previous contributions (in May and september 2022) still contained some puzzles with SER performed on an isomorph of the listed puzzle. Those puzzles were produced before I became aware of the isomorph dependency of SER, and before I changed my scripts accordingly in July 2022.
A large part of the puzzles in the present batch are probably T&E(3). It was not an easy task to check novelty compared to the impressive lists posted by mith in the thread 'T&E(3) Puzzles (split from "hardest sudokus" thread)' on 7 November 2022, containing many non minimal puzzles. Finally I decided to compare the minlexes of the solutions of my new puzzles with the minlexes of the solutions of the 44251 trees in the file "max_expands_20221106". It appeared that 2003 of the puzzles in my present batch belong to existing trees. Therefore the remaining part (31593 puzzles) in this batch need new trees. According to my calculations at least 445 new trees are needed.
The list can be downoaded from:
In the list a third column marks the puzzles belonging to existing trees. The number given is the tree number in mith's list.
The hidden table below shows the top of the list starting with 78 11.8s.
Hidden Text: Show
Code: Select all
`98.76.5..7.58.49...64..5....78.46.9...957.......9.8....4.........6....32....8..5.   11.8/1.2/1.298.76.54.7.58..9.6..4....8.69....7.8.57..6.94.......5..49.3........2.........8...   11.8/1.2/1.298.76.54.7.58..9.6.......8.69....7.84......5..57..6.94.49.3........2.........8...   11.8/1.2/1.298.76.5..7.58.49....6..5...6.795....4....8....98.47.6..74.....3.......5.........2   11.8/1.2/1.298.76.5..7.58.49...46..5...6.795.....98.47.6......8....74.....3.......5.........2   11.8/1.2/1.29876.........958.......4...7.8......36.2..7...293.768.2.6....97..3...2.8......36.   11.8/1.2/1.298.76.5..7.58.49...64....7.6.758....45.9....7..8.......4..........4..63......8.2.   11.8/1.2/1.298.76.5..7.54.......6.59...59..7..6..6489......7..5...4.8..........8.4.3........2   11.8/1.2/1.298.76.5..7.58.49....6..5...6.795....4..6.8....98.47....74....3........2.........5   11.8/1.2/1.298.76.54.7.58..9.6..4....8.69....7.8.57....94......65..49.3........2.........8...   11.8/1.2/1.298.76.54.7.58..9.6.......8.69....7.84.....65..57....94.49.3........2.........8...   11.8/1.2/1.298.76.5..7.59.4....64..89..8........4.78.6.5..965.......8....9....4...32.....7...   11.8/1.2/1.298.76.5..7.58.49...46..5...6.795.....98.47......6.8....74....3........2.........5   11.8/1.2/1.298.76.5..7.5.946....48.5...6.7......59...6....489.7.6..7.....5....4..........8.32   11.8/1.2/1.298.76.5..7.58.49...64..5...8..9.6....76.48.9...957.....4...........8..5........32   11.8/1.2/1.2987.........96........5....87.4..32...3...9.8..2....473.8.......4...2.3..29.4387.   11.8/1.2/1.2   92987.........96........5....87....43.2.4...9.8..3....274.8.......39.2487..2...3.4.   11.8/1.2/1.2   9298.76.5..7.5.496...4.......67.89....5..4.6.7..94.5........8..........8.3......4.2   11.8/1.2/1.298.76.5..7.5.946....48.5...6.8.7....59...6....479.8.6..7.....5....4............32   11.8/1.2/1.298.76.5..7.59.4....64..89..8.74.6.5.4...8.....965.......8....9......7..........32   11.8/1.2/1.298.76....7.5..98...46..5...5...74.9...79.6..4...85....4.....6.3...64............2   11.8/1.2/1.2987.........96........5....87....43.2.4...9.8.39....274.8.......93.2487..2...3.4.   11.8/1.2/1.2   91987.........96........5....87.4..32..39...4.7..2....982.8.......93.4278..4...32..   11.8/1.2/1.2   9198.76.5..7.4..98...56......8..5.6.9..67.8......9.74.......4..........6.3......4.2   11.8/1.2/1.298.76.5..7.4..98...56..8...8..5.6.9.5.9.74....679.........4..........6.3......4.2   11.8/1.2/1.298.76.5..7.5.496...4.5.....67.89....5..4.6.7..94..7.......8..........8.3......4.2   11.8/1.2/1.298.76....7.5..98...46..5...5...74.9..9.85.......9.6..74.....6.3...64............2   11.8/1.2/1.298.76....7.5..98...46..5...5....4.9...785.......9.6..74.....6.3...64............2   11.8/1.2/1.298.76.5..7.5.94....4.8.....8..6.9.7..9.47...6..7.58...6.....4.3....46...........2   11.8/1.2/1.298.76.5..7.5.94....4.8.....8....9.7..9.47...6.6..58...6.....4.3....46...........2   11.8/1.2/1.298.76.5..7.5.94....4.8.....8..6.9.7..6.47...9..7.58...6.....4.3....46...........2   11.8/1.2/1.298.76.5..7.5.94....4.8.....8..6...7..9..58....6.47...96.....4.3....46...........2   11.8/1.2/1.298.76.5..7.5.94....4.8.....8....6.7..9..58....6.47...96.....4.3....49...........2   11.8/1.2/1.298.76.5..7.5.94....4.8.....8..9.6.7..6.47...9..7.58...6.....4.3....49...........2   11.8/1.2/1.298.76....7.5..89...64..58..6.........5.....32....4..8.5...76.9...785.......9.4...   11.8/1.2/1.298.76.5..7.5.94....468.....8....6.7..9..58......47...96.....4.3....49...........2   11.8/1.2/1.298.76.5..7.5.94....468.....8..9.6.7...7.58......47...96.....4.3....49...........2   11.8/1.2/1.2987......6..54.........86..8.3...72.29.....63...2..9..72.....9.3.8...2.7.6....38.   11.8/1.2/1.298.76.5..7.58.49...64..9.7.6.857.....5.9....7....48....46.........4..63........2.   11.8/1.2/1.298.76.5..7.54.9.....6.5....6....5.4.4..87.....9.6.4.5..7..........98.4.......73.2   11.8/1.2/1.298.76.5..7.5.......468.....8....6.7..9..58......47...96.....4.3....94...........2   11.8/1.2/1.298.76.5..7.5.......4.8.....8..9.6.7..6.47...9..7.58...6.....4.3....94...........2   11.8/1.2/1.298.76.5..7.5.......468.....8..9.6.7...7.58......47...96.....4.3....94...........2   11.8/1.2/1.2987......6..54.........86..73.....9..6....28...2...3.739.....622.8...73....3..9..   11.8/1.2/1.2987.........9..6......54...83.....62.29...73...6.3.8..6.....29.37.....8...2...3.7   11.8/1.2/1.298.76.5..7.5.......4.8.....8....6.7..9..58....6.47...96.....4.3....94...........2   11.8/1.2/1.298.76....7.5..89...64..58..6.........5.....32...4...8.5..6.7.9...758........94...   11.8/1.2/1.2987......6..54.........8...73....96..6....8.2..2....7339....62.2.8...3.7...3....9   11.8/1.2/1.298.76.5..7.5.84....4.9.....8..6.9.7..9..58....6.47...86.....4.3....46...........2   11.8/1.2/1.298.76.5..7.4.9.6...5.....9.6..54...959..87.....7......4.....83....8.4..........2.   11.8/1.2/1.298.76.5..7.58.49...4...9.7.6.857.....5.9....7....48....64.........4..63........2.   11.8/1.2/1.2987.........9.........65...84....32..93....47..2.4...847....28.2......93.39...7.4   11.8/1.2/1.298.76.5..7.58.49.......9.7.6.857....45.9....7.....8....64.........4..63........2.   11.8/1.2/1.298.76.5..7.54.9.....6.5....6......5.4..87.....9.6.5.4..7..........98.4.......73.2   11.8/1.2/1.2987......6..54.........8...8.3...72.29.....63...2..9..72.....963.8...2.7.6....38.   11.8/1.2/1.2987.........9..6......54...83.....62.92...73...6.3.8..6.....29.37.....8..29...3.7   11.8/1.2/1.2987.........9..6......54...83.....2..92...7.3..6.3.8..6.....2.937.....68.29...37.   11.8/1.2/1.298.76.5..7.45...6..6..948..54..8...6.7965.........9...4.7..........4.73........2.   11.8/1.2/1.298.76.5..7.58.49...64..9.7.6.857....45.9....7.....8....46.........4..63........2.   11.8/1.2/1.298.76.5..7.54.9.....6.5....6....5.4.4..87.....9.6...5..7.........9..73.2...98.4..   11.8/1.2/1.2987......6..54.....5.......32.78.5...7.3.4.8.....52.....38..7.2....2.35........48   11.8/1.2/1.298.76.5..7.5..89...645.9...59...4....486.5.7...7.8......6....9....4............32   11.8/1.2/1.298.76.5..7.5.84....4.9.....8..6.7.9..7..58....6.49...86.....4.3....46...........2   11.8/1.2/1.2987.........9.........65...84....32..39....47..2.4...847....28.2......93..3...7.4   11.8/1.2/1.2987.........9..6......54...83.....2..29...7.3..6.3.8..6.....2.937.....68..2...37.   11.8/1.2/1.298.76.5..7.58.49...64....7.6.758.....5.9....7..8.4.....4..........4..63......8.2.   11.8/1.2/1.298.76....7.5.9.8...46......8....7.96.6....47.......5.845.37.......2.9..4.....5...   11.8/1.2/1.298.76.5..7.4.9..8..56......8....79.6.6....75........4854.37.......2.9........4...   11.8/1.2/1.298.76.5..7.4.9..8..56......8....79.6.6....75........485..37.......2.94.......4...   11.8/1.2/1.298.76.54.7.5.......4...98..67....43........28........656.4.7....9.85...4....96...   11.8/1.2/1.298.76....7.5.9.8...46......8....7.96.6....47.......5.84..37.......2.9.54.....5...   11.8/1.2/1.298.76....7.5.9.8...46......8....7.96.6....47.......5.845.37.......2.9.5.....4....   11.8/1.2/1.2987......6..54.....5.......3.278.4....8.35.7....4.2....3..7.8.2...2..34........57   11.8/1.2/1.298.76....7.5.9.8...46......8....7.96.6....47.......5.84..37.......2.9.5.....45...   11.8/1.2/1.298.76.5..7.5.9..8..46......8....76.9.6.....47......85.45.37.......2.9.......45...   11.8/1.2/1.29876.....5.....64..4.......3.2...87...8.7.3.4.......62.3.2.87.....74........63.2.   11.8/1.2/1.29876.....6.........5....64.7...9.3.423....79........62..32.79.....94........63.2.   11.8/1.2/1.29876.....5.....64..4.......32....87..7..8..36......4.2..37.2.8....34.2......68...   11.8/1.2/1.298.76.5..7.59.4....64.58...6.9..5...54.6......784.9......89.46........32........1   11.7/11.7/3.498.76.5..7.59.4....64.58...6.7..5...54.6......984.7......87.46........32........1   11.7/11.7/3.498.76.5..7.58.49....6.59...89...7...5.7.......64.85.7.....46.........4.3.......21   11.7/11.7/2.698.76.5..7.54..8...46......56.8.7....79.46.....459.....97....8....6....3.......21   11.7/11.7/2.698.76.5..7.59.48...4..58...89.......5.7.9.....64.87.9.....46.........6.3.......21   11.7/11.7/2.698.76.5..7.59.48...4..58...87.......5.9.7.....64.89.7.....46.........6.3.......21   11.7/11.7/2.698.76.5..7.58.49...4..59...89.......5.7.8.....64.97.8.....46.........6.3.......21   11.7/11.7/2.698.76.5..7.59.48...4..58...89...7...5.7.......64.95.7.....46.........6.3.......21   11.7/11.7/2.698.76.5..7.54..8...46......8.459.....79.46....6.8.7....97....5....6....3.......21   11.7/11.7/2.698.76.5..7.58.49....6.59...89.......5.7.8.....64.97.8.....46.........4.3.......21   11.7/11.7/2.698.76.5..7.58.49...4..59...89...7...5.7.......64.85.7.....46.........6.3.......21   11.7/11.7/2.698.76.5..7.59.48...4..58...87...9...5.9.......64.75.9.....46.........6.3.......21   11.7/11.7/2.698.76.5..7.59.48...64.85...87.45....5...79....496.8........6.........43........21   11.7/11.7/2.698.76.5..7.59.48...64.85...89.45....5...97....476.8........6.........43........21   11.7/11.7/2.698.76.5..7.59.48...46.85...87.65....5...79....694.8.......4..........63........21   11.7/11.7/2.698.76.5..7.59.48...64.58...8.76.5...5...97....9648........4..........63........21   11.7/11.7/2.698.76.5..7.59.48...64.85...89.45....5...97....476.8.......4..........63........21   11.7/11.7/2.698.76.5..7.59.48...64.58...8.96.5...5...79....7648........4..........63........21   11.7/11.7/2.698.76.5..7.59.48...46.85...89.65....5...97....674.8.......4..........63........21   11.7/11.7/2.698.76.5..7.59.4....64.587..6.8.7....54.6.9....97.85...4..............93........21   11.7/11.7/2.698.76.5..7.59.48...64.85...87.45....5...79....496.8.......4..........63........21   11.7/11.7/2.698.76.5..7.59.48...46.58...8.94.5...5...79....7468.........6.........43........21   11.7/11.7/2.698.76.5..7.59.48...46.58...8.74.5...5...97....9468.........6.........43........21   11.7/11.7/2.698.76.5..7.58.49...64.59...8...97...59.48.....476.5........6.........43........21   11.7/11.7/2.698.76.5..7.58.49...46.95...89.65....5...87....674.9.......4..........63........21   11.7/11.7/2.698.76.5..7.59.4....64.587..6.7.8....54.6.9....98.75...4..............93........21   11.7/11.7/2.698.76.5..7.59.4....64.587..6.8.7....54.6.9....97.85.....9............43........21   11.7/11.7/2.698.76.5..7.58.49...46.59...8...97...59.68.....674.5.......4..........63........21   11.7/11.7/2.698.76.5..7.59.4....64.587..6.7.8....54.6.9....98.75.....9............43........21   11.7/11.7/2.698.76.5..7.58.49...46.95...8...57...59.68.....674.9.......4..........63........21   11.7/11.7/2.6987......6...........5......4.32.85..3..514.2...4.8.31...8.5.14...21...3....3428.   11.7/11.1/2.69876.....54.........3......8..45.62...5.8..94...9.2....6824..59.5....28.......4.6   11.7/11.0/3.4987......65..........6.....4..93.21.2...613.4.......96...3.94.....14..29....2.1.3   11.7/11.0/3.49876.....54.............9..6...3219.3..1.65.2...95.......56.31....2.16.......3.25   11.7/11.0/2.898.76.54.7.54..9...64.......79.84....5.9.6......57.....48...7........63........28   11.7/10.6/3.498.76.54.7.54..9...64.......79.84....5.9.......657.....48...7........63........28   11.7/10.6/3.49876.....54.............9..6...3251.3..1.6.92...95.......56.13....2.1.6......32.5   11.7/10.6/2.898.76.5..7.58.49...64......6.758....4..9...7..98..7....46............4.3.......21   11.7/10.5/2.6987......6...........85.....4.3.251..3..14.28...58......2..5.4....2.8.31...14.2..   11.7/10.3/2.698.76.5..7.58.49...64......4..9.6.7..98..7.....758.....46............4.3.......21   11.7/10.2/2.698765....4..............86..5.3.218..2.51.6.3....8.......2...36...13.5.8.....521.   11.7/9.5/2.898.76.5..7.59.48...64.85...89.45....5....7....476.8.......4.9........63........21   11.7/9.4/2.698.76.5..7.59.48...64.85...87.45....5....9....496.8.......4.7........63........21   11.7/9.4/2.698.76.5..7.59.4....64.587..6...7....54.6.9....97.85.....9...8........43........21   11.7/9.4/2.698.76.54.7.54..9...64.......5.9.6.....9.84.....657.....48...7........63........28   11.7/2.0/2.098765....43.........2......8..43.65...48..9.3....96....583..4.9.4....86........35   11.7/2.0/2.0987......6..85......4.......3.5.261..1..86.23...31.......62.5.8......16........32   11.7/2.0/2.0   19661987......6..85......4.......3.5.261..1..863.2...31.......62..58......2.3......16.   11.7/2.0/2.0   1966298.76.5..7.58.49......59...89.......5.7.......64.87.......46.7.......4.3.......21   11.7/2.0/2.0   1966298.76.5..7.58.49......59...89.......5.7.......64.87.......46.8.......6.3.......21   11.7/2.0/2.0   1966198.76.5..7.59.4....64.587..6.7.8.....98.75....4.6.9.....9...8........43........21   11.7/2.0/2.098.76.54.7.54..9...64.......7..84....5.9.6.....657.....48...7........63........28   11.7/2.0/2.098.76.5..7.59.48...64.85...89.45....5...97....476.........4.9........63........21   11.7/2.0/2.098.76.5..7.59.48...64.85...87.45....5...79....496.........4.7........63........21   11.7/2.0/2.0987......65.9...........6..4..39.21.1..2.6.34......9.6...42...3...1.3.6......91.2   11.7/2.0/2.098.76.5..7.59.4....64.587..6.8.7.....97.85....4.6.9.....9...8........43........21   11.7/2.0/2.098.76.5..5.7.......46...8...9.4...86.6587...4....96.......5..39......7.8.......2.   11.7/1.5/1.598.76.5..7.5.......648......9..846...47..685........94...5.8.......39.7.....2....   11.7/1.5/1.598.76.5..5.74.8....4..5.8..89...5...6.5..7....7469......9....8......6.32.....4..1   11.7/1.5/1.5987......6..8...........5...4.38.21..1.2.5.34......8.5..31.8.5....42...3.....31.2   11.7/1.5/1.5987......6..5......4.......3...965...9.73.62....2.5....3.67.9.5....5236........72   11.7/1.5/1.5987......65.4.......3......5...964....985.62....2.4......68.9.4....4256........82   11.7/1.5/1.598.76.5..7.54..9...64......85.9.7....97.4......658.....48.........6...8.......3.2   11.7/1.2/1.298.76.5..7.58.49...64..5...8.6....32.4..............5..7..46.9...957.......9.8...   11.7/1.2/1.298.76.5..7.5.......645.....8.74.6.5.4..89.....96..5.4....9.73.2....8..........4..   11.7/1.2/1.298.76.5..7.4.5.....6.......8.7....4.5..89.....96.47.5....9.........863.2......4..   11.7/1.2/1.298.76.5..7.54..9...64......45.9.7....79.8......654.....48.........6...8.......3.2   11.7/1.2/1.298.76.5..7.4..96....5.84...6.7.5.....9........48..7.5....94..32.....8..........6.   11.7/1.2/1.298.76.5..7.4..5....6...89..8...96...5.64.7......58....4......32..7...4.......4.9.   11.7/1.2/1.2   9298.76.5..7.5.946....48.5...6.7......59...6....489.7.6....4..8.......8.32.......5.   11.7/1.2/1.298.76.5..7.4..5....6..489..8...96...5.64.7......58....4......32..7...4.........9.   11.7/1.2/1.2   9298.76.5..7.49......56.4.9..8......32.7....8......8..9.6...59...54.87.......6.4...   11.7/1.2/1.2   2019987.........96.8......5....84.......3.9.2.78...2..34..7..2..3.4.94...27..3.....98   11.7/1.2/1.298.76.5..7.59.4....64..89..8........4.78.6.5..965........4...32.....74.........9.   11.7/1.2/1.298.76.5..7.59.4....64.589..8......3247....8.........9.6...49....4.87..6......5...   11.7/1.2/1.2   2007598.76.5..7.54.......6.95...59..7..6..6485...9..7......4.8..........8.4.3........2   11.7/1.2/1.298.76.5..7.5.94....648.....6..4.9.7....67...8....58...4.9.....3..6....21.........   11.7/1.2/1.2   2008598.76.5..7.59.4....64.589..8......3247....8.........9..4.87..6....6.5.......49...   11.7/1.2/1.2   2007598.76.5..7.58.4....64.95...89.....6.5.........479.6..8...4.7.3......9.21.........   11.7/1.2/1.2   2008698.76.54.7.5.9..6...48.....6.834.......2.6............5.....47....6..8.5.....7.96   11.7/1.2/1.2`
Possible future contributions will be minlex based.
hendrik_monard

Posts: 88
Joined: 19 April 2021
Location: Leuven (Louvain) Belgium

### Re: The hardest sudokus (new thread)

.
Hi Hendrik
hendrik_monard wrote:This new batch contains 33596 minimal puzzles in the SER(ating) range 11.6 to 11.8.

Great job of producing so many new high SER puzzles.
As I understand it, you're still using the SER as your main search criterion.
Do you have any filters for the intermediate puzzles produced by the algorithm (number of clues/candidates)?

hendrik_monard wrote:A large part of the puzzles in the present batch are probably T&E(3).

The most time consuming part of checking this would be to prove that they are not in T&E(2). I'll try on the first few puzzles you posted here.
However, I don't see how "a large part" could be in T&E(3) if the SER is your search criterion. People have been trying for more than 20 years to produce high SER puzzles and none of them was ever found to be in T&E(3). The first puzzle retrospectively found to be in T&E(3) was Loki, manually created by mith based on a totally new impossible pattern.
What's different in your algorithm? Or did you use seeds from mith database?

hendrik_monard wrote:It was not an easy task to check novelty compared to the impressive lists posted by mith in the thread 'T&E(3) Puzzles (split from "hardest sudokus" thread)' on 7 November 2022, containing many non minimal puzzles.

Minimal puzzles were the good concept for the old database, before mith started to use expansion by Singles and re-search from the expanded form. After he started using this procedure, he could find many more minimal puzzles than previous researchers, but many of these puzzles are identical to other ones for all practical purposes. The good concept for doing their analysis without being overwhelmed by redundancies became the min-expands.
I think the good comparison to make would be between databases of minlex min-expands (mith's format).
Is your algorithm using expansion and re-search (and does it produce lots of minimals with the same expanded form)?

hendrik_monard wrote:The list can be downoaded from:
...
Possible future contributions will be minlex based.

denis_berthier
2010 Supporter

Posts: 4004
Joined: 19 June 2007
Location: Paris

### Re: The hardest sudokus (new thread)

.
I tried to solve in T&E(2).
Only the following 28 puzzles among the 158 available require T&E(3):
Code: Select all
`9876.........958.......4...7.8......36.2..7...293.768.2.6....97..3...2.8......36.   11.8/1.2/1.2         #6987.........96........5....87.4..32...3...9.8..2....473.8.......4...2.3..29.4387.   11.8/1.2/1.2   92    #16987.........96........5....87....43.2.4...9.8..3....274.8.......39.2487..2...3.4.   11.8/1.2/1.2   92    #1798.76.5..7.5.94....468.....8..9.6.7...7.58......47...96.....4.3....49...........2   11.8/1.2/1.2         #22987.........96........5....87.4..32..39...4.7..2....982.8.......93.4278..4...32..   11.8/1.2/1.2   91    #2398.76.5..7.58.49....6.59...89...7...5.7.......64.85.7.....46.........4.3.......21   11.7/11.7/2.6        #8198.76.5..7.54..8...46......56.8.7....79.46.....459.....97....8....6....3.......21   11.7/11.7/2.6        #8298.76.5..7.59.48...4..58...89.......5.7.9.....64.87.9.....46.........6.3.......21   11.7/11.7/2.6        #8398.76.5..7.59.48...4..58...87.......5.9.7.....64.89.7.....46.........6.3.......21   11.7/11.7/2.6        #8498.76.5..7.58.49...4..59...89.......5.7.8.....64.97.8.....46.........6.3.......21   11.7/11.7/2.6        #8598.76.5..7.59.48...4..58...89...7...5.7.......64.95.7.....46.........6.3.......21   11.7/11.7/2.6        #8698.76.5..7.54..8...46......8.459.....79.46....6.8.7....97....5....6....3.......21   11.7/11.7/2.6        #8798.76.5..7.58.49....6.59...89.......5.7.8.....64.97.8.....46.........4.3.......21   11.7/11.7/2.6        #8898.76.5..7.58.49...4..59...89...7...5.7.......64.85.7.....46.........6.3.......21   11.7/11.7/2.6        #8998.76.5..7.59.48...4..58...87...9...5.9.......64.75.9.....46.........6.3.......21   11.7/11.7/2.6        #90987......6..85......4.......3.5.261..1..86.23...31.......62.5.8......16........32   11.7/2.0/2.0   19661 #125987......6..85......4.......3.5.261..1..863.2...31.......62..58......2.3......16.   11.7/2.0/2.0   19662 #12698.76.5..7.58.49......59...89.......5.7.......64.87.......46.7.......4.3.......21   11.7/2.0/2.0   19662 #12798.76.5..7.58.49......59...89.......5.7.......64.87.......46.8.......6.3.......21   11.7/2.0/2.0   19661 #128987......65.9...........6..4..39.21.1..2.6.34......9.6...42...3...1.3.6......91.2   11.7/2.0/2.0         #13398.76.5..7.4..5....6...89..8...96...5.64.7......58....4......32..7...4.......4.9.   11.7/1.2/1.2   92    #14798.76.5..7.4..5....6..489..8...96...5.64.7......58....4......32..7...4.........9.   11.7/1.2/1.2   92    #14998.76.5..7.49......56.4.9..8......32.7....8......8..9.6...59...54.87.......6.4...   11.7/1.2/1.2   2019  #150987.........96.8......5....84.......3.9.2.78...2..34..7..2..3.4.94...27..3.....98   11.7/1.2/1.2         #15198.76.5..7.59.4....64.589..8......3247....8.........9.6...49....4.87..6......5...   11.7/1.2/1.2   20075 #15398.76.5..7.5.94....648.....6..4.9.7....67...8....58...4.9.....3..6....21.........   11.7/1.2/1.2   20085 #15598.76.5..7.59.4....64.589..8......3247....8.........9..4.87..6....6.5.......49...   11.7/1.2/1.2   20075 #15698.76.5..7.58.4....64.95...89.....6.5.........479.6..8...4.7.3......9.21.........   11.7/1.2/1.2   20086 #157`

Not a "large part", but anyway even one would raise questions about how it can get into your list.
denis_berthier
2010 Supporter

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Location: Paris

### Re: The hardest sudokus (new thread)

I forgot to share the access to the file with all. I have now corrected this on my google drive.
hendrik_monard

Posts: 88
Joined: 19 April 2021
Location: Leuven (Louvain) Belgium

### Re: The hardest sudokus (new thread)

.
Thanks, it works.

I've checked one more point about the 28 T&E(3) puzzles among the 158 ones that were available this morning: none of them breaches the new upper limit of complexity: T&E(W2, 2).
denis_berthier
2010 Supporter

Posts: 4004
Joined: 19 June 2007
Location: Paris

### Re: The hardest sudokus (new thread)

To explain my modus operandi, let me first explain how it emerged.
I got interested in sudokus about ten years ago. I learned a lot from Andrew Stuart's website “sudokuwiki.org” and wrote my first Basic solver along his concept of basic strategies.
Later I discovered on internet an early version of a database of 'hard sudokus' : HardestDatabase110626, with golden Nugget, Kolk, Imam bayildi etc.
I studied relationships between individual puzzles with my equivalence analyser. I noticed how small differences between puzzles could increase the ratings.
At first I built a sudoku generator placing random numbers on random positions in an emtpy 9x9 table in a Word document respecting Sudoku rules. Valid puzzles were further analysed and in subsequent steps made harder with the techniques discovered as indicated above.
It took me a couple of years to come to the conclusion that this was not a very efficient technique.The maximum rating reached was SER 11.4.
In the meantime, I discovered this forum and Champagne's database ph_1710 and later ph_1910. I perfected my 'modifier' scripts by applying them on those databases. What struck me was that when I modified a puzzle in this way, the resulting puzzle, with a higher (or lower) rating, was practically always already present in the database. My conclusion was that the overwhelming majority of puzzles in those databases are derivatives from pre-existing puzzles. Nevertheless I found one new 11.8 that I submitted with my first post in this thread in April 2021.
Regarding your question about algorithms: indeed, one type of them consists in adding clues (from the solution) and subsequently identifying minimals. This type of algorithm does not modify the solution, so all the resulting puzzles are in the same tree (expression used by mith). Another type of algorithm changes the solution (f.i by changing one or more clues) and the resulting puzzles thus belong to a different tree. This second type of algorithms can have a more profound effect, positive or negative, on the rating. It is also my experience that most of the interesting results come from a combination of both types of algorithms.
About minimals: you have a point there. Indeed, one could limit the novelty to the expanded version only. But there is the following observation keeping in mind the preceding alinea: a combination of the two types of algorithms leads sometimes to a remarkable result (f.i. an 11.9 in my previous batch last September), but it does so only for a single one of the minimals. This means that in my modus operandi, I would have to test all minimals anyway in combination with the other type of algorithm (modifying the solution). The question remains therefore: should all the relevant minimals be published or not? If not, everyone wanting to 'build' on the expanded version should identify separately the relevant minimals. Sudokus are forever and perhaps in the future, a clever young developer may with the right modifications on the right minimal open the door to a new class of puzzles, that is if AI will not do it first
Regarding your question on filters: I first use stage 2 (of 4) in my Logical solver, which I suppose is akin to T&E(1). It is fast and, if it doesn't solve the puzzle, skfr is used as a second filter before proceeding to SER, the ultimate filter. I put no limits on the number of clues or candidates.
Finally about your consideration in fine: what I also have learned about hard sudokus is that the large majority of them are not generated from scratch, but are derived from precursors, applying suitable modifications. I have observed that the potential for deriving hard puzzles from puzzles in previous databases, of which ph_2010 was the most recent, was practically exhausted, at least with the 'modifiers' I use. When last year new puzzles became available, there was a new potential for deriving other hard sudokus with my optimized modifiers. If the original puzzle happens to be in T&E(3) then there is a reasonable chance that some derivatives keep that characteristic, which explains why a (not so large) substantial part of the puzzles in my latest results remain in T&E(3). Mith has opened a rich source for further derivations in the years to come. We may all be grateful to him.
hendrik_monard

Posts: 88
Joined: 19 April 2021
Location: Leuven (Louvain) Belgium

### Re: The hardest sudokus (new thread)

hendrik_monard wrote:About minimals: you have a point there. Indeed, one could limit the novelty to the expanded version only. But there is the following observation keeping in mind the preceding alinea: a combination of the two types of algorithms leads sometimes to a remarkable result (f.i. an 11.9 in my previous batch last September), but it does so only for a single one of the minimals. This means that in my modus operandi, I would have to test all minimals anyway in combination with the other type of algorithm (modifying the solution). The question remains therefore: should all the relevant minimals be published or not? ...

I had a similar discussion with mith a few months ago, the conclusion being that we need to keep two separate databases:
- one for minimals (for generating more puzzles);
- and one for min-expands (for studying solutions without wasting too much time with redundancies).

hendrik_monard wrote:I have observed that the potential for deriving hard puzzles from puzzles in previous databases, of which ph_2010 was the most recent, was practically exhausted, at least with the 'modifiers' I use. When last year new puzzles became available, there was a new potential for deriving other hard sudokus with my optimized modifiers. If the original puzzle happens to be in T&E(3) then there is a reasonable chance that some derivatives keep that characteristic, which explains why a (not so large) substantial part of the puzzles in my latest results remain in T&E(3).

The reason why I asked this question about the seeds is: for any n, there must be many more puzzles in T&E(n) than in T&E(n+1). When n = 1, "many" is of the order of 30,000,000. When n=2, we have no precise idea, but the ratio must be very high also.
As a result, starting from a puzzle in T&E(2), chances of finding one in T&E(3) by any kind of vicinity search are very low, but starting from a puzzle in T&E(3) chances are high of falling down to T&E(2 or even 1) (e.g. if the modification destroys a T&E(3) pattern).
Last edited by denis_berthier on Tue May 16, 2023 2:57 am, edited 1 time in total.
denis_berthier
2010 Supporter

Posts: 4004
Joined: 19 June 2007
Location: Paris

### Re: The hardest sudokus (new thread)

.
I ran one more quick calculation for the same 158 puzzles. I wondered which of them have the anti-tridagon pattern. And the answer is: ALL.
(By anti-tridagon, I always mean the non-degenerate form [the only form that requires T&E(3) to be proven contradictory, with the 3 digits in the 12 cells] + any number of guardians).

The interesting part here is, until now, we knew that tridagons can appear for puzzles in T&E(2), but we had only few examples.

[UPDATE]
All the puzzles in the full list (33596) have an anti-tridagon pattern.
12166 (36.2%) of them can be solved in W2+S3.
It seems that, in the mean, the puzzles are easier than those in mith's list, but I haven't run full calculations of their W+OR5W ratings to be 100% certain of it.
.
denis_berthier
2010 Supporter

Posts: 4004
Joined: 19 June 2007
Location: Paris

### Re: The hardest sudokus (new thread)

I have been away from this forum for some years. I am wondering, is there an updated list of all the puzzles found, like the lists that champagne used to provide? Or else, what is the latest list? I did find some puzzles back then and now I would like to see the newly found ones. From this thread I understand that some participants have found quite a few new high rated ones.
Paquita

Posts: 72
Joined: 11 November 2018

### Re: The hardest sudokus (new thread)

Hi Paquita,

You'll find the main breakthrough in hardest puzzles in this tread: http://forum.enjoysudoku.com/t-e-3-puzzles-split-from-hardest-sudokus-thread-t40514.html
In a few words, mith has found a puzzle that happened to be the first one not in T&E(3).
The above thread will provide all the details.
You can also see here: http://forum.enjoysudoku.com/the-tridagon-rule-t39859.html for the specific rules that allow to solve them.
denis_berthier
2010 Supporter

Posts: 4004
Joined: 19 June 2007
Location: Paris

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