I took the time to have a closer look at the list posted by mith on March 21st. (
the-hardest-sudokus-new-thread-t6539-1230.html#p318907)
It reminds me of a list I made in september 2021. I wanted to know if in ph_2010, all puzzles with equivalent solutions were 'closely' related.
This list was the result of the analysis of all 11.2+ puzzles in ph_2010. It contains groups of puzzles with equivalent solutions. Only groups with at least two members are listed.
The largest group (of puzzles with SER >= 11.2 and equivalent solutions) counted 523 members, all closely related.
The first line of each group is the canonical morph of the common (equivalent) solution of all members of the group.
column 2: line number in ph_2010
col. 3: ID
col. 4: first digits of original puzzle
col. 5: additional puzzle data (unfortunately, on my screen this column goes to a new line)
This is the top of the list (first 7 groups):
- Code: Select all
987654321653921874214873695832495716791368452546712938428137569365289147179546283
9.....3....3..1.7....8....5.....5.1..9..6.4.....7....842...7....6.2...4...9.4.2.. 3 2 12..3....4....1.2... 11.90;11.90;11.30;elev;second flush;2;23;
9.....3....3..1.74...8....5.....5.1..9..6.4.....7....842...7....6.2.......9.4.2.. 33092 39354 98.7..6..5...4...... 11.20;1.20;1.20;GP;12_07;39354;23;
987654321653921874241783956829536417715492638364178295572869143438217569196345782
.8.6...2.....2...42....39..8..5...1..15.......6..7.........9..3..82...6.....4.7.. 5 4 .2.4...8.....8...68. 11.90;11.90;9.90;elev;3;4;22;
.8.6...2.........42....39..8..5...1..15.......6..7........69..3..82...6.....4.7.. 6406 910 .2.4...8.........68. 11.30;11.30;9.30;elev;721;910;22;
987654321654321987321987654896135472735248196142796835519473268473862519268519743
9.......1..43...8..2....6......35.7...5..8....4.7......1....2..4...6...9..85...4. 12 7 1.......9..67...2..8 11.80;11.80;11.60;elev;15;7;22;
9.......1..43...8..2....6......35.7.7.5.48......7......1....2..4...6...9..85...4. 19553 15522 98.76....75....6.... 11.20;11.20;11.10;GP;kz1a;15522;23;
987654321653921874124783659849362715762815943531497268476139582315278496298546137
......3..6....1.7..2.7....9..9...7.57...1..4..3....2..4..1...8...5..8.......46... 15 11 98.7.....6...5...... 11.80;11.80;11.40;GP;H1;11;22;
......3..6....1.7..2.78...9..9.....57...1..4..3....2..4..1...8...5..8.......46... 2261 423 98.7..6....5.9..4... 11.40;11.40;2.60;GP;H72;423;22;
......3..6....1.7..2.7....9..9.6...57...1..4..3....2..4..1...8...5..8.......46... 3276 529 98.7.....6.....97... 11.40;1.20;1.20;GP;H86;529;22;
..76..3..6....1.7..2.7....9..9.....57...1..4..3....2..4..1...8...5..8.......4...7 13504 15710 98.7.......7.6...... 11.30;1.20;1.20;GP;Kz1 b;15710;23;
..76..3..6....1....2.7....9..9...7.57...1..4..3....2..4..1...8...5..8.......4...7 13649 18770 98.7.....6...5.9.... 11.30;1.20;1.20;GP;KZ1C;18770;23;
..76..3..6....1.7..2.7....9..9.6...57...1..4..3....2..4..1...8...5..8.......4.... 20400 18307 98.7.......7.6...... 11.20;11.20;10.60;GP;KZ1C;18307;23;
......3..6....1.7..2.7....9..9.....57...1..4..3....2..4..1...8...5..8.......46..7 38715 3312 98.7.....6.....7.... 11.20;1.20;1.20;GP;H654;3312;22;
987654321653921874124873695875346219496512738312789546748295163569137482231468957
..7.5....6....1....2.8...9....3....9.9.....38......54..4.2....35....7.....1.6.... 17 12 1.......2..94...5..6 11.80;11.80;11.20;tax;gsf-2007-05-24-003 64879;12;21;
..7.5....6....1....2.8...9....3..2.9.9.....38......5...4.2....35....7.....1.6.... 80 100058 98.7.....7.6...8.... 11.70;11.70;11.20;GP;12_11;100058;21;
..7.5....6....1....2.8...9....3..2.9.9.....38......54..4.2....35....7.....1.6.... 1708 3269155 .......12.....34.5.. 11.40;11.40;11.20;MITH;2020_10;3269155;22;
987654321653921874214873965869145237375269148142387659728516493531492786496738512
.8.6...2......1..4....7.9......4...7.....91....23...5..285......3.....8.4.6...... 18 13 6.......2.9.4...5... 11.80;11.80;11.10;tax;coloin-04-10;13;21;
.8.6...2......1..4....7.9......4...7.....91....23...5...85....353.....8.4.6...... 21188 287382 .......12.....3..4.. 11.20;11.20;10.40;dob;12_12_03;287382;22;*
987654321654321987312978564876192453245763198193845276731289645528436719469517832
.8.....2....3...87......5.4..6.9.....4.7....81....5....3.2...4.5....6.....9.1.... 19 14 1.......2.9.4...5... 11.80;11.80;10.80;tax;coloin-04-10;14;21;
.8....32....3...87......5....6.9.....4.7....81....5....3.2...4.5....6.....9.1.... 77 39 1.......2.9.4...5... 11.70;11.70;11.20;tax;coloin-04-10;39;21;
It appears that in the overwhelming majority of groups, the members are closely related.
One of the very rare exceptions is the first member of this group:
- Code: Select all
987654321654321987312897456865139274723465819491278563546783192238916745179542638
.8...4.2.6.4.2..87......4..86..3.2.4.2..6.8....1..8..35....3......9......7..4.6.. 34734 1886884 98.76.5..7..8..9.... 11.20;1.20;1.20;GP;2011_12;1886884;26;
.8.6.432.6...2..8.........6.6..3...47....5.....1.......4..8...22.89..7...7..426.. 39599 1834996 98.76.5..5....9.7... 11.20;1.20;1.20;GP;2016_04_23;1834996;26;
.8.6.432.....2..8.........6.6..3...47....5.....1.......46.8...22.89..7...7..426.. 39609 1834952 98.76.5..5....9..... 11.20;1.20;1.20;GP;2016_04_23;1834952;26;
And now something completely different.
My script for finding new hard puzzles stopped yesterday when skfr did not return a rating result for this puzzle:
..2.3...4...2.53.15..14.8..987......6...........85.....4.3.251....58.4.2....14.8.
I use this command line (in VBA script) for skfr:
res = Wshshell.Run("skfr_win64_v2_0_1.exe", vbHide, True)
However, SER returns this result for the same puzzle:
..2.3...4...2.53.15..14.8..987......6...........85.....4.3.251....58.4.2....14.8. ED=11.0/1.2/1.2