The New Sudoku Players' Forum

Website · by **denis_berthier** » Sat Nov 04, 2023 2:38 pm

.
In the tridagon thread (http://forum.enjoysudoku.com/the-tridagon-rule-t39859-120.html),
I analysed the last collections of T&E(2) puzzles published by Paquita:
http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1644.html
http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1648.html
http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1650.html

and I remarked that they have:
- unusually high proportions of non-degenerate tridagons (resp. 97.01%, 99.97% and 100%);
- unusually high proportions of puzzles in B6B;
- no puzzle in B7B.

Let me add to the above collections, the one published by Hendrik Monhard:
http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1628.html
https://drive.google.com/file/d/1LxrL5R5vmYqj6f7FBEmPL5ot7OZY1pXH/view?usp=drive_link
It contains 55,088 puzzles, 46,079 of which are in T&E(2), the rest in T&E(3).
The puzzles in T&E(3) all have a non-degenerate tridagon pattern and they are all in B2BB=T&E(B2, 2), same as all the known T&E(3) puzzles.

Let's therefore concentrate on the T&E(2) sublist. This is where the main news are.

First big news is, it has 77 puzzles in B7B. (Until now, we knew only 10 different ones.)

Code: Select all: puzzle ER/EP/ED creation_date position_in_T&E(2)_list 98.76.54.7.5.4.8....6....9.67...5...4.8...75..59....68...3....9...2..........4... 11.7/1.2/1.2 220515 #3079 98.76.5..7.4.8.....56...8..8.5..7.4.6..59.....79.48.6....9....3......4..........2 11.7/1.2/1.2 220515 #3080 98.76.54.7.5..4....6...8.9.85.9.6...4.6.87......45...8..7...3........2..........9 11.7/1.2/1.2 220515 #3081 98.76.54.7.5.9.....64..8.9.85.9.6...4.6.87......45...8..7...3........2..........9 11.7/1.2/1.2 220515 #3233 98.76.54.7.5.498...6.8.....49..87....579.6......45...9..6....3........2.........8 11.7/1.2/1.2 220515 #3234 98.76.54.7.5..4....6...8.9.8..9.6...4.6.87..5...45...8..7...3........2..........9 11.7/1.2/1.2 220515 #3235 98.76.54.7.5.9.....64..8.9.8..9.6...4.6.87..5...45...8..7...3........2..........9 11.7/1.2/1.2 220515 #3236 98.76.5..7.5.498...648......9..87....579.6.4....45..9...6.....3.......8.........2 11.7/1.2/1.2 220515 #3237 98.76.5..7.5..9....645.8...8...75.9.5.649...7...8.....6.....4.3...6.4...........2 11.8/1.2/1.2 220928 #5743 98.76.5..7.58.49...46.5.....78.46.9...958.......9.7....6.........4....32.....8.5. 11.8/1.2/1.2 220928 #5744 98.76.5..7.5.496...4.......67.89....5..4.6.7..94.5........8..........8.3......4.2 11.8/1.2/1.2 230514 #15340 98.76.5..7.4..98...56......8..5.6.9..67.8......9.74.......4..........6.3......4.2 11.8/1.2/1.2 230514 #15344 98.76.5..7.4..98...56..8...8..5.6.9.5.9.74....679.........4..........6.3......4.2 11.8/1.2/1.2 230514 #15345 98.76.5..7.5.496...4.5.....67.89....5..4.6.7..94..7.......8..........8.3......4.2 11.8/1.2/1.2 230514 #15346 98.76.5..7.5..89...645.9...59...4....486.5.7...7.8......6....9....4............32 11.8/1.2/1.2 230514 #15382 98.76.5..7.6.4......58.....6.859..4.45..7.....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #34412 98.76.5..7.5.496...4.5.....67.89....5..4.6.7..94.7........8..........8.3......4.2 11.6/1.2/1.2 230514 #37154 98.76....7.6..5....458.....6...98.....7..48.....57.9..5.4....98.....6..........32 11.6/1.2/1.2 230514 #37188 98.76.5..7.5.496...4.......67.89....5....6.7..94.5........84.........8.3......4.2 11.6/1.2/1.2 230514 #37325 98.76.5..7.5..96...4.......67.89....5..4.6.7..94.5........84.........8.3......4.2 11.6/1.2/1.2 230514 #37396 98.76.5..7.6.4......58.....6.859..4.4...7.....9.6...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #37433 98.76.5..7.4..98...5.......8..5.6.9..67.8......9.74...6.....4.3....4..........6.2 11.6/1.2/1.2 230514 #37439 98.76....7.6..58...458.....6...98.....7..4......57..9.5.4...9.8.....6.........3.2 11.6/1.2/1.2 230514 #37475 98.76.5..7.4..98...56......8..5...9..67.8......9.74......64..........6.3......4.2 11.6/1.2/1.2 230514 #37485 98.76.5..7.6.45.....58.....6.8.9..4.45..7.....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #37517 98.76.5..7.6.4......58.....6.759..4.45..78....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #38028 98.76.5..7.4..98...56..8...8..5.6.9.5.7.94....6..7........4..........6.3......4.2 11.6/1.2/1.2 230514 #38836 98.76.5..7.4..98...56..8...8..5.6.9.5.9.74....67.9........4..........6.3......4.2 11.6/1.2/1.2 230514 #38844 98.76.5..7.4..98...5.......8..5...9..67.8......9.74...6.....4.3...64..........6.2 11.6/1.2/1.2 230514 #38891 98.76.5..7.6.4......58.9...6..5...4.45..78....976......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #38922 98.76.5..7.6.45.....58.9...6......4.45..78....976......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #38927 98.76.5..7.5.496...4.5.....67.89....5..4.6.7..94..5.......8..........8.3......4.2 11.6/1.2/1.2 230514 #38939 98.76.5..7.5.496...4.5.....69.87....5..4.6.7...4.9........8..........8.3......4.2 11.6/1.2/1.2 230514 #38944 98.76.5..7.6.45.....58.....6...9..4.45..78....976......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #38967 98.76.5..7.4..98...56..8...8..5...9.5.9.74....679........64..........6.3......4.2 11.6/1.2/1.2 230514 #39001 98.76.5..7.6.4......58.9...6.75...4.4...78....9.6...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39044 98.76.5..7.6.4......58.....6.759..4.4...78....9.6...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39045 98.76.5..7.6.4......58.....6..59..4.4...78....986...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39049 98.76.5..7.6.4......58.....6..59..4.45..78....976......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39052 98.76....7.6.54....548.....64..98.....76.58......7.9..4.5....98.....6..........32 11.6/1.2/1.2 230514 #39058 98.76.5..7.4..98...56..8...8..5.6.9..678.......9.74.......4..........6.3......4.2 11.6/1.2/1.2 230514 #39059 98.76.5..7.5..96...4.5.....67.89....5..4.6.7..94..7.......84.........8.3......4.2 11.6/1.2/1.2 230514 #39081 98.76.5..7.5.496...4.5.....67.89....5....6.7..94..7.......84.........8.3......4.2 11.6/1.2/1.2 230514 #39140 98.76.5..7.5.496.....5.....69.87....5..4.6.7...4.9....4.....8.3....8..........4.2 11.6/1.2/1.2 230514 #39162 98.76.5..7.6.45.....58.....6...9..4.45..78....986......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39167 98.76.5..7.5..96...4.5.....69.87....5..4.6.7...4.9....4.....8.3....8..........4.2 11.6/1.2/1.2 230514 #39170 98.76....7.6.54....548.....64..98.....7..58.....67.9..4.5....98.....6..........32 11.6/1.2/1.2 230514 #39193 98.76.5..7.5.496...4.5.....67.89....5....6.7..94.7........84.........8.3......4.2 11.6/1.2/1.2 230514 #39197 98.76.5..7.6.4......58.9...6.75...4.45..78....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39200 98.76.5..7.4..98...5...8...8..5...9..678.......9.74...6.....4.3...64..........6.2 11.6/1.2/1.2 230514 #39211 98.76.5..7.5.496...4.5.....69.87....5....6.7...4.9........84.........8.3......4.2 11.6/1.2/1.2 230514 #39224 98.76.5..7.6.45.....58.....6.7.9..4.45..78....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39261 98.76.5..7.5..96...4.5.....69.87....5..4.6.7...4.9........84.........8.3......4.2 11.6/1.2/1.2 230514 #39265 98.76.5..7.5.496...4.5.....67.89....5....6.7..94..5.......84.........8.3......4.2 11.6/1.2/1.2 230514 #39318 98.76.5..7.5..96...4.5.....67.89....5..4.6.7..94.7........84.........8.3......4.2 11.6/1.2/1.2 230514 #39336 98.76.5..7.4..98...56..8...8..5...9..678.......9.74......64..........6.3......4.2 11.6/1.2/1.2 230514 #39422 98.76.5..7.6.4......58.....6..59..4.45..78....986......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39431 98.76.5..7.6.45.....58.9...6.7....4.45..78....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39443 98.76.5..7.4..98...5...8...8..5.6.9..678.......9.74...6.....4.3....4..........6.2 11.6/1.2/1.2 230514 #39447 98.76....7.6..58...458.....65..98.....75.4.......7..9.5.4...9.8.....6.........3.2 11.6/1.2/1.2 230514 #39455 98.76....7.6..5....458.....65..98.....75.48......7.9..5.4....98.....6..........32 11.6/1.2/1.2 230514 #39458 98.76.5..7.5..96...4.5.....67.89....5..4.6.7..94..5.......84.........8.3......4.2 11.6/1.2/1.2 230514 #39464 98.76.5..7.4..98...56..8...8..5.6.9..6.87......7.94.......4..........6.3......4.2 11.6/1.2/1.2 230514 #39681 98.76.5..7.6.4......58.....6..59..4.4...78....976...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39797 98.76.5..7.4..98...5...8...8..5...9..6.87......7.94...6.....4.3...64..........6.2 11.6/1.2/1.2 230514 #39950 98.76....7.5...9...46..5...5..98.....6.5.7.8...8.46....7..........6.4.98.......32 11.6/1.2/1.2 230514 #39952 98.76.5..7.4..98...56..8...8..5...9.5.7.94....6..7.......64..........6.3......4.2 11.6/1.2/1.2 230514 #39953 98.76.5..7.4..98...5...8...8..5.6.9..6.87......7.94...6.....4.3....4..........6.2 11.6/1.2/1.2 230514 #39955 98.76....7.5...9...46..58..5..98.....6.5.7.....8.46....7..........6.4.98.......32 11.6/1.2/1.2 230514 #39957 98.76.5..7.4..98...56..8...8..5...9..6.87......7.94......64..........6.3......4.2 11.6/1.2/1.2 230514 #39959 98.76.5..7.6..5....4..8....8..6...5.5...98.4..97.4....67....4.5...9...........3.2 11.6/1.2/1.2 230514 #39960 98.76.5..7.6..5....45.8....8..6......9754........98.4.67....4.5...9...........3.2 11.6/1.2/1.2 230514 #39961 98.76.5..7.6..5....4..8....8..6.....5...98.4..9754....67....4.5...9...........3.2 11.6/1.2/1.2 230514 #39962 98.76.5..7.5.496.....5.....69.87....5....6.7...4.9....4.....8.3....84.........4.2 11.6/1.2/1.2 230514 #39965 98.76....7.6..5....45.8....8..6..5...9754........984..67.....54...9............32 11.6/1.2/1.2 230514 #39966 98.76.5..7.6.4......58.9...6..5...4.4...78....976...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #40118 98.76.5..7.4..98...56..8...8..5...9.5.9.74....67.9.......64..........6.3......4.2 11.6/1.2/1.2 230514 #40187

Second big news is, it has puzzles beyond B7B. Indeed, it has 15 puzzles in B9B and 1 in B10B and they don't even have the highest SER.

Code: Select all: puzzle ER/EP/ED creation_date position_in_T&E(2)_list BpB_classif 98.76.5..7.48......56......56..8..4.4.89.6....7945......7..........9...3....7.2.1 11.6/1.2/1.2 220515 #4706 B9B 987......6...........85.....4.3..21....42..58....184.3..2..31.....54.32....1...84 11.6/1.2/1.2 220928 #15309 B9B 987......65.9...........6..4..32.16.3..1.4..2....96......4...19...2.13......3.42. 11.7/1.2/1.2 230514 #19131 B9B 987......65.9...........6..4..32.91.2..4.13.6....6.......2...93...13.4......942.1 11.7/1.2/1.2 230514 #21539 B9B 987......65.9...........6..4..32.91.2..4.13.6....6.......2...93...13.46......42.1 11.7/1.2/1.2 230514 #22103 B9B 98765.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....27......5.8 11.7/1.2/1.2 230514 #29398 B10B 987......6...........85.....4.3.521....42..58....1.4.3..2..31.....54.32....1...84 11.6/1.2/1.2 230514 #31148 B9B 987......6..8...........5...4.32..1....4.12.8....5834...32....1...13.45.....84.2. 11.6/1.2/1.2 230514 #31627 B9B 98.76.5..7.58.49...64.9....64..78.5.5.8.......9.54.....7............6..3.......21 11.6/1.2/1.2 230514 #34255 B9B 98.76.5..7.5.......64.8....8..5.7.4..9784.....5..96...6.9.........9....3......2.1 11.6/1.2/1.2 230514 #37229 B9B 98.76.5..7.5.......64.9....6..5.7.4.5...89....7864.....9..........8....3......2.1 11.6/1.2/1.2 230514 #38797 B9B 98.76.5..7.59.4.......8....6.95.....47.6.8.....8.7..4..6......3....96.........2.1 11.6/1.2/1.2 230514 #38898 B9B 98.76.5..7.59.4.....6.8....6.95.....47.6.8.....8.7..4..9....3.2....96...........1 11.6/1.2/1.2 230514 #38903 B9B 98.76.5..7.5..9....64.8....8..5.7.4..9784.....5..96...6.9.........6..3.2........1 11.6/1.2/1.2 230514 #38924 B9B 98.76.5..7.59.4.....6.8....6.75.....49.6.8.....8.9..4..7....3.2....76...........1 11.6/1.2/1.2 230514 #39788 B9B 98.76.5..7.59.4.......8....6.75.....49.6.8.....8.9..4..6......3....76.........2.1 11.6/1.2/1.2 230514 #39823 B9B

In the same way as I couldn't believe my eyes when I found that Loki was not in T&E(2), I couldn't believe that these puzzles were not in B7B or lower and that they were not even in B8B. But all the checks I made lead to the conclusion that the results are correct.

Notice however that all these puzzles have a non-degenrate tridagon and they can be easily solved with short chains and Trid-ORk-chains when it is used (except 4 of the 77 B7B ones that require longer chains).

Note that all these results where made possible by the SHC:
(http://forum.enjoysudoku.com/the-sudoku-hierarchical-classifier-shc-t42075.html).
Without it, the computations could be done by SudoRules, but they would take so much more time as to become impractical.
.

by **coloin** » Tue Nov 14, 2023 11:56 am

Hi Denis Thank you for your program and I have used it on the puzzles I generated over the past couple of months....

Firstly ... I have expanded my minimal puzzles further than mini-expanding with singles, and its possible to get a maxi-expand to "pearl"

Your 16 puzzles with B9B and above originate from 8 solution grids, and here are the maxi-expands

Code: Select all: 98.76.5..7.48.5....56..9...56..87.4.4.89.6....7945......7..........9...3....7.2.1 ED=11.6/11.6/6.6 987......6.....8.....85.....4.3.521....42..58....184.34.2.831.....54.32....1.2.84 ED=11.6/11.6/2.6 98765.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....277.9...5.8 ED=11.7/11.7/2.6 98.76.5..7.58.49...64.95...64..78.5.5.86......9754.....7......5.....6..3.....7.21 ED=11.6/11.6/2.6 98.76.5..7.5..9....64.85...8.65.7.4..9784....45..96...6.9.........9....3...6..291 ED=11.6/11.6/6.6 98.76.5..7.5..8....64.95...6.95.7.4.54..89....7864.....9..........8....3...9..2.1 ED=11.6/11.6/6.6 98.76.5..7.59.4.....6.85...6.754....49.6.8....58.97.4..7....362....76....6......1 ED=11.6/11.6/6.6 987......65.9...........69.4..32.16.3..1.49.2....96......4...19...2.13.6....3942. ED=11.6/11.6/3.4

These minimize to 50 minimal puzzles all presumably with same rating

Hidden Text: Show

Code: Select all: 98.76.5..7.48......56......56..8..4.4.89.6....7945......7..........9...3....7.2.1 28 98.76.5..7.48.5.....6......56..8..4.4.89.6....7945......7..........9...3....7.2.1 28 98.76.5..7.48......56......56..87.4.4.89.6....7945......7..........9...3......2.1 28 98.76.5..7.48.5.....6......56..87.4.4.89.6....7945......7..........9...3......2.1 28 9.7......6.....8......5.....4.3..21....42..58....184.3..2.831.....54.32....1....4 27 9.7......6.....8......5.....4.3..21....42..58....184.34.2.831.....54.32....1..... 27 9.7......6.....8.....85.....4.3..21....42..58....184.3..2..31.....54.32....1...84 28 987......6...........85.....4.3..21....42..58....184.3..2..31.....54.32....1...84 28 987......6.....8......5.....4.3..21....42..58....184.3..2..31.....54.32....1...84 28 9.7......6.....8.....85.....4.3.521....42..58....1.4.3..2..31.....54.32....1...84 28 987......6...........85.....4.3.521....42..58....1.4.3..2..31.....54.32....1...84 28 9.7......6.....8.....85.....4.3.521....42..58....1.4.3..2.831.....54.32....1....4 28 9.7......6.....8.....85.....4.3..21....42..58....184.34.2..31.....54.32....1...8. 28 987......6...........85.....4.3..21....42..58....184.34.2..31.....54.32....1...8. 28 987......6.....8......5.....4.3..21....42..58....184.34.2..31.....54.32....1...8. 28 9.7......6.....8.....85.....4.3.521....42..58....1.4.34.2..31.....54.32....1...8. 28 987......6...........85.....4.3.521....42..58....1.4.34.2..31.....54.32....1...8. 28 9.7......6.....8.....85.....4.3.521....42..58....1.4.34.2.831.....54.32....1..... 28 98765.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....27......5.8 28 only one minimal ! 98.76.5..7.58.49...64.9....64..78...5.8.......9.54.....7......5.....6..3.......21 28 98.76....7.58.49...64.95...64..78.5.5.8.......9..4.....7......5.....6..3.......21 28 98.76.5..7.58.49...64.9....64..78.5.5.8.......9.54.....7............6..3.......21 28 98.76.5..7.58.49...64.95...64..78.5.5.8.......9..4.....7............6..3.......21 28 98.76.5..7.........64.85...8....7.4..9784.....5..96...6...........9....3......291 26 98.76.5..7.........64.85...8....7.4..9784.....5..96...6.9.........9....3......2.1 26 98.76.5..7.5.......64.8....8..5.7.4..9784.....5..96...6...........9....3......291 27 98.76.5..7....9....64.85...8....7.4..9784.....5..96...6.9..............3......291 27 98.76.5..7....9....64.85...8....7.4..9784.....5..96...6.9..............3...6..2.1 27 98.76.5..7.5.......64.8....8..5.7.4..9784.....5..96...6.9.........9....3......2.1 27 98.76.5..7.5..9....64.8....8..5.7.4..9784.....5..96...6.9..............3......291 28 98.76.5..7.5..9....64.8....8..5.7.4..9784.....5..96...6.9..............3...6..2.1 28 .8.76.5..7.5.......64.9....6.95.7.4.5...89....7864.....9..........8....3......2.1 26 98.76.5..7.5.......64.9....6..5.7.4.5...89....7864.....9..........8....3......2.1 26 98.76.5..7.59.4.......8....6.75.....49.6.8.....8.9..4.......3.2....76....6......1 26 98.76.5..7.59.4.......8....6.75.....49.6.8.....8.9..4.......362....7.....6......1 26 98.76.5..7..9.4.......85...6.75.....49.6.8....58.9..4.......3.2....76....6......1 27 98.76.5..7..9.4.......85...6.75.....49.6.8....58.9..4.......362....7.....6......1 27 98.76.5..7.59.4.....6.8....6.75.....49.6.8.....8.9..4.......362....76...........1 27 98.76.5..7.59.4.....6.8....6.75.....49.6.8.....8.9..4..7....3.2....76...........1 27 98.76.5..7..9.4.....6.85...6.75.....49.6.8....58.9..4.......362....76...........1 28 98.76.5..7..9.4.....6.85...6.75.....49.6.8....58.9..4..7....3.2....76...........1 28 .87......65.............69.4..32.16.3..1.4..2....96......4...19...2.13......3942. 27 .87......65.9...........69.4..32.16.3..1.4..2....96......4...19...2.13......3.42. 27 987......65.9...........6..4..32.16.3..1.4..2....96......4...19...2.13......3.42. 27 .87......65.............69.4..32.16.3..1.49.2....96......4...1....2.13.6....3942. 28 .87......65.9...........69.4..32.16.3..1.49.2.....6......4...1....2.13.6....3942. 28 .87......65.9...........69.4..32.16.3..1.49.2.....6......4...19...2.13......3942. 28 987......65.9...........6..4..32.16.3..1.49.2.....6......4...19...2.13......3942. 28 .87......65.9...........69.4..32.16.3..1.49.2.....6......4...19...2.13.6....3.42. 28 987......65.9...........6..4..32.16.3..1.49.2.....6......4...19...2.13.6....3.42. 28

Here are the puzzles that I found in T&E(2) greater than B6B. They are in minlexsolution grid format as this is easier to work with and visualise differences.

Code: Select all: .23.56......18.23......24..3.5...9..29........64.9.3.253.....24.46..359.9.2..56.3## ED=11.7/11.7/8.9 ## B7B 12.4.6.8.4.718.....68.72.1.24.7.86.1.71.....88.6..1....14...82......7.43........5## ED=11.7/11.7/8.9 ## B7B 12..567...571.92..6.972.1..26........7569..129.12.....592....71......9.4...9..5.3## ED=11.6/11.6/2.6 ## B7B 123...7.9.56..9....89......2..6.139........21.1....6.7...96.21...12.3.76..2.179.3## ED=11.7/11.7/2.6 ## B8B

These too have many less minimal puzzles than the rest of my collection of maxi-expands

Hidden Text: Show

Code: Select all: .23.56......18.........24..3.5...9...9........64.9.3.2........4.46..359.9.2..56.3u .2..56......18..3......24..3.5...9...9........64.9.3.2.3......4.46..359.9.2..56.. .23.56......18..3......24..3.5...9...9........64.9.3.2........4.46..359.9.2..56.. ..3.56......18.........24....5...9..29........64.9.3.2.3.....24.46..359.9.2..56.3 ..3.56......18.........24....5...9..29........64.9.3.25......24.46..359.9.2..56.3 ..3.56......18.........24..3.5...9..29........64.9.3.2.......24.46..359.9.2..56.3 ..3.56......18.2.......24....5...9..29........64.9.3.2.3......4.46..359.9.2..56.3 .23.56......18.........24....5...9..29........64.9.3.2.3......4.46..359.9.2..56.3 ..3.56......18.2.......24....5...9..29........64.9.3.25.......4.46..359.9.2..56.3 .23.56......18.........24....5...9..29........64.9.3.25.......4.46..359.9.2..56.3 ..3.56......18.2.......24..3.5...9..29........64.9.3.2........4.46..359.9.2..56.3 ..3.56......18.2.......24....5...9..29........64.9.3.2.3.....24.46..359.9....56.3 .23.56......18.........24....5...9..29........64.9.3.2.3.....24.46..359.9....56.3 ..3.56......18.2.......24....5...9..29........64.9.3.25......24.46..359.9....56.3 .23.56......18.........24....5...9..29........64.9.3.25......24.46..359.9....56.3 ..3.56......18.2.......24..3.5...9..29........64.9.3.2.......24.46..359.9....56.3 .23.56......18.........24..3.5...9..29........64.9.3.2.......24.46..359.9....56.3 ....56......18..3......24..3.5...9..29........64.9.3.2.3.....24.46..359.9.2..56.. ..3.56......18..3......24....5...9..29........64.9.3.2.3.....24.46..359.9.2..56.. ..3.56......18..3......24....5...9..29........64.9.3.25......24.46..359.9.2..56.. ..3.56......18..3......24..3.5...9..29........64.9.3.2.......24.46..359.9.2..56.. ....56......18.23......24..3.5...9..29........64.9.3.2.3......4.46..359.9.2..56.. ..3.56......18.23......24....5...9..29........64.9.3.2.3......4.46..359.9.2..56.. .23.56......18..3......24....5...9..29........64.9.3.2.3......4.46..359.9.2..56.. ..3.56......18.23......24....5...9..29........64.9.3.25.......4.46..359.9.2..56.. .23.56......18..3......24....5...9..29........64.9.3.25.......4.46..359.9.2..56.. ..3.56......18.23......24..3.5...9..29........64.9.3.2........4.46..359.9.2..56.. .2..56......18..3......24..3.5...9..29........64.9.3.2.3.....24.46..359.9....56.. ..3.56......18.23......24....5...9..29........64.9.3.2.3.....24.46..359.9....56.. .23.56......18..3......24....5...9..29........64.9.3.2.3.....24.46..359.9....56.. ..3.56......18.23......24....5...9..29........64.9.3.25......24.46..359.9....56.. .23.56......18..3......24....5...9..29........64.9.3.25......24.46..359.9....56.. ..3.56......18.23......24..3.5...9..29........64.9.3.2.......24.46..359.9....56.. .23.56......18..3......24..3.5...9..29........64.9.3.2.......24.46..359.9....56.. .2.4.6...4.7.8.....6..72.1.24.7..6...71.....88.6..1....14...82......7.43........5 12.4.6...4.7.8.....6..72.1.24.7..6...7......88.6..1....14...82......7.43........5 .2.4.6.8.4.7.8.....6..72.1.24.7..6...71......8.6..1....14...82......7.43........5 12.4.6.8.4.7.8.....6..72.1.24.7..6.1.7.......8.6..1....14...82......7.43........5 12.4.6.8.4.718.....6..72...24.7..6.1.7.......8.6..1....14...82......7.43........5 12.4.6.8.4.7.8.....6..72.1.24.7.86...7.......8.6..1....14...82......7.43........5 12.4.6...4.718.....68.72...24.7..6...71.....88.6..1....14...82......7.43........5 12.4.6.8.4.718.....6..72...24.7..6...71.....88.6..1....14...82......7.43........5 12.4.6...4.718.....68.72...24.7..6.1.7......88.6..1....14...82......7.43........5 .2.4.6.8.4.71......68.72.1.24.7.86...71......8.6..1....14...82......7.43........5 12.4.6.8.4.71......68.72...24.7.86...71......8.6..1....14...82......7.43........5 12.4.6.8.4.718.....6..72...24.7.86...71......8.6..1....14...82......7.43........5 12.4.6.8.4.71......68.72...24.7.86.1.7.......8.6..1....14...82......7.43........5 12.4.6.8.4.71......68.72.1.24.7.86...7.......8.6..1....14...82......7.43........5 ....567...571.....6.972.....6........7569..12..12.....5.2....71......9.4...9..5.3 ....567...571.....6.972.1...6........7569..12..12.....5.2....7.......9.4...9..5.3 1...567...571.....6.972.....6........7569..12..12.....5.2....7.......9.4...9..5.3 ....567...571.....6.972.....6........7569..12..12.....592....71......9.4......5.3 ....567...571.....6.972.1...6........7569..12..12.....592....7.......9.4......5.3 1...567...571.....6.972.....6........7569..12..12.....592....7.......9.4......5.3 ....567...571.9...6.972.....6........756...129.12.....5.2....71......9.4...9..5.3 ....567...571..2..6.972.....6........7569..1.9.12.....5.2....71......9.4...9..5.3 ....567...571.92..6.972.....6........756...1.9.12.....5.2....71......9.4...9..5.3 ....567...571..2..6.972....26........7569..1...12.....5.2....71......9.4...9..5.3 ....567...571.9...6.972.1...6........756...129.12.....5.2....7.......9.4...9..5.3 1...567...571.9...6.972.....6........756...129.12.....5.2....7.......9.4...9..5.3 ....567...571..2..6.972.1...6........7569..1.9.12.....5.2....7.......9.4...9..5.3 1...567...571..2..6.972.....6........7569..1.9.12.....5.2....7.......9.4...9..5.3 ....567...571.92..6.972.1...6........756...1.9.12.....5.2....7.......9.4...9..5.3 1...567...571.92..6.972.....6........756...1.9.12.....5.2....7.......9.4...9..5.3 ....567...571..2..6.972.1..26........7569..1...12.....5.2....7.......9.4...9..5.3 1...567...571..2..6.972....26........7569..1...12.....5.2....7.......9.4...9..5.3 ....567...571.9...6.972.....6........756...129.12.....592....71......9.4......5.3 ....567...571..2..6.972.....6........7569..1.9.12.....592....71......9.4......5.3 ....567...571..2..6.972....26........7569..1...12.....592....71......9.4......5.3 ....567...571.9...6.972.1...6........756...129.12.....592....7.......9.4......5.3 1...567...571.9...6.972.....6........756...129.12.....592....7.......9.4......5.3 ....567...571..2..6.972.1...6........7569..1.9.12.....592....7.......9.4......5.3 1...567...571..2..6.972.....6........7569..1.9.12.....592....7.......9.4......5.3 ....567...571..2..6.972.1..26........7569..1...12.....592....7.......9.4......5.3 1...567...571..2..6.972....26........7569..1...12.....592....7.......9.4......5.3 ....567...571.92..6.972....26........756...1.9.12.....592....71......9.4......5.3 ....567...571.92..6.972.1..26........756...1.9.12.....592....7.......9.4......5.3 1...567...571.92..6.972....26........756...1.9.12.....592....7.......9.4......5.3 1.3...7...56..9....89......2..6..39........21.1....6.7...96.2....12.3..6....179.3 1.3...7...56..9....89......2..6.139........21......6.7...96.2....12.3..6....179.3 1.3...7...56..9....89......2..6..39........21.1....6.7...96.21....2.3..6....179.3 123...7...56..9....89.........6..39........21.1....6.7...96.2....12.3..6..2.179.3 123...7...56..9....89.........6.139........21......6.7...96.2....12.3..6..2.179.3 123...7...56..9....89.........6..39........21.1....6.7...96.21....2.3..6..2.179.3

EDIT
the 77 puzzles in B7B originate from 6 solution grids.
Here are the maxi-expands for these - they are in minlexsolutiongrid format which shows the swopped pairs in the first 3 These minimize to the same 77 minimal puzzles.

Code: Select all: 12..56....571.9..66.927...127.69.....917.5.....6.12.9.......8.2...52......2...3.5 ED=11.6/11.6/2.6 12..56....571.9..66.927...127.96.....917.5.....6.12.9.......3.2...52......2...8.5 ED=11.6/11.6/2.6 12..56....571.9..66.927...129.76.....719.5.....6.12.9.......3.2...52......2...8.5 ED=11.6/11.6/2.6 ...4.6.....7....36.......5.24.6.7...7.8.14..2.6182......274.1...14.68...87.2.1... ED=11.6/11.6/9.2 12.....89.5.1..2.66.82..15....9..........4.....5..7....86.9..125.2...96.91..628.5 ED=11.7/11.7/10.5 ..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

the 8 maxi-expands in minlexsolutiongrid format for those with BpB>8 are

Code: Select all: .2.4.678....18.2.6.8..27.142......4.3...6....9.5.........6.2.78...81.4.28.2.7.16. 1.3.56....5718..3.68.7.3....3587....8.63.1....1..653.8.6....4.....6.7.........962 12..56..9.571.9...6.972....2.....34.7.....8.....2......7.56....5.2.17.6..619.2... 1.3.5.7.9.57....3669..3.51...13.567.36....1.5.75....93..6..2........39.....8.4... 1.3.5.7.9.57....3669..7.15..165..39.53......17.9...6.5.....2.6...1..5......8.4.1. 1.3.5.7.9.......3669..7.15.....386..3.6.........264...5.9....6773....91..61...5.. 1.3..67.9.57..9.3669....15..16....9337....5.19.5....7....8.....7316.5.......4.... 1.3.56..9.571.9...69.73.........7.4..3.............82.3.6.95...57...169..1967....

Website · by **denis_berthier** » Tue Nov 14, 2023 4:41 pm

Hi Coloin
Great work.

coloin wrote:Hi Denis Thank you for your program

Do you mean SudoRules? If you mean SHC, it's François's program.

coloin wrote:Firstly ... I have expanded my minimal puzzles further than mini-expanding with singles, and its possible to get a maxi-expand to "pearl"

I'm not sure what you mean by "maxi-expand to "pearl"".
With mith, we understand min-expand as expansion by Singles and max-expand as further addition of candidates until adding more would make the puzzle loose one depth of T&E. [Indeed, we considered only the case of a puzzle in T&E(3), but I think this is the right definition of max-expand in the general case.]

coloin wrote:Your 16 puzzles with B9B and above originate from 8 solution grids, and here are the maxi-expands
[...]
These minimize to 50 minimal puzzles all presumably with same rating
Code: Select all
... 98765.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....27......5.8 28 only one minimal ! ...

There's no reason for all the minimals of an expansion to have the same rating (be it SER or BpB).
Indeed the puzzle with only 1 minimal is the original puzzle with BpB = 10 - still the only known one with such a high BpB classif as of now.
The other 49 puzzles have BpB = 9, which drastically increases the number of known minimal puzzles with BpB = 9.

coloin wrote:Here are the puzzles that I found in T&E(2) greater than B6B. They are in minlexsolution grid format as this is easier to work with and visualise differences.
...
These too have many less minimal puzzles than the rest of my collection of maxi-expands

The first 78 puzzles are in B7B and the last 6 in B8B, which provides the first 6 examples of minimal puzzles in B8B.

[Edit]: all the puzzles in the list of 50 and in the list of 84 have a non-degenerate tridagon pattern with few guardians.
All of them can be solved with short ORk-chains based on this pattern, except the last 6 ones in the list of 84 (the 6 B8B puzzles), that require longer chains.
.

by **coloin** » Tue Nov 14, 2023 5:51 pm

Thanks Denis for providing me with Francois's program i should have said !

I expanded the puzzles so that the overal SE rating was unchanged up to the limit when ED rating [ER/EP/ED] where ER=EP. P in this case stands for Pearl.

coloin wrote: ....These minimize to 50 minimal puzzles all presumably with same rating

perhaps I also should have said presumably with at least this BpB rating ... as SE does have a flaw whereby adding a clue increases the rating / removing a clue reduces the rating. I understand this annoying situation does not occur with your program

!!!

Website · by **denis_berthier** » Wed Nov 15, 2023 3:51 am

.
OK, thanks for the clarifications.

coloin wrote:I expanded the puzzles so that the overal SE rating was unchanged up to the limit when ED rating [ER/EP/ED] where ER=EP. P in this case stands for Pearl.

I think expansion can usefully be extended much beyond (indeed to the point of reaching the limit of T&E(1)), in order to find more puzzles with large BpB classif.

coloin wrote: ... as SE does have a flaw whereby adding a clue increases the rating / removing a clue reduces the rating. I understand this annoying situation does not occur with your program !!!

I confirm. This is totally impossible with T&E-depth and the B, BpB or BpBB classifications and other SER problems such as dependence on isomorphisms are also impossible.

by **coloin** » Wed Nov 15, 2023 12:17 pm

The invert of the BpB has 18 solutions, and so there are 18 similar maxi-expands in BpB 10.
All 23 resulting minimal puzzles will probably have the same solution path and are BpB 10 too.

Code: Select all: 98765.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....277.9...5.8 ** original 78965.......4..........3...87..2.9.6.92.6..576.5...82.25.....9..68....729.7...5.8 78965.......4..........3...87..2.9.6.95.6..276.2...85.25.....9..68....729.7...5.8 78965.......4..........3...87..2.9.6.95.6..726.2...85.25.....9..67....289.8...5.7 78965.......4..........3...87..2.9.6.95.6..726.2...85.25.....9..68....279.7...5.8 78965.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..67....289.8...5.7 78965.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....279.7...5.8 87965.......4..........3...78..2.9.6.92.6..576.5...82.25.....9..68....729.7...5.8 87965.......4..........3...78..2.9.6.95.6..276.2...85.25.....9..68....729.7...5.8 87965.......4..........3...78..2.9.6.95.6..726.2...85.25.....9..67....289.8...5.7 87965.......4..........3...78..2.9.6.95.6..726.2...85.25.....9..68....279.7...5.8 87965.......4..........3...78..6.9.2.95.2..766.2...85.25.....9..67....289.8...5.7 87965.......4..........3...78..6.9.2.95.2..766.2...85.25.....9..68....279.7...5.8 97865.......4..........3...78..2.9.6.95.6..726.2...85.25.....9..67....288.9...5.7 97865.......4..........3...78..6.9.2.95.2..766.2...85.25.....9..67....288.9...5.7 98765.......4..........3...87..2.9.6.92.6..576.5...82.25.....9..68....727.9...5.8 98765.......4..........3...87..2.9.6.95.6..276.2...85.25.....9..68....727.9...5.8 98765.......4..........3...87..2.9.6.95.6..726.2...85.25.....9..68....277.9...5.8 98765.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....27......5.8 ** original 78965.......4..........3...87..2.9.6.9..6..57..5...82.25.....9..68....729.7...5.8 78965.......4..........3...87..2.9.6.92.6..57..5...8..25.....9..68....729.7...5.8 78965.......4..........3...87..2.9.6.95.6..27..2...85.25.....9..68....729.7...5.8 78965.......4..........3...87..2.9.6.95.6..72..2...85.25.....9..67....289.8...5.7 78965.......4..........3...87..2.9.6.95.6..72..2...85.25.....9..68....279.7...5.8 78965.......4..........3...87..6.9...95.2..76..2...85.25.....9..67....289.8...5.7 78965.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....279.7...5.8 87965.......4..........3.......2.9.6.9..6..57..5...82.25.....9..68....729.7...5.8 87965.......4..........3.......2.9.6.92.6..57..5...8..25.....9..68....729.7...5.8 87965.......4..........3.......2.9.6.95.6..27..2...85.25.....9..68....729.7...5.8 87965.......4..........3.......2.9.6.95.6..72..2...85.25.....9..67....289.8...5.7 87965.......4..........3.......2.9.6.95.6..72..2...85.25.....9..68....279.7...5.8 87965.......4..........3.......6.9...95.2..76..2...85.25.....9..67....289.8...5.7 87965.......4..........3.......6.9...95.2..76..2...85.25.....9..68....279.7...5.8 97865.......4..........3.......2.9.6.95.6..72..2...85.25.....9..67....288.....5.7 97865.......4..........3....8..2.9.6.95.6..72..2...85.25.....9..67....28......5.7 97865.......4..........3.......6.9...95.2..76..2...85.25.....9..67....288.....5.7 97865.......4..........3....8..6.9...95.2..76..2...85.25.....9..67....28......5.7 98765.......4..........3...87..2.9.6.9..6..57..5...82.25.....9..68....72......5.8 98765.......4..........3...87..2.9.6.92.6..57..5...8..25.....9..68....72......5.8 98765.......4..........3...87..2.9.6.95.6..27..2...85.25.....9..68....72......5.8 98765.......4..........3...87..2.9.6.95.6..72..2...85.25.....9..68....27......5.8

Website · by **denis_berthier** » Wed Nov 15, 2023 12:21 pm

coloin wrote:The invert of the BpB has 18 solutions, and so there are 18 similar maxi-expands in BpB 10.

Can you define "invert" and "similar" ?

by **coloin** » Wed Nov 15, 2023 12:51 pm

denis_berthier wrote:Can you define "invert" and "similar" ?

Code: Select all: 98765.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....277.9...5.8 .....1234523.7861941629.785..13.5.4.3..8.41...4.917..3..47863.11..5394...3.142.6. invert grid has 18 sol

All the puzzles will have have this invert - so all the PM grids will be the same so they will have the same solution path

Code: Select all: * * * * * * ** * * *** * 14 clue UA 98765.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....277.9...5.8 ** original 78965.......4..........3...87..2.9.6.92.6..576.5...82.25.....9..68....729.7...5.8

Code: Select all: +-------------------+-------------------+-------------------+ | 9 8 7 | 6 5 12 | 1234 134 134 | | 135 123 136 | 4 1789 12789 | 12367 1368 1359 | | 145 124 146 | 12789 1789 3 | 12467 1468 1459 | +-------------------+-------------------+-------------------+ | 8 7 134 | 135 6 145 | 9 134 2 | | 134 9 5 | 138 2 148 | 134 7 6 | | 6 134 2 | 1379 13479 1479 | 8 5 134 | +-------------------+-------------------+-------------------+ | 2 5 134 | 1378 13478 14678 | 1346 9 134 | | 134 6 8 | 1359 1349 1459 | 134 2 7 | | 7 134 9 | 123 134 1246 | 5 1346 8 | +-------------------+-------------------+-------------------+ +-------------------+-------------------+-------------------+ | 7 8 9 | 6 5 12 | 1234 134 134 | | 135 123 136 | 4 1789 12789 | 1267 168 59 | | 145 124 146 | 12789 1789 3 | 1267 168 59 | +-------------------+-------------------+-------------------+ | 8 7 134 | 135 2 145 | 9 134 6 | | 134 9 2 | 138 6 148 | 134 5 7 | | 6 134 5 | 1379 13479 1479 | 8 2 134 | +-------------------+-------------------+-------------------+ | 2 5 134 | 1378 13478 14678 | 1346 9 134 | | 134 6 8 | 1359 1349 1459 | 134 7 2 | | 9 134 7 | 123 134 1246 | 5 1346 8 | +-------------------+-------------------+-------------------+

Website · by **denis_berthier** » Wed Nov 15, 2023 1:29 pm

.
I wouldn't use the word "invert" to mean the complementary givens of a 1-solution grid.
What about "similar"? Do you mean isomorphic?

by **coloin** » Wed Nov 15, 2023 5:51 pm

The invert was coined by dobrichev and yes it is the complement of the givens !
as the command to do this is
gridcheckernew --similar --invert . < file.txt > fileinvert.txt

but i should have said that the pattern of the 18 maxi-expands is similar / the same.

They are all individually different - but have the same solution. I imagine we have many ? twin puzzles which share a UA in the givens

Website · by **denis_berthier** » Wed Nov 15, 2023 7:26 pm

.
Hi Coloin
The complement of the givens of P always has a solution, but it may not be unique. If it is unique, it has a certain number of minimals and the complement of each of them is obviously an extension of P. I don't know in what precise sense it can be considered a "max" extension.
Anyway, any of these extensions of P can generate minimals. But there's no a priori complexity relation between them and P.

However, in your example, it is true that the 23 minimals are in B10B - which is a large extension of the number of known puzzles in B10B (only one until now).
.

by **hendrik_monard** » Fri Nov 24, 2023 6:10 pm

denis_berthier wrote:.
Hi Coloin
The complement of the givens of P always has a solution, but it may not be unique. If it is unique, it has a certain number of minimals and the complement of each of them is obviously an extension of P. I don't know in what precise sense it can be considered a "max" extension.
Anyway, any of these extensions of P can generate minimals. But there's no a priori complexity relation between them and P.

However, in your example, it is true that the 23 minimals are in B10B - which is a large extension of the number of known puzzles in B10B (only one until now).
.

Hi Denis,
I checked the list of 23 minimals of coloin and discovered that 5 of them are isomorphs of 5 puzzles I posted in May 2023 which were also in the list of 50k puzzles you examined recently. They were however not in the list of 92 puzzles with BpB > 6.
Apparently, for those 5 puzzles the BpB ranking was not done. Is it possible that in my list of 50k puzzles there are other puzzles with BpB > 6 not (yet) identified ?
In the following list, each pair contains the puzzle from coloin's list followed by the maxlex isomorph I posted in May 2023

87965.......4..........3.......6.9...95.2..76..2...85.25.....9..67....289.8...5.7 M4M15612
98765.......4..........3...89....75.7.6...8.2.25.....95.9.2.6.72......85....6..9.;M4M15612

97865.......4..........3.......2.9.6.95.6..72..2...85.25.....9..67....288.....5.7 M4M15670
98765.......4..........3...86....92..52....7...9...8.557..6.28.2......59....2.6.7;M4M15670

97865.......4..........3....8..2.9.6.95.6..72..2...85.25.....9..67....28......5.7 M4M15680
98765.......4..........3...86....92..52....7.......8.557..6.28.2......59.9..2.6.7;M4M15680

97865.......4..........3.......6.9...95.2..76..2...85.25.....9..67....288.....5.7 M4M11662
98765.......4..........3...86....92..52....7...9...8.557..2.68.2......59....6...7;M4M11662

97865.......4..........3....8..6.9...95.2..76..2...85.25.....9..67....28......5.7 M4M11656
98765.......4..........3...86....92..52....7.......8.557..2.68.2......59.9..6...7;M4M11656

Website · by **denis_berthier** » Fri Nov 24, 2023 6:21 pm

Hi Hendrik,

The 10 puzzles are indeed in B10B.

hendrik_monard wrote:[ Is it possible that in my list of 50k puzzles there are other puzzles with BpB > 6 not (yet) identified ?

Quick answer: yes.

I've just checked the BpB file for your 50k puzzles: it contains negative values, which means the default buffer-size was too small. These computations were done before we decided with François to increase the default values of several parameters (precisely after I found puzzles in your file with BpB = 9 or 10). One can say that puzzles with negative BpB values have not really been submitted to the classification.
I should have checked that there were no negative values, but I forgot to do it.
I have long calculations running, but they should end soon and I'll relaunch the calculations for your puzzles next week with the new default parameters.
.

Website · by **denis_berthier** » Sun Nov 26, 2023 1:41 pm

denis_berthier wrote:
hendrik_monard wrote:[ Is it possible that in my list of 50k puzzles there are other puzzles with BpB > 6 not (yet) identified ?

Quick answer: yes.

I've just checked the BpB file for your 50k puzzles: it contains negative values, which means the default buffer-size was too small. These computations were done before we decided with François to increase the default values of several parameters (precisely after I found puzzles in your file with BpB = 9 or 10). One can say that puzzles with negative BpB values have not really been submitted to the classification.
I should have checked that there were no negative values, but I forgot to do it.

We decided to introduce an explicit message at the end of computations for files, so that not noticing negative values shouldn't happen again.

After redoing the calculations:

The new 77 B7B puzzles are unchanged:

Code: Select all: 98.76.54.7.5.4.8....6....9.67...5...4.8...75..59....68...3....9...2..........4... 11.7/1.2/1.2 220515 #3079 98.76.5..7.4.8.....56...8..8.5..7.4.6..59.....79.48.6....9....3......4..........2 11.7/1.2/1.2 220515 #3080 98.76.54.7.5..4....6...8.9.85.9.6...4.6.87......45...8..7...3........2..........9 11.7/1.2/1.2 220515 #3081 98.76.54.7.5.9.....64..8.9.85.9.6...4.6.87......45...8..7...3........2..........9 11.7/1.2/1.2 220515 #3233 98.76.54.7.5.498...6.8.....49..87....579.6......45...9..6....3........2.........8 11.7/1.2/1.2 220515 #3234 98.76.54.7.5..4....6...8.9.8..9.6...4.6.87..5...45...8..7...3........2..........9 11.7/1.2/1.2 220515 #3235 98.76.54.7.5.9.....64..8.9.8..9.6...4.6.87..5...45...8..7...3........2..........9 11.7/1.2/1.2 220515 #3236 98.76.5..7.5.498...648......9..87....579.6.4....45..9...6.....3.......8.........2 11.7/1.2/1.2 220515 #3237 98.76.5..7.5..9....645.8...8...75.9.5.649...7...8.....6.....4.3...6.4...........2 11.8/1.2/1.2 220928 #5743 98.76.5..7.58.49...46.5.....78.46.9...958.......9.7....6.........4....32.....8.5. 11.8/1.2/1.2 220928 #5744 98.76.5..7.5.496...4.......67.89....5..4.6.7..94.5........8..........8.3......4.2 11.8/1.2/1.2 230514 #15340 98.76.5..7.4..98...56......8..5.6.9..67.8......9.74.......4..........6.3......4.2 11.8/1.2/1.2 230514 #15344 98.76.5..7.4..98...56..8...8..5.6.9.5.9.74....679.........4..........6.3......4.2 11.8/1.2/1.2 230514 #15345 98.76.5..7.5.496...4.5.....67.89....5..4.6.7..94..7.......8..........8.3......4.2 11.8/1.2/1.2 230514 #15346 98.76.5..7.5..89...645.9...59...4....486.5.7...7.8......6....9....4............32 11.8/1.2/1.2 230514 #15382 98.76.5..7.6.4......58.....6.859..4.45..7.....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #34412 98.76.5..7.5.496...4.5.....67.89....5..4.6.7..94.7........8..........8.3......4.2 11.6/1.2/1.2 230514 #37154 98.76....7.6..5....458.....6...98.....7..48.....57.9..5.4....98.....6..........32 11.6/1.2/1.2 230514 #37188 98.76.5..7.5.496...4.......67.89....5....6.7..94.5........84.........8.3......4.2 11.6/1.2/1.2 230514 #37325 98.76.5..7.5..96...4.......67.89....5..4.6.7..94.5........84.........8.3......4.2 11.6/1.2/1.2 230514 #37396 98.76.5..7.6.4......58.....6.859..4.4...7.....9.6...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #37433 98.76.5..7.4..98...5.......8..5.6.9..67.8......9.74...6.....4.3....4..........6.2 11.6/1.2/1.2 230514 #37439 98.76....7.6..58...458.....6...98.....7..4......57..9.5.4...9.8.....6.........3.2 11.6/1.2/1.2 230514 #37475 98.76.5..7.4..98...56......8..5...9..67.8......9.74......64..........6.3......4.2 11.6/1.2/1.2 230514 #37485 98.76.5..7.6.45.....58.....6.8.9..4.45..7.....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #37517 98.76.5..7.6.4......58.....6.759..4.45..78....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #38028 98.76.5..7.4..98...56..8...8..5.6.9.5.7.94....6..7........4..........6.3......4.2 11.6/1.2/1.2 230514 #38836 98.76.5..7.4..98...56..8...8..5.6.9.5.9.74....67.9........4..........6.3......4.2 11.6/1.2/1.2 230514 #38844 98.76.5..7.4..98...5.......8..5...9..67.8......9.74...6.....4.3...64..........6.2 11.6/1.2/1.2 230514 #38891 98.76.5..7.6.4......58.9...6..5...4.45..78....976......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #38922 98.76.5..7.6.45.....58.9...6......4.45..78....976......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #38927 98.76.5..7.5.496...4.5.....67.89....5..4.6.7..94..5.......8..........8.3......4.2 11.6/1.2/1.2 230514 #38939 98.76.5..7.5.496...4.5.....69.87....5..4.6.7...4.9........8..........8.3......4.2 11.6/1.2/1.2 230514 #38944 98.76.5..7.6.45.....58.....6...9..4.45..78....976......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #38967 98.76.5..7.4..98...56..8...8..5...9.5.9.74....679........64..........6.3......4.2 11.6/1.2/1.2 230514 #39001 98.76.5..7.6.4......58.9...6.75...4.4...78....9.6...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39044 98.76.5..7.6.4......58.....6.759..4.4...78....9.6...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39045 98.76.5..7.6.4......58.....6..59..4.4...78....986...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39049 98.76.5..7.6.4......58.....6..59..4.45..78....976......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39052 98.76....7.6.54....548.....64..98.....76.58......7.9..4.5....98.....6..........32 11.6/1.2/1.2 230514 #39058 98.76.5..7.4..98...56..8...8..5.6.9..678.......9.74.......4..........6.3......4.2 11.6/1.2/1.2 230514 #39059 98.76.5..7.5..96...4.5.....67.89....5..4.6.7..94..7.......84.........8.3......4.2 11.6/1.2/1.2 230514 #39081 98.76.5..7.5.496...4.5.....67.89....5....6.7..94..7.......84.........8.3......4.2 11.6/1.2/1.2 230514 #39140 98.76.5..7.5.496.....5.....69.87....5..4.6.7...4.9....4.....8.3....8..........4.2 11.6/1.2/1.2 230514 #39162 98.76.5..7.6.45.....58.....6...9..4.45..78....986......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39167 98.76.5..7.5..96...4.5.....69.87....5..4.6.7...4.9....4.....8.3....8..........4.2 11.6/1.2/1.2 230514 #39170 98.76....7.6.54....548.....64..98.....7..58.....67.9..4.5....98.....6..........32 11.6/1.2/1.2 230514 #39193 98.76.5..7.5.496...4.5.....67.89....5....6.7..94.7........84.........8.3......4.2 11.6/1.2/1.2 230514 #39197 98.76.5..7.6.4......58.9...6.75...4.45..78....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39200 98.76.5..7.4..98...5...8...8..5...9..678.......9.74...6.....4.3...64..........6.2 11.6/1.2/1.2 230514 #39211 98.76.5..7.5.496...4.5.....69.87....5....6.7...4.9........84.........8.3......4.2 11.6/1.2/1.2 230514 #39224 98.76.5..7.6.45.....58.....6.7.9..4.45..78....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39261 98.76.5..7.5..96...4.5.....69.87....5..4.6.7...4.9........84.........8.3......4.2 11.6/1.2/1.2 230514 #39265 98.76.5..7.5.496...4.5.....67.89....5....6.7..94..5.......84.........8.3......4.2 11.6/1.2/1.2 230514 #39318 98.76.5..7.5..96...4.5.....67.89....5..4.6.7..94.7........84.........8.3......4.2 11.6/1.2/1.2 230514 #39336 98.76.5..7.4..98...56..8...8..5...9..678.......9.74......64..........6.3......4.2 11.6/1.2/1.2 230514 #39422 98.76.5..7.6.4......58.....6..59..4.45..78....986......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39431 98.76.5..7.6.45.....58.9...6.7....4.45..78....9.6......7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39443 98.76.5..7.4..98...5...8...8..5.6.9..678.......9.74...6.....4.3....4..........6.2 11.6/1.2/1.2 230514 #39447 98.76....7.6..58...458.....65..98.....75.4.......7..9.5.4...9.8.....6.........3.2 11.6/1.2/1.2 230514 #39455 98.76....7.6..5....458.....65..98.....75.48......7.9..5.4....98.....6..........32 11.6/1.2/1.2 230514 #39458 98.76.5..7.5..96...4.5.....67.89....5..4.6.7..94..5.......84.........8.3......4.2 11.6/1.2/1.2 230514 #39464 98.76.5..7.4..98...56..8...8..5.6.9..6.87......7.94.......4..........6.3......4.2 11.6/1.2/1.2 230514 #39681 98.76.5..7.6.4......58.....6..59..4.4...78....976...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #39797 98.76.5..7.4..98...5...8...8..5...9..6.87......7.94...6.....4.3...64..........6.2 11.6/1.2/1.2 230514 #39950 98.76....7.5...9...46..5...5..98.....6.5.7.8...8.46....7..........6.4.98.......32 11.6/1.2/1.2 230514 #39952 98.76.5..7.4..98...56..8...8..5...9.5.7.94....6..7.......64..........6.3......4.2 11.6/1.2/1.2 230514 #39953 98.76.5..7.4..98...5...8...8..5.6.9..6.87......7.94...6.....4.3....4..........6.2 11.6/1.2/1.2 230514 #39955 98.76....7.5...9...46..58..5..98.....6.5.7.....8.46....7..........6.4.98.......32 11.6/1.2/1.2 230514 #39957 98.76.5..7.4..98...56..8...8..5...9..6.87......7.94......64..........6.3......4.2 11.6/1.2/1.2 230514 #39959 98.76.5..7.6..5....4..8....8..6...5.5...98.4..97.4....67....4.5...9...........3.2 11.6/1.2/1.2 230514 #39960 98.76.5..7.6..5....45.8....8..6......9754........98.4.67....4.5...9...........3.2 11.6/1.2/1.2 230514 #39961 98.76.5..7.6..5....4..8....8..6.....5...98.4..9754....67....4.5...9...........3.2 11.6/1.2/1.2 230514 #39962 98.76.5..7.5.496.....5.....69.87....5....6.7...4.9....4.....8.3....84.........4.2 11.6/1.2/1.2 230514 #39965 98.76....7.6..5....45.8....8..6..5...9754........984..67.....54...9............32 11.6/1.2/1.2 230514 #39966 98.76.5..7.6.4......58.9...6..5...4.4...78....976...5..7..........98.4.5......3.2 11.6/1.2/1.2 230514 #40118 98.76.5..7.4..98...56..8...8..5...9.5.9.74....67.9.......64..........6.3......4.2 11.6/1.2/1.2 230514 #40187

There are 28 B8B puzzles:

Code: Select all: 98.76.5..7.5.946....48.....6..9.7....7..8..6..49.56.......48.........83.......42. 11.7/1.2/1.2 220515 #3662 98.76.5..7.5..4....64..89..6.759.....5.8.6.....8.4..5....47..........73.......42. 11.7/1.2/1.2 220515 #3663 98.76.5..7.5.946....48.....6..9.7....7.48..6..49.56...4.....83......8.........42. 11.7/1.2/1.2 220515 #3664 98.76.5..7.5..4....64..89..6.759.....5.8.6.....8.47.5..7....43....4...........72. 11.7/1.2/1.2 220515 #3665 98.76.5..7.5.94....648.....6..9.7....7..8..6..49.56.......48.........83.......42. 11.7/1.2/1.2 220515 #3885 98.76.5..7.58.49...64..5...6...8..9.5.9.47....789.....4.6............63.......42. 11.7/1.2/1.2 220515 #3915 98.76.5..7.59.4....64..87..6.957.....5.8.6.....8.4..5....49..........93.......42. 11.7/1.2/1.2 220515 #3916 98.76.5..7.58.49...64..5...64..8..9.5.9.47....789.......6.........4..63.......42. 11.7/1.2/1.2 220515 #3920 98.76.5..7.59.4....64..87..6.957.....5.8.6.....8.49.5..9....43....4...........92. 11.7/1.2/1.2 220515 #3921 98.76.5..7.5.94....648.....6..9.7....7.48..6..49.56...4.....83......8.........42. 11.7/1.2/1.2 220515 #4009 98.76.5..7.58.46...46..9...5.79.....49...8....6854.....7.....65....8..32......... 11.7/1.2/1.2 220515 #4212 98.76.5..7.58.4....64.95...64..8..9.5.9.47....789.......6.........4..63.......42. 11.7/1.2/1.2 220515 #4213 98.76.5..7.58.49.......5...6.4............63.......42.5.9.47...46..8..9..789..... 11.7/1.2/1.2 220928 #6222 98.76.5..7.5.......64..87..6.957.....5.8.6.....8.94.5....94..........93.......42. 11.7/1.2/1.2 220928 #6224 98.76.5..7.58.49...4...5...6...........4..63.......42.5.9.47...46..8..9..789..... 11.7/1.2/1.2 220928 #6234 98.76.5..7.5..9....64..87..6.957.....5.8.6.....8.94.5..9....43.....4..........92. 11.7/1.2/1.2 220928 #6236 98.76.5..7.58.4.......95...6.4............63.......42.5.9.47...46..8..9..789..... 11.7/1.2/1.2 220928 #6479 98.76.5..7.58.4....4..95...6...........4..63.......42.5.9.47...46..8..9..789..... 11.7/1.2/1.2 220928 #6480 98.76.5..7.54..6...4..58...6.8..5...4..69.....7.8.4.....7....32...9.7.65......... 11.7/1.2/1.2 220928 #7950 98.76.5..7.4..96...5.......6...97....7865......98.4.6....48..........83.......42. 11.7/1.2/1.2 220928 #9259 98.76.5..7.54..6...4..58...6.8.75...4..69.....7.8.4.....7....32...9...65......... 11.7/1.2/1.2 220928 #9409 98.76.5..7.54......46.58...6.8..5...4..69.....7.8.4.6...7....32...9.7.56......... 11.7/1.2/1.2 220928 #9778 98.76.5..7.54......46.58...6.8.75...4..69.....7.8.4.6...7....32...9...56......... 11.7/1.2/1.2 220928 #9779 98.76.5..7.4..9....56..8...8.....43....4...........82.6...97....7865......98.4.6. 11.7/1.2/1.2 220928 #9976 98.76.5..7.4..9....56......6...97....7865......98.4.6....48..........83.......42. 11.7/1.2/1.2 220928 #9977 98.76.5..7.4..96...5...8...8.....43....4...........82.6...97....7865......98.4.6. 11.7/1.2/1.2 220928 #10025 98765.......4.3............8.67..5...5....89..29.....66...2.7.92...6..58..5....2. 11.6/1.2/1.2 230514 #33700 98765.......4.3............8.67..5...5....89..29.....66...2.7.92......58..5...62. 11.6/1.2/1.2 230514 #44463

There are 160 B9B puzzles:

Code: Select all: 987......6..8.......5......4..38.21....2.4..8....163...6..32.41...4..83....1..6.2 11.6/1.2/1.2 220223 #1241 987......6..8.......5......4..3..21....24...8....613...6..23.41...4..83....18.6.2 11.6/1.2/1.2 220223 #1242 987......6..8.......5.......5.43.21....2.8..4....15.83..43.18.2.....235........41 11.6/1.2/1.2 220223 #1243 98.76.5..7.5..9....64..8....97.46.8...659.......8.7....4......3.....4.5........21 11.6/1.2/1.2 220223 #1439 98.76.5..7.54.9....64..8...4..8.7....97..6.8...659.....4......3.....4.5........21 11.6/1.2/1.2 220223 #1440 987......6.........5.......4..73.21....2.64.3....14..7..63.1.24....4.37.....276.1 11.6/1.2/1.2 220223 #1470 98.76.5..7.48......56......56..8..4.4.89.6....7945......7..........9...3....7.2.1 11.6/1.2/1.2 220515 #4706 98.76.5..7.5.94........8...6.8.47...45.9.6....7.85..4..9....3.2.6......1.....9... 11.6/1.2/1.2 220515 #4707 98.76.5..7.5.84....645.9...6.849..7...98.5.......76...4.......3.....8..........21 11.6/1.2/1.2 220515 #4708 98.76.5..7.5.94........8...6.8.47...45.9.6....7985..4..6......3.....9.........2.1 11.6/1.2/1.2 220515 #4709 987......6..85......4......3..28.51....5.6.3.....136.2.6..3512....1...63....2.8.5 11.7/1.2/1.2 220928 #8123 9876.....5.....8....4......3..2..18....3..6.5....51.23.5.12..36...5.32......86.1. 11.7/1.2/1.2 220928 #8508 9876.....5.....8....4......3..26.18....3..6.5....51.23.5.12..36...5.32......8..1. 11.7/1.2/1.2 220928 #8509 987......6..85......4......3..28.51....5.6.3.....136.2.6..3.12....1.8.63....2.8.5 11.7/1.2/1.2 220928 #8512 9876.....5.....86...4......3..2..18....3..6.5....51.23.5.12..3....5.32.8....86.1. 11.7/1.2/1.2 220928 #8668 987......6..85......4......3.628.51....5.6.3.....13..2.6..3512....1...63....2.8.5 11.7/1.2/1.2 220928 #9475 987......6..85......4......3..28.51....5.6.3.....136.2.6..3512....62.8.5...1....3 11.7/1.2/1.2 220928 #9476 9876.....5.....8....4......3..2..18....3..6.5....51.23.5.12..36....8651......32.. 11.7/1.2/1.2 220928 #9805 9876.....5.....8....4......3.52..18....3..6.5....1..23.5.1.2.36...53.2......68.1. 11.7/1.2/1.2 220928 #9806 9876.....5.....8....4......3..26.18....3..6.5....51.23.5.12..36....8.51......32.. 11.7/1.2/1.2 220928 #9807 9876.....5.....8....4......3.526.18....3..6.5.....1.23.5.12..36...5.32......8..1. 11.7/1.2/1.2 220928 #9808 987......6..85......4......3..28.51....5.6.3.....136.2.6..3.12....62.8.5...1.8..3 11.7/1.2/1.2 220928 #9809 9876.....5.....86...4......3..2..18....3..6.5....51.23.5.12..3.....8651......32.8 11.7/1.2/1.2 220928 #9810 987......6..85......4......3.628.51....5.6.3.....13..2.6..3.12....1.8.63....2.8.5 11.7/1.2/1.2 220928 #9811 9876.....5.....86...4......3.52..18....3..6.5....1..23.5.1.2.3....53.2.8....68.1. 11.7/1.2/1.2 220928 #9812 98.76.5..7.5.......649.....6.985..4..784.6....5..7........9...3....8.2.1......... 11.6/1.2/1.2 220928 #13199 98.76.5..7.5.84......9.....65.8.7.4.4.8.96....9..5.....7......3.6....2.1......... 11.6/1.2/1.2 220928 #13216 98.76.5..7.45.8.....6.4....5.89.6....9.48..6..4...7....7...........9...3.......21 11.6/1.2/1.2 220928 #13395 98.76.5..7.45.8.....6.4....64...7...5.89......9.48..6..7...........9...3.......21 11.6/1.2/1.2 220928 #13402 987......6..8...........5..4.32...1....13.4.5....8...2...42..81...3.12......5.3.4 11.6/1.2/1.2 220928 #13487 98.76.5..7.5.84......9.5...6..8.7.4.4.8.96.5..9.4......7......3.6....2.1......... 11.6/1.2/1.2 220928 #13491 98.76.5..7.54.89....6..9...6.8.74.5.4..98.......5.6.....7....32..4.....1......... 11.6/1.2/1.2 220928 #13492 98.76.5..7.5.84......9.....6..8.7.4.4.8.96.5..9..5.....7......3.6....2.1......... 11.6/1.2/1.2 220928 #13493 987......6...........85....4.3..21.....54.23....1...8....43..58...2.841.....1.3.2 11.6/1.2/1.2 220928 #13498 987......6...........85....4.3..21.....54.23....1...8....43..58...2..41.....153.2 11.6/1.2/1.2 220928 #13499 98.76.5..7.5.48.....6..9...8.4.........4...3........215.86.7....6.9....7..9.54... 11.6/1.2/1.2 220928 #13896 987......6..8...........5...4.32.1.......534......1.28..31....2...2.345.....48.1. 11.6/1.2/1.2 220928 #14058 987......6...........85.....4..3.21....42..85...1.8..3..2..13.....54.1.2...3...48 11.6/1.2/1.2 220928 #14064 987......6...........85.....4..3521....42..85...1....3..2..13.....54.1.2...3...48 11.6/1.2/1.2 220928 #14065 98.76.5..7..4.89....6.5....6.8..4.5.45.98.....7...6.....4.....3.....7..........21 11.6/1.2/1.2 220928 #14089 98.76.5..7.54.89....6..9...6.8..4.5.4..98.....7.5.6.....4.....3.....7..........21 11.6/1.2/1.2 220928 #14097 987......6...........85....4.3..21.....54.23....1...8..4.2.531....43..58....1.4.2 11.6/1.2/1.2 220928 #15304 98.76.5..7.54.89....6.9....6.8.47.5.4..98.......5.6.....7....32..4.....1....7.... 11.6/1.2/1.2 220928 #15305 98.76.5..7.58.4.......95...6...87.4.4.89.6.5..9.4......7......3.6....2.1...6..... 11.6/1.2/1.2 220928 #15308 987......6...........85.....4.3..21....42..58....184.3..2..31.....54.32....1...84 11.6/1.2/1.2 220928 #15309 98.76.5..7.54.89....6.9....6.8.47.5.4..98.....7.5.6.....4.....3....7...........21 11.6/1.2/1.2 220928 #15312 98.76.5..7.58.4.....6.95...6...87.4.4.89.6.5..9.4......7......3...6...........2.1 11.6/1.2/1.2 220928 #15314 987......65..........6.....4..93.21.2...613.4.......96...3.94.....14..29....2.1.3 11.7/11.0/3.4 230514 #15421 987......65.9...........6..4..32.91.3..1.4.62....96......4..1.9...2.1.3.....3.24. 11.7/1.2/1.2 230514 #15747 987......65.9...........6..4..32.91.3..1.4..2....96......4..1.9...2.1.36....3.24. 11.7/1.2/1.2 230514 #16267 98.76.5..7.45.......6..89..64..9....5.8..6....974.5.8.47............473.........2 11.7/1.2/1.2 230514 #16810 987......65..........6.....4..93.21.2....13.4.......96...3.94.....14..29....261.3 11.7/1.2/1.2 230514 #19072 987......65.9...........6..4..32.16.3..1.4..2....96......4...19...2.13......3.42. 11.7/1.2/1.2 230514 #19131 987......6..8...........5...4.32.1.....1.4.82....58.3...32.581......1.54......2.3 11.7/1.2/1.2 230514 #21315 987......65.9...........6..4..32.91.2..4.13.6....6.......2...93...13.4......942.1 11.7/1.2/1.2 230514 #21539 987......65.9...........6..4..32.91.2..4.13.6....6.......2...93...13.46......42.1 11.7/1.2/1.2 230514 #22103 987......6...........85.....4..3.2.....2.8.43.....158...1.83.52...4.513.....2.8.. 11.7/1.2/1.2 230514 #22379 987......6..8...........5...4.32.1.....1.4.82....58.3...32.185......5.14......2.3 11.7/1.2/1.2 230514 #22477 987......6..8...........5...4..3.2.....2.4.83....58.1...13.582.....12.54......3.. 11.7/1.2/1.2 230514 #22492 987......6...........85.....4..3.21....2.8.34.....15.8..1.83.25...4.5..3...12.8.. 11.7/1.2/1.2 230514 #22494 987......6...........85.....4..3521....24..58...1..3.4..258.1.3...4.3..5....1..8. 11.7/1.2/1.2 230514 #22676 987......6..8...........5...4.32.1.....1.4.82....584.3..32.18.5....8.2.......5.14 11.7/1.2/1.2 230514 #22679 987......6..8...........5...4.32..51...1.42.8....5834...32.581......14.........23 11.7/1.2/1.2 230514 #22681 987......6...........85.....4..3.21....24..58...1.83.4..258.1.3...4.3..5....1..8. 11.7/1.2/1.2 230514 #22683 98.76.5..7.4.586...5.4.....6.8..5...57.64.....49.8..6...7..........9..3........21 11.7/1.2/1.2 230514 #22711 98.76.5..7.4.586...5.4.....6.8..5...57.64.....49.8..5...7..........9...3.......21 11.7/1.2/1.2 230514 #22753 987......6..8...........5...4.32..51...1.42.8....5834...32.581.....314.........2. 11.7/1.2/1.2 230514 #22949 987......6..8...........5...4..3.2.....2.4.83....58.1...13.285.....15.24......3.. 11.7/1.2/1.2 230514 #23382 987......6...........85.....4..3.21....2.8.34.....15.8..1.85.23...4.3..5...12.8.. 11.7/1.2/1.2 230514 #23400 987......6...........85.....4..3.2.....2.8.43.....158...1.85.32...4.315.....2.8.. 11.7/1.2/1.2 230514 #23440 98.76.5..7.54.8....64.59...8.6.7..9..4..8......76.5...6......32....46...........1 11.7/1.2/1.2 230514 #23544 987......6..8...........5...4.32..51...1.42.8....5834...32.5.1.....8..2.....314.. 11.7/1.2/1.2 230514 #23564 987......6..8...........5...4.32.1.....1.4.82....584.3..32.18.5....35.14......2.. 11.7/1.2/1.2 230514 #23565 987......6..8...........5...4.32.1.....1.4.82....584.3..32.18.5.....5.14......23. 11.7/1.2/1.2 230514 #23571 98.76.5..7.5..8....645.9...8.74.6.9...6.75......89....4.......3...6.4..........21 11.7/1.2/1.2 230514 #23579 987......6...........85.....4.5.321....42..58....183.4..23..1.5...1...8.....45..3 11.7/1.2/1.2 230514 #23587 98.76.5..7.5.486....4......67.45....5.89.6....49.8..5...7..........9..3........21 11.7/1.2/1.2 230514 #23588 987......6...........85.....4.5.321....42..58....183.4..23..1.5...1...8.....4..23 11.7/1.2/1.2 230514 #23593 987......6...........85.....4.5.321....42..58....1.3.4..238.1.5...1...8.....4..23 11.7/1.2/1.2 230514 #23610 98.76.5..7.54.8....64.59...8.6.7..9..4.98......7..5...4.......3....46..........21 11.7/1.2/1.2 230514 #23625 98.76.5..7.54.8....64.59...8.6.7..9..4..8......76.5...4.......3....46..........21 11.7/1.2/1.2 230514 #23685 98.76.5..7.54.8....64.59...8.6.7..9..4.98......7..5...6......32....46...........1 11.7/1.2/1.2 230514 #23695 987......6..8...........5...4.32..51...1.42.8....5834...32.5.1.....8..2......14.5 11.7/1.2/1.2 230514 #23704 987......6...........85.....4.5.321....42..58....1.3.4..238.1.5...1...8.....45..3 11.7/1.2/1.2 230514 #23774 987......6...........85.....4.5.321....42..58....183.4..23..1.5...1.2.8.....4...3 11.7/1.2/1.2 230514 #23794 987......6..8...........5...4.32..51...1.42.8....5834...32.5.1.....8..23.....14.. 11.7/1.2/1.2 230514 #23808 98.76.5..7.5.486....45.....67.45....5.8..6....49.8..6...7..........9...3.......21 11.7/1.2/1.2 230514 #23856 98.76.5..7.5.486....45.....67.45....5.8..6....49.8..5...7..........9..3........21 11.7/1.2/1.2 230514 #23867 987......6...........85.....4.5.321....42..58....1.3.4..238.1.5...1.2.8.....4...3 11.7/1.2/1.2 230514 #23912 98.76.5..7.5..8....645.9...8.74.6.9..4.8.......6.75...6......32...6.4...........1 11.7/1.2/1.2 230514 #24139 98.76.5..7.54.8....64.59...8.6.7..9..97..5....4..8....6......32....46...........1 11.7/1.2/1.2 230514 #24165 98.76.5..7.5.486....4..9...67.45....5.8.......49.8..6...7..........9...3.......21 11.7/1.2/1.2 230514 #24194 98.76.5..7.5.486....4..9...67.45....5.8..6....49.8..5...7..........9..3........21 11.7/1.2/1.2 230514 #24195 98.76.5..7.5..8....645.9...8.74.6.9..4.8.......6.75...4.......3...6.4..........21 11.7/1.2/1.2 230514 #24196 98.76.5..7.54.8....64.59...8.6.7..9..97..5....4..8....4.......3....46..........21 11.7/1.2/1.2 230514 #24216 98.76.5..7.5.486....4......67.45....5.89......49.8..6...7..........9...3.......21 11.7/1.2/1.2 230514 #24229 98.76.5..7.5.48....645.9...8.7....9..4.8.......6.75...6......32...4.6...........1 11.7/1.2/1.2 230514 #24746 98.76.5..7.5..8....645.9...8.7..4.9..4.8.......6.75...6......32...4.6...........1 11.7/1.2/1.2 230514 #24828 987......6...........85.....4.3.521....42..58....1.3.4..2.8.1.3...1...8.....43..5 11.7/1.2/1.2 230514 #24861 987......6..8...........5...4.32..1....1.42.8....5834...32.185.....354.1.......2. 11.7/1.2/1.2 230514 #24872 987......6...........85.....4.3..21....42..58....183.4..25..1.3...1...8.....43..5 11.7/1.2/1.2 230514 #24890 987......6..8...........5...4.32..51...1.428.....583.4..32.1.......8...2.....541. 11.7/1.2/1.2 230514 #24976 98.76.5..7.5.48....645.9...8.7....9..4.8.......6.75...4.......3...4.6..........21 11.7/1.2/1.2 230514 #24984 987......6...........85.....4.3.521....42..58....183.4..2...1.3...1...8.....43..5 11.7/1.2/1.2 230514 #25028 98.76.5..7.5..8....645.9...8.7..4.9..4.8.......6.75...4.......3...4.6..........21 11.7/1.2/1.2 230514 #25118 987......6..8...........5...4.32..1....1.42.8....5834...32.185......54.1.......23 11.7/1.2/1.2 230514 #25119 987......6..8...........5...4.32..51...1.428.....583.4..32.18......3541.........2 11.7/1.2/1.2 230514 #25394 987......6..8...........5...4.32..1....1.42.8....5834...32.1.5.....8..2......54.1 11.7/1.2/1.2 230514 #25409 98.76.5..7.5..8....645.9...8.7..4.9..96.75......8.....4.......3...4.6..........21 11.7/1.2/1.2 230514 #25422 987......6..8...........5...4.32..51...1.428.....583.4..32.18.......541........32 11.7/1.2/1.2 230514 #25507 98.76.5..7.5..8....645.9...8.7..4.9...6.75......89....4.......3...4.6..........21 11.7/1.2/1.2 230514 #25672 98.76.5..7.45.9.....6.4....8.7..........7.38.........25.98.4.6..786......4..5..9. 11.7/1.2/1.2 230514 #28358 98.76.5..7.54.89...64......8.79.....5...76....9658.......64..........43........21 11.6/9.0/3.4 230514 #30737 98.76.5..7.5.......648.....6.895..4.5...7.....794.6....9...........9.3.2....8...1 11.6/1.2/1.2 230514 #30965 98.76.5..7.5..9....648.....6.895..4.5...7.....794.6....9...........8...3......2.1 11.6/1.2/1.2 230514 #30981 987......6...........85....4.3..21.....54.23....1...8..4.2..31....43..58....184.2 11.6/1.2/1.2 230514 #30989 98.76.5..7.59.4....64.587..8.6.49.7...9..5......87....4.......3.....6..........21 11.6/1.2/1.2 230514 #31090 987......6...........85.....4.3.521....42..58....1.4.3..2..31.....54.32....1...84 11.6/1.2/1.2 230514 #31148 98.76.5..7.54.89...64......8.79.....5...76....9.58....6.....43....64...........21 11.6/1.2/1.2 230514 #31258 987......6..8...........5..4.32...1....13.4.5....8...2.4.32...1...4.128.....583.4 11.6/1.2/1.2 230514 #31426 987......6..8...........5...4.35..21...2.84.5.....183...21..38....43..52......1.4 11.6/1.2/1.2 230514 #31499 987......6..8...........5...4.32..1....4.12.8....5834...32....1...13.45.....84.2. 11.6/1.2/1.2 230514 #31627 98.76.5..7.58.4.......95...6...87.4.4.89.6.5..9..5.....7......3.6....2.1...6..... 11.6/1.2/1.2 230514 #31636 98.76.5..7.5..9....648.....8..9.6.5.5...87.4..7.45....69....4........3.2........1 11.6/1.2/1.2 230514 #31653 98.76.5..7.58.4.....6.95...6...87.4.4.89.6.5..9..5.....7......3...6...........2.1 11.6/1.2/1.2 230514 #31658 98.76.5..7.5.......64.8....8..5.7.4..7984.....5..96...6...........9....3......2.1 11.6/1.2/1.2 230514 #34141 98.76.5..7.5..89...46......8.79.....5...74....9458.......64..........63........21 11.6/1.2/1.2 230514 #34164 98.76.5..7.5..9....648.....8..9.6.4.4...87.5..7..5....69....4........3.2........1 11.6/1.2/1.2 230514 #34180 98.76.5..7.54.........58...6.984..5.47.6.......8.97.4..6......3...9...........2.1 11.6/1.2/1.2 230514 #34202 98.76.5..7.5.946...648......9748..5..4.6.........57.....8.....3...9............21 11.6/1.2/1.2 230514 #34203 98.76.5..7.58.49...64.9....64..78.5.5.8.......9.54.....7............6..3.......21 11.6/1.2/1.2 230514 #34255 987......6..8...........5...4.35..21...2.84.5.....138...21...3....43..52....8.1.4 11.6/1.2/1.2 230514 #34278 987......6...........85.....4.3.251....54..28....81..3..2.1..3....43.8.....2.514. 11.6/1.2/1.2 230514 #34488 987......6..8...........5...4.35..21...2.84.5.....138...21..83....43..52......1.4 11.6/1.2/1.2 230514 #34638 98.76.5..7.5..89...64......8.79.4...5...7.....9658.......64..........43........21 11.6/1.2/1.2 230514 #34925 98.76.5..7.5.......64.8....8...........9...3.......21.6..5.7..4.7964.....5..98... 11.6/1.2/1.2 230514 #37093 987......6...........85.....4.3.251....54..28....1...3..2..1.3....43.8.....2.514. 11.6/1.2/1.2 230514 #37102 98.76.5..7.5.......64.8....8..5.7.4..9784.....5..96...6.9.........9....3......2.1 11.6/1.2/1.2 230514 #37229 98.76.5..7.59.4.......8....6.95.....47.8.6....58.7..4..6......3....9..........2.1 11.6/1.2/1.2 230514 #37290 98.76.5..7.58.4.....6.9....6.857..4..79.4..5..5.9........68.4........3.2........1 11.6/1.2/1.2 230514 #37449 98.76.5..7.54.89...46......8.79.6...5...7.....9458.......64..........63........21 11.6/1.2/1.2 230514 #38092 98.76.5..7.54.89....6......8.79.6...5...74....9.58....4.....63....64...........21 11.6/1.2/1.2 230514 #38154 98.76.5..7.58.4.....6.9....6.857..4.4..9......79.4..5....68.4........3.2........1 11.6/1.2/1.2 230514 #38264 98.76.5..7.5.48....649.....8.7..4.9...6.57......89....4.......3.....6..........21 11.6/1.2/1.2 230514 #38790 98.76.5..7.5.......64.9....6..5.7.4.5...89....7864.....9..........8....3......2.1 11.6/1.2/1.2 230514 #38797 98.76.5..7.5.......64.8....8.9.........9...3.......21.6..5.7..4.9764.....5..98... 11.6/1.2/1.2 230514 #38894 98.76.5..7.59.4.......8....6.95.....47.6.8.....8.7..4..6......3....96.........2.1 11.6/1.2/1.2 230514 #38898 98.76.5..7.59.4.....6.8....6.95.....47.6.8.....8.7..4..9....3.2....96...........1 11.6/1.2/1.2 230514 #38903 98.76.5..7.5..9....64.8....8..5.7.4..9784.....5..96...6.9.........6..3.2........1 11.6/1.2/1.2 230514 #38924 98.76.5..7.59.4.......8....6.75.....49.8.6....58.9..4..6......3....7..........2.1 11.6/1.2/1.2 230514 #38956 98.76.5..7.59.4.....6.8....6.75.....49.6.8.....8.9..4..7....3.2....76...........1 11.6/1.2/1.2 230514 #39788 98.76.5..7.59.4.......8....6.75.....49.6.8.....8.9..4..6......3....76.........2.1 11.6/1.2/1.2 230514 #39823 98.76.5..7.5..9....64.8....8.9.........8..32........1.6..5.7..4.9764.....5..98... 11.6/1.2/1.2 230514 #39835 98.76.5..7.5.......46.8....89..........9...3.......21.6..5.7..445..98....7964.... 11.6/1.2/1.2 230514 #39988 98.76.5..7.54.9.......8....6.754....49.8......58.97.4..6......3...67..........2.1 11.6/1.2/1.2 230514 #39998 98.76.5..7.54.9.......8....6.754....49.8.6....58.9..4..6......3...67..........2.1 11.6/1.2/1.2 230514 #40003 98.76.5..4.7..96....5..8...67.5.....5.9.86....48.7..6..9...........4..3........21 11.6/1.2/1.2 230514 #41213 98.76.5..4.7..96....5..8...67.5.....5.9.86....48.7..5..9...........4...3.......21 11.6/1.2/1.2 230514 #41237 98.76.5..7.5.49......8.....6.745....49..86....589...4..6......3...67..........2.1 11.6/1.2/1.2 230514 #41347 98.76.5..7.5.......46.9....89..........8...3.......21.6..5.7..445..89....7864.... 11.6/1.2/1.2 230514 #41559

There are 6 B10B puzzles:

Code: Select all: 98765.......4..........3...86....92..52....7.......8.557..2.68.2......59.9..6...7 11.7/1.2/1.2 230514 #25642 98765.......4..........3...86....92..52....7...9...8.557..2.68.2......59....6...7 11.7/1.2/1.2 230514 #25648 98765.......4..........3...89....75.7.6...8.2.25.....95.9.2.6.72......85....6..9. 11.7/1.2/1.2 230514 #29369 98765.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....27......5.8 11.7/1.2/1.2 230514 #29398 98765.......4..........3...86....92..52....7...9...8.557..6.28.2......59....2.6.7 11.7/1.2/1.2 230514 #29420 98765.......4..........3...86....92..52....7.......8.557..6.28.2......59.9..2.6.7 11.7/1.2/1.2 230514 #29429

All these puzzles have a non-degenerate tridagon pattern.

[Edit 2023 Nov. 29]: fix the B8B, B9B and B10B lists. In the original post, the numbers of puzzles were correct but the puzzles with these BpB values weren't correctly extracted from the full lists of puzzles. Thanks to Coloin for noticing a problem with the previous B10B list.
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by **hendrik_monard** » Mon Dec 25, 2023 2:18 pm

I am examining if there could be a role for SHC in my generating script(s). First, I am investigating the genealogy of my high BpB ranking puzzles, especially how the BpB evolves along the paths leading to these puzzles. On the path to one of them I came across this fine specimen:
987......6..8...........5...4.32..51...1.42.8....5834...32.581.....134.........2. B13B
Denis, could there be a bug in SHC, or is it a genuine B13B?

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Re: The BpB classification of T&E(2) puzzles

Re: The BpB classification of T&E(2) puzzles

Re: The BpB classification of T&E(2) puzzles

Re: The BpB classification of T&E(2) puzzles

Re: The BpB classification of T&E(2) puzzles