.
I've made a review of all mith's 11.8 puzzles wrt to T&E(2).
As they are scattered in several pages, I can't be sure I haven't missed anything.
Below, they are grouped in 4 series. In the absence of any name or number, I had numbered the first of them for my personal use.
It is still unclear to me whether puzzles from different series can be equivalent after applying Singles and minlexing.
Series 1: I had started computing their BpB classification; it is therefore included in the below list (a - sign such as in B5B- means in B5B or less). This implies they are all in T&E(2).
- Code: Select all
.....9.......8..76...7...85..5.....7.9.....5.1....23...1...4...34..9......681....;11.8;11.8;2.6; mith11.8#1; B5B-
........1.......2...3..45......6...7..5..8....9.3..4...39..58...8.9.....2...1..7. ED=11.8/1.2/1.2; mith11.8#2; B5B-
........1....23.....45...2...3..5.6..6....1..78.6....9..6.5.....1.4....89.....7.. ED=11.8/11.8/2.6 (DCFC+DFC); mith11.8#3; B6B
........1.....234..34....2.......1.5.....3.6....15...7.68..4...7...9....9..5....3 ED=11.8/11.8/2.6; mith11.8#4; B5B-
........1....12.....34...5.....6...2.7....53..8.5..4...378.....1....9...94....7.. ED=11.8/1.2/1.2; mith11.8#5; B5B
........1.....2.34....3.56...2.64....7.8.....8..9....6..5....4..8....1.771......9 ED=11.8/11.8/2.6; mith11.8#6; B5B-
........1.....2.34....3.56...2.46....7.8......8.9....6..5....4.71......98.....1.7 ED=11.8/11.8/2.6; mith11.8#7; B5B-
........1.....2.34....3.56...2.46....7.8.....8..9....6..5....4..8....1.771......9 ED=11.8/11.8/2.6; mith11.8#8; B6B
........1.....2.34....3.56...2.46....7.8.....8..9....6..4....5.18......77.....1.9 ED=11.8/11.8/2.6; mith11.8#9; B5B-
........1.....2.34....3.56...2.46....7.8......8.9....6..4....5.71......98.....1.7 ED=11.8/11.8/2.6; mith11.8#10; B5B-
........1......23......4..5...26.....23.784..86.4.3....7.63....34.8.2...6.2..7.8. ED=11.8/1.2/1.2 mith11.8#11; B6B-
........1......23......4..5...26.....23.784..86...3....7.6.....34.8.2...6.2.47.8. ED=11.8/1.2/1.2 mith11.8#12; B6B-
........1....23.....45...6...5..17...7.8...5.9....5..3.56....7..8.4.....2.......9 ED=11.8/1.2/1.2 mith11.8#13; B6B-
........1.......2.....13.45...3.56....5.78....3716.....6.73...8.785.1...3.1.86.5. ED=11.8/1.2/1.2 mith11.8#14; B6B-
........1.......2.....13.45...3.56...371.....6.5.78....6.73...8.785.1...3.1.86.5. ED=11.8/1.2/1.2 mith11.8#15; B6B-
........1.......2.....13.45...3.56....5.78....3716.5...785.1...3.1.86...56.73...8 ED=11.8/1.2/1.2 mith11.8#16; B6B-
........1.......2.....13.45...3.56...371..5..6.5.78....785.1...3.1.86...56.73...8 ED=11.8/1.2/1.2 mith11.8#17; B6B-
........1.....2.3...4.5.6....748.....3...1..84.85......4....7...9.....237...6.8.. ED=11.8/11.8/2.6 mith11.8#18; B6B-
........1.....2.3....45.6....3....7..4..6....5..8..9....7..1..2.8.6..5..9...4.... ED=11.8/1.2/1.2 mith11.8#19; B6B-
Series 2: I had planned to compute their BpB classification and numbered them, but in the meantime mith discovered the first 11.9 not in T&E(2). So I set up for just checking which of them fails to be in T&E(2)
- Code: Select all
........1.......2......3..4..2..56...37.682...5.27.8...2673....3.58.6...78..5.... ED=11.8/1.2/1.2 mith11.8#20
........1.......2......3..4..2..56...37.682...5.27.8...2673.....8..5....3.58.6.7. ED=11.8/1.2/1.2 mith11.8#21
........1.......2......3..4..2.356.7.3.6.82...5.72.8...26.7....3.5.86...78.5..... ED=11.8/1.2/1.2 mith11.8#22
........1.......2......3..4..2.356...376.82...5.72.8...26.7....3.5.86...78.5..... ED=11.8/1.2/1.2 mith11.8#23
........1.......2......3..4..2.356...376.82...5.72.8...26.7.....8.5.....3.5.86.7. ED=11.8/1.2/1.2 mith11.8#24
........1.....2.......3..45..1.23....267.81..73.61.8...17.6.....8.......2.3.87..6 ED=11.8/1.2/1.2 mith11.8#25 not in T&E(2)
........1.......2......3..4..2..56.7.3..682...5.27.8...2673....3.58.6...78..5.... ED=11.8/1.2/1.2 mith11.8#26
........1.......2......3..4..3.5.2....627.8...8...65.7.78.6....5.273....63.8.5... ED=11.8/1.2/1.2 mith11.8#27
........1.......2......3..4..5..67...6.28.5..83..7.2...58.6....6.35.7...72.83.... ED=11.8/1.2/1.2 mith11.8#28
........1.......2......3..4..5..67...6.28.5..83..7.2...5..6....6.35.7.8.72.83.... ED=11.8/1.2/1.2 mith11.8#29
........1.......2......3..4..3.5.2....627.8...8.3.65.7.78.6....5.27.....63.8.5... ED=11.8/1.2/1.2 mith11.8#30
........1.......2......3..4..5.367...6.82.5..83.7..2...586.....6.3.57...72..8.... ED=11.8/1.2/1.2 mith11.8#31
........1.......2......3..4..5.367...6.82.5..83.7..2...5.6.....6.3.57.8.72..8.... ED=11.8/1.2/1.2 mith11.8#32
#5 is known to be equivalent to Loki after applying Singles and minlexing.
Series 3 is what came immediately after the discovery of Loki. It contains only the 74 minlexed expanded (by Singles) forms of the 146 puzzles. As T&E(n) is invariant under isomorphisms and under application of Singles, this is enough.
- Code: Select all
.......12....13..4..12..5....46....5.7....6..86..9......64...5..9...7...3...8.... 23c
........1.....2.......3..45.16.23...27.8.61..3.871.6...32.68..718..7....6.7...... 29c not in T&E(2)
........1.......2...3..45......6...7..5..8....9.3..4...39..58...8.9.....2..81..7. 22c
........1.....2.3....14.5....2....6..3......78..9..4...68..7...4..81....9...5.8.. 22c
........1.....2.3...4.5.6.....7...8...6.9...5.2...3....7.8.9...6...1...99.1...4.. 22c
........1..2..3.4..5..6.7.......1.8....4....32...9.6....9.2.5..56.8.....72....... 22c
.......12....13.4...14..5....2.....5.3..6....7....8.....41...5..6..3.9..8....7... 22c
.....1..2....3..4....5..6....1..2....7......89...4.3...98.....73..9...5.5...6.9.. 22c
........1.....2.3....14.5....3.....6.7.....828..9..1...86..7...4..89....5...1.8.. 23c
........1.....2.3....45.6....1.7..62.8.6..7..67.........3..9...4..5..8..85.7..... 23c
........1.....2.3...4.5.6...16....27.4....8..8...6.9...7...3...4.58.....6..59.... 23c
........1.....2.3...4.5.6...16....72.4....8..8...6.9...7...3...4.58.....6..59.... 23c
........1.....2.3...4.5.6...3...1...4.78.....6..54.....4....7...96....127...6.8.. 23c
........1.....2.3...4.5.6...37....82.4....7..6..7..9...8...1...4.56.....7..59.... 23c
........1....12....134...5.....6...2.7....53..8.5..4...378.....1....9...94....7.. 23c
........1....23.....45...6...5..17...7.8...5.9....5..3.56....7..894.....2.......9 23c
........1..2..3.4..4..5.6.....36...5.3.1..7..2....8.3...9.3...7.2...4.9.8........ 23c
........1..2..3.4..4.15........6.15..5.7..48.8.......9..3..2....7..1.6..9.......8 23c
........1..2..3.4..5..6.7.......1.3....4....85...7.2....5.2.9..29.....8.76.9..... 23c
.......12.....3..4..4.2.5....2.6...5.7....6..86.9.......6.1..5..9...8...3..7.6... 23c
.......12....13..4..14..5....26...5..7....6..8...9.4....41....5.3..8....9....7... 23c
.......12....13.45..14..6....45....1.7....2..8...9......61...2..9..8....3....7... 23c
.....1..2....2..3...24..5....1..46...7......38......9...6.4.....3.6....79..5...86 23c
.....1..2..2....3..4..5.6.......7.16.8..6....6..5..9....3..5..7.5.8.....9...4.5.. 23c
........1.....2.3...4.5.6.....3.7.8..6..1.7.3.7....1.4.46.7....28...9...9..8..... 24c
........1.....2.3..34.5..2.....35..6.652...4.7...46......5..8...52..4.6.9........ 24c
........1..1..2.3..4..5.2.......6.....37...2686....9....6..7..2.5.4..6..9...6..8. 24c
.......12..1..3.4..4..1.5....6..7....2..4...58..3.......7.98....9..3..5.3..6..9.. 24c
........1.....2.....3.4..5.....3.5.4..5..67.3.3.....6..87.64.3.3.6.5..4.9..8.3... 26c
........1......23......4..5...26.....23.784..86.4.3....786.....34.8.2...6.2.47.8. 28c
..............1.23...45.6.1..1.47....7681...584...6..7.5478....6.81..7..7...6.... 29c
..............1.23...45.6.1..1.47....7681..5.84...6..7.5478....6.81..7..7...6.... 29c
........1......23......4..5...26.....23.784..86.4.3....7863....34.8.2...6.2.47.8. 29c
........1......23......4.56....43..5.3752..8.5.47.8.2...84.....34..87...7.235.... 29c
........1......23.....14.56..7..6....86.5...741..78.....864..7..547.1...76..85... 29c
........1.......2......3..4.25.367..3.782.5..68.7.52...63.57...27.38....5.86..... 30c
........1.......2......3..4.25.367..3.87.52..67.82.5...63.57...2.738....58.6..... 30c
........1.......2......3..4.25.367..37.82.5..6.87.52...63.57...2.738....58.6..... 30c
........1.......2......3..4.25.367..38.7.52..6.782.5...63.57...27.38....5.86..... 30c
........1.......23....24.....564.7...847.2...67..85....4625....5.74.8.6.82..67... 30c
........1.....2.34.35.......62......7.3.25..885...67...7853....32..68...5.62.7.8. 30c not in T&E(2)
........1.....234.....56.7...65.87...25.17...87.62.....682....72.7.6....51.87.... 30c
..............1.23...45.6.1..7.6.....861..7..54.78.....15.47...4.85.6..776.81...4 31c
..............1.23...45.6.1..7.6.....861..7..54.78.....15.47...4.85.6..776.81..4. 31c
..............1.23.14...5.6..5..7....6..857...7841.....8675...154.1.8..77.1.64... 31c
..............1.23.14...5.6..5..7....6..857...7841.....8675...454.1.8..77.1.64... 31c
..............1.23.14...5.6..5..7....6..857...7841.....8675..1.54.1.8..77.1.64... 31c
..............1.23.14...5.6..5..7....6..857...7841.....8675..4.54.1.8..77.1.64... 31c
........1.......2......3..4.25.367.83.782.5..68.7.52...63.57...27.38....5.86..... 31c
........1.......2......3..4.25.367.83.87.52..67.82.5...63.57...2.738....58.6..... 31c
........1.......2......3..4.25.367.837.82.5..6.87.52...63.57...2.738....58.6..... 31c
........1.......2......3..4.25.367.838.7.52..6.782.5...63.57...27.38....5.86..... 31c
........1......23......4.56..7.4.....8253....43.7.8....54.87.2.27.4.3..53.825..7. 31c
........1......23.....14.56..71.6....8645...741..78.....864..7..547.1...76..85... 31c
........1.....234.....56.7...187.....862.5..727..61....52.17....6.5.87..8.762.... 31c
..............1.23...45.6.1..7.64....861.57..54.78.....15.47...4.85.6..776.81.... 32c
..............1.23...45.6.1..7.65....861.47..54.78.....15.47...4.85.6..776.81.... 32c
..............1.23..4.2.56...7.13....8324...714.7.8....21.74...4.813..7.73.8.2... 32c
..............1.23..4.2.56...7.43....8321...714.7.8....21.74...4.813..7.73.8.2... 32c
..............1.23.14...5.6.7658....54..17..88.16.4....8714....1.5..8...46.7.58.. 32c
..............1.23.14...5.6.7658....54..17..88.16.4....8714....16.7.58..4.5..8... 32c
........1.......2......3..4.2356.7..5.82.76..67..382.5.578....22.635....83..72... 32c
........1.......2......3..4.2356.7..5.82.76..76..382.5.578....22.635....38..72... 32c
........1.......2......3..4.25.36...37.8.52.66.872.5...63.58.7.28.67....5.73...6. 32c
........1.......2......3..4.25.367.83.782.5..68.7.52...63.57.8.27.38....5.86..... 32c
........1.......2......3..4.25.367.83.87.52..67.82.5...63.57.8.2.738....58.6..... 32c
........1.......2......3..4.25.367.837.82.5..6.87.52...63.57.8.2.738....58.6..... 32c
........1.......2......3..4.25.367.838.7.52..6.782.5...63.57.8.27.38....5.86..... 32c
........1.......2.....13.45...3.56...3716.5..6.5.78....785.1...3.1.86.5.56.73...8 32c
........1.......2......3..4.2356.7..5.82.76.367..382.5.578....22.635....83..72... 33c
........1.......2......3..4.2356.7..5.82.76.376..382.5.578....22.635....38..72... 33c
........1......23......4.56..7.42....8253....43.7.8..2.54.87.2.27.4.3..53.825..7. 33c
........1.....2.34..2...56..23.78.5.5.82.6...67.53..8..5736.....8..25...2.68.7..5 33c
........1.......2......34.5.26.37..434.8.62.78.742.6...73.68.4.28.74....6.43...7. 34c
Notice there are 2 puzzles not in T&E(2). Here are their respective resolution state after applying T&E(2).
- Code: Select all
PUZZLE 2 IS NOT SOLVED. 50 VALUES MISSING.
Final resolution state:
478 256 3 459 4589 4579 28 67 1
457 456 145 156 48 2 39 678 39
89 269 19 16 3 17 278 4 5
459 1 6 459 2 3 57 5789 48
2 7 459 8 459 6 1 359 34
3 459 8 7 1 459 6 259 249
459 3 2 1459 6 8 459 19 7
1 8 459 23 7 459 3459 235 6
6 459 7 23 459 14 4589 1238 238
- Code: Select all
PUZZLE 41 IS NOT SOLVED. 50 VALUES MISSING.
Final resolution state:
2469 489 479 3678 478 39 256 25 1
16 18 179 678 5 2 89 3 4
24 3 5 1469 1489 149 89 67 267
149 6 2 78 78 1349 345 149 35
7 149 3 149 2 5 16 1469 8
8 5 149 13 149 6 7 1249 23
149 7 8 5 3 149 124 126 69
3 2 149 149 6 8 145 457 579
5 149 6 2 149 7 134 8 39
Series 4 is what came after the 3rd. It's unclear to me if they are related to previous puzzles, ut anyway, they're all in T&E(2).
- Code: Select all
........1......23......4.56....43..5.3752..8.5.47.8.2...8......34..87...7.235.... ED=11.8/1.2/1.2
........1......23.....14.56..7..6....86.5...741..78.....864..7..54..1...76..85... ED=11.8/1.2/1.2
........1......23......4.56.....3..5.3725..8.5.4.78.2...8.4....34.8.7...7.253.... ED=11.8/1.2/1.2
........1......23.....14.56..6.75....458.1....7.64..8..67.5...8.8...6...4.1..7... ED=11.8/1.2/1.2
........1.......2......3..4..2.356...3.72.8..75.6.82...8.5.....3.5.86.7.62..7.... ED=11.8/1.2/1.2
........1.......2......3..4..325.6...57.8.2...6.3.78....6.7.....825.....73.6.8.5. ED=11.8/1.2/1.2
Conclusion: as of now, in addition to Loki (and its equivalent 11.8 form), there are two 11.8 puzzles not in T&E(2):
........1.....2.......3..45.16.23...27.8.61..3.871.6...32.68..718..7....6.7...... 29c not in T&E(2)
........1.....2.34.35.......62......7.3.25..885...67...7853....32..68...5.62.7.8. 30c not in T&E(2)