The New Sudoku Players' Forum

[Serg]

I was wrongly understanding the principle of forming horizontally symmetric 18-clue patterns list (thanks to Pat for his clarification). So, I didn't find really any new symmetric patterns by "twins" search.

Serg

[dobrichev]

Hi, ronk, dobrichev!
Thank you for your replies. dobrichev, thank you for your link. Your results are very interesting for me. I've searched twin puzzles in exactly the same way as you.

Now I can't remember what exactly I counted, since there were cases where puzzles A and B are twins, B and C are twins, but A and C are not. So 96 is probably not the pair count but the number of puzzles which have 1 or more twins.

Sounds somewhat strange... Puzzles A, B, C in your example all have the same completition, aren't they? If so, they all are twins (maybe "multiplies"?).

Serg

Serg, you are right.

In 17s there are no complicated cases.
Below are the 96 pairs. In the left column, the puzzles are ordered by their row minlex representation. The right column is the puzzle with the permuted UA values. Each pair occurs twise in the list - once with one puzzle in minlex form, and second time with puzzles swapped and other puzzle in minlex form. 96 puzzles are forming 48 distinct pairs. There are no repeating puzzles in the left column, therefore there are no "multiplets".


.................1..1..2.34...........4.....2.5..6.7.......1....6.5..8..78....6..;.................1..1..2.34...........4.....2.5..6.7.......1....8.5..6..76....8..
.................1..1..2.34...........4.....2.5..6.7.......1....6.5..8..98....6..;.................1..1..2.34...........4.....2.5..6.7.......1....8.5..6..96....8..
.................1..1..2.34...........4.....2.5..6.7.......1....8.5..6..76....8..;.................1..1..2.34...........4.....2.5..6.7.......1....6.5..8..78....6..
.................1..1..2.34...........4.....2.5..6.7.......1....8.5..6..96....8..;.................1..1..2.34...........4.....2.5..6.7.......1....6.5..8..98....6..
.................1..2..3..4.....1..2.....4....56....7.....5.68...3......4...8..5.;.................1..2..3..4.....1..2.....4....56....7.....8.65...3......4...5..8.
.................1..2..3..4.....1..2.....4....56....7.....8.65...3......4...5..8.;.................1..2..3..4.....1..2.....4....56....7.....5.68...3......4...8..5.
.................1..2.34...............5.1.6...36...5.....7.28..5.9.....41.......;.................1..2.34...............6.1.5...35...6.....7.28..5.9.....41.......
.................1..2.34...............5.1.6...36...5.....7.28..6.9.....41.......;.................1..2.34...............6.1.5...35...6.....7.28..6.9.....41.......
.................1..2.34..........3....15.....5.6....7...51...6..8......4.3....2.;.................1..2.34..........3....51.....5.6....7...15...6..8......4.3....2.
.................1..2.34..........3....51.....5.6....7...15...6..8......4.3....2.;.................1..2.34..........3....15.....5.6....7...51...6..8......4.3....2.
.................1..2.34..........3..5.....4.16.7.........8.32..7.......61...5...;.................1..2.34..........3..5.....4.61.7.........8.32..7.......16...5...
.................1..2.34..........3..5.....4.61.7.........8.32..7.......16...5...;.................1..2.34..........3..5.....4.16.7.........8.32..7.......61...5...
................12.....3..4.....56....1.......27..........1...76..8..3..8..62....;................12.....3..4.....56....1.......27..........1...78..6..3..6..82....
................12.....3..4.....56....1.......27..........1...76..82....8..6..3..;................12.....3..4.....56....1.......27..........1...78..62....6..8..3..
................12....13..4....4..21..5.....6.78.........5..8..2........9..8.....;................21....13..4....4..12..5.....6.78.........5..8..2........9..8.....
................12....13..4....5..21..6.....7.89.........6..9..2........4..9.....;................21....13..4....5..12..6.....7.89.........6..9..2........4..9.....
................12....13.4.....4..21..5....6..78.........5..8..2........9..8.....;................21....13.4.....4..12..5....6..78.........5..8..2........9..8.....
................12....13.4.....5..21..6....7..89.........6..9..2........4..9.....;................21....13.4.....5..12..6....7..89.........6..9..2........4..9.....
................12....34...........5..61.....78....3.........21....4..6..4..85...;................21....34...........5..61.....78....3.........12....4..6..4..85...
................12....34...........5..62.....78....3.........21....4..6..4..85...;................21....34...........5..62.....78....3.........12....4..6..4..85...
................12..3..4........135...6...7...2...8.......6.53..8..2....4........;................12..3..4........153...6...7...2...8.......6.35..8..2....4........
................12..3..4........153...6...7...2...8.......6.35..8..2....4........;................12..3..4........135...6...7...2...8.......6.53..8..2....4........
................12..3..4..5.............23...16.....7....6....3.8....4..61.7.....;................12..3..4..5.............23...61.....7....6....3.8....4..16.7.....
................12..3..4..5.............23...16.....7....6....361.7.....8.....4..;................12..3..4..5.............23...61.....7....6....316.7.....8.....4..
................12..3.45.................43.617..2..8......34...2.......71.......;................12..3.45.................43.671..2..8......34...2.......17.......
................12..3.45.................43.617..2..8......34..2........71.......;................12..3.45.................43.671..2..8......34..2........17.......
................12..3.45.................64..17.8.........3.....2.....816...54...;................12..3.54.................64..17.8.........3.....2.....816...45...
................12..3.45.................65..17.8.........3.....2.....816...54...;................12..3.54.................65..17.8.........3.....2.....816...45...
................12..3.45.........1........34.26.7..........34...7.......62..8....;................12..3.45.........1........34.62.7..........34...7.......26..8....
................12..3.45.........1........34.26.7..........34..62..8....7........;................12..3.45.........1........34.62.7..........34..26..8....7........
................12..3.45........6......1.23...7...........7.48..6..8..7.2........;................12..3.45........6......1.23...7...........8.47..6..7..8.2........
................12..3.45........6......1.23...7...........8.47..6..7..8.2........;................12..3.45........6......1.23...7...........7.48..6..8..7.2........
..............1..2....2..34.....5.43..6.....7.89.........6..8....2......3..8.....;..............1..2....2..43.....5.34..6.....7.89.........6..8....2......3..8.....
..............1..2....2..34.....5.43..6.....7.89.........6..8....2......4..8.....;..............1..2....2..43.....5.34..6.....7.89.........6..8....2......4..8.....
..............1..2..3....4.........4..5.6...7..635.....1........8....53.2....4...;..............1..2..3....4.........4..6.5...7..536.....1........8....53.2....4...
..............1..2..3....4.........4..5.6...7..635.....1........8....63.2....4...;..............1..2..3....4.........4..6.5...7..536.....1........8....63.2....4...
..............1..2..3....4.........4..5.6...7..635.....1....35..8.......2....4...;..............1..2..3....4.........4..6.5...7..536.....1....35..8.......2....4...
..............1..2..3....4.........4..5.6...7..635.....1....36..8.......2....4...;..............1..2..3....4.........4..6.5...7..536.....1....36..8.......2....4...
..............1..2..3....4.........4..5.6...7..635.....1....53..8.......2....4...;..............1..2..3....4.........4..6.5...7..536.....1....53..8.......2....4...
..............1..2..3....4.........4..5.6...7..635.....1....63..8.......2....4...;..............1..2..3....4.........4..6.5...7..536.....1....63..8.......2....4...
..............1..2..3....4.......1.5...23.....6......7....6......834.....7....5.1;..............1..2..3....4.......5.1...23.....6......7....6......834.....7....1.5
..............1..2..3....4.......1.5...36.....2..7.......63..7.4........51......8;..............1..2..3....4.......1.5...63.....2..7.......36..7.4........51......8
..............1..2..3....4.......1.5...36.....2.7........63..7.4........51......8;..............1..2..3....4.......1.5...63.....2.7........36..7.4........51......8
..............1..2..3....4.......1.5.2..3....6.......7....6.....8.34....7.....5.1;..............1..2..3....4.......5.1.2..3....6.......7....6.....8.34....7.....1.5
..............1..2..3....4.......5.1...23.....6......7....6......834.....7....1.5;..............1..2..3....4.......1.5...23.....6......7....6......834.....7....5.1
..............1..2..3....4.......5.1...36.....2..7.......63..7.4........51......8;..............1..2..3....4.......5.1...63.....2..7.......36..7.4........51......8
..............1..2..3....4.......5.1...36.....2.7........63..7.4........51......8;..............1..2..3....4.......5.1...63.....2.7........36..7.4........51......8
..............1..2..3....4.......5.1.2..3....6.......7....6.....8.34....7.....1.5;..............1..2..3....4.......1.5.2..3....6.......7....6.....8.34....7.....5.1
..............1..2..3....4.....2...5...3......5....1.6...7.......243....8.....6.1;..............1..2..3....4.....2...5...3......5....6.1...7.......243....8.....1.6
..............1..2..3....4.....2...5...3......5....6.1...7.......243....8.....1.6;..............1..2..3....4.....2...5...3......5....1.6...7.......243....8.....6.1
..............1..2..3....4.....3.....5......67.....1.5....8......934.....2....5.1;..............1..2..3....4.....3.....5......67.....5.1....8......934.....2....1.5
..............1..2..3....4.....3.....5......67.....5.1....8......934.....2....1.5;..............1..2..3....4.....3.....5......67.....1.5....8......934.....2....5.1
..............1..2..3....4.....35.......6...727......1....8..9..15......72.......;..............1..2..3....4.....35.......6...772......1....8..9..15......27.......
..............1..2..3....4.....35.......6...727......1....8..9.1.5......72.......;..............1..2..3....4.....35.......6...772......1....8..9.1.5......27.......
..............1..2..3...45........3..6..4....17...........5.......23.8..71......6;..............1..2..3...45........3..6..4....71...........5.......23.8..17......6
..............1..2..3...45........3..6..4....71...........5.......23.8..17......6;..............1..2..3...45........3..6..4....17...........5.......23.8..71......6
..............1..2..3.4..5........6....7.2.....5...43....3......1......828......1;..............1..2..3.4..5........6....7.2.....5...43....3......8......121......8
..............1..2..3.4..5........6....7.2.....5...43....3......8......121......8;..............1..2..3.4..5........6....7.2.....5...43....3......1......828......1
..............1..2.34.....5........36....7.8.7...26.........6.....8.......534....;..............1..2.34.....5........37....6.8.6...27.........6.....8.......534....
..............1..2.34.....5........36....7.8.7...26.........7.....8.......534....;..............1..2.34.....5........37....6.8.6...27.........7.....8.......534....
..............1..2.34.....5........36....7.8.7...96.........6.....8.......534....;..............1..2.34.....5........37....6.8.6...97.........6.....8.......534....
..............1..2.34.....5........36....7.8.7...96.........7.....8.......534....;..............1..2.34.....5........37....6.8.6...97.........7.....8.......534....
..............1..2.34.....5....3.......45...67............4..7.1.....8..86....1..;..............1..2.34.....5....3.......45...67............4..7.8.....1..16....8..
..............1..2.34.....5....3.......45...67............4..7.16....8..8.....1..;..............1..2.34.....5....3.......45...67............4..7.86....1..1.....8..
..............1..2.34....5.......6......3....2....6........27....584.....43...1..;..............1..2.43....5.......6......3....2....6........27....584.....34...1..
..............1..2.34....5.......6......3....2....6........27...43...1...5.84....;..............1..2.43....5.......6......3....2....6........27...34...1...5.84....
........1.......2...3..4.........3....5...4.6.7..1.........36.4.8.......21.7.....;........1.......2...3..4.........3....5...6.4.7..1.........34.6.8.......21.7.....
........1.......2...3..4.........3....5...6.4.7..1.........34.6.8.......21.7.....;........1.......2...3..4.........3....5...4.6.7..1.........36.4.8.......21.7.....
........1.......2...3..4.........3.5.....64...1..7........8......4...5.37..21....;........1.......2...3..4.........5.3.....64...1..7........8......4...3.57..21....
........1.......2...3..4.........5.3.....64...1..7........8......4...3.57..21....;........1.......2...3..4.........3.5.....64...1..7........8......4...5.37..21....
........1.......2...3..4........53.6.7.......21...........1.......7.84..4.....6.3;........1.......2...3..4........56.3.7.......21...........1.......7.84..4.....3.6
........1.......2...3..4........56.3.7.......21...........1.......7.84..4.....3.6;........1.......2...3..4........53.6.7.......21...........1.......7.84..4.....6.3
........1.......2...3..4..5......5.......64..27..........27..8...4.8..7...6......;........1.......2...3..4..5......5.......64..27..........28..7...4.7..8...6......
........1.......2...3..4..5......5.......64..27..........28..7...4.7..8...6......;........1.......2...3..4..5......5.......64..27..........27..8...4.8..7...6......
........1.......2...3..45..........5.....64..27..........27..8...4.8..7...6......;........1.......2...3..45..........5.....64..27..........28..7...4.7..8...6......
........1.......2...3..45..........5.....64..27..........28..7...4.7..8...6......;........1.......2...3..45..........5.....64..27..........27..8...4.8..7...6......
........1.......23.....4.......3......4.5.6...76...4.....8.7...2........315......;........1.......23.....4.......3......6.5.4...74...6.....8.7...2........315......
........1.......23.....4.......3......5.6.4...74...5.....8.7...2........316......;........1.......23.....4.......3......4.6.5...75...4.....8.7...2........316......
........1.......23..4..5.........6...2..7....17.32.........6.......54....3......8;........1.......23..4..5.........6...7..2....12.37.........6.......54....3......8
........1.......23..4..5.........6...2..7....37.12........3...8..6.......45......;........1.......23..4..5.........6...7..2....32.17........3...8..6.......45......
........1.......23..4..5........6....1..3.....2.....7.....2......57..8..6.8...5..;........1.......23..4..5........6....1..3.....2.....7.....2......87..5..6.5...8..
........1.......23..4..5........6....1..3.....2.....7.....2......87..5..6.5...8..;........1.......23..4..5........6....1..3.....2.....7.....2......57..8..6.8...5..
........1.......23..4..5.......1..32.5........67.........1.65.....8.....2......4.;........1.......32..4..5.......1..23.5........67.........1.65.....8.....2......4.
........1.......23..4..5.......1..32.5........67.........1.65.....8.....3......4.;........1.......32..4..5.......1..23.5........67.........1.65.....8.....3......4.
........1.......23..4.56.........5...3.......27.3..........4.....8.65....2......7;........1.......23..4.65.........5...3.......27.3..........4.....8.56....2......7
........1.......23..4.56.........5...3.......27.3.........4......8.65....2......7;........1.......23..4.65.........5...3.......27.3.........4......8.56....2......7
........1......23...4.56........7........8.4..1....32....2.......7......8.6.....7;........1......32...4.56........7........8.4..1....23....2.......7......8.6.....7
........1......23...4.56........7........8.4..1....32....3.......7......8.6.....7;........1......32...4.56........7........8.4..1....23....3.......7......8.6.....7
........1.....2.....1....34....1.....2....56..5.7..2......3........4...78....6...;........1.....2.....1....34....1.....5....26..2.7..5......3........4...78....6...
........1.....2.....1....34....1.....2.5..6...6....27.....3........4...58....7...;........1.....2.....1....34....1.....6.5..2...2....67.....3........4...58....7...
........1.....2.....3....4.........3.1....5.67..48........7...9...84.....26......;........1.....2.....3....4.........3.1....5.67..84........7...9...48.....26......
........1.....2.....3....4.........3.1....5.67..48.......7....9...84.....26......;........1.....2.....3....4.........3.1....5.67..84.......7....9...48.....26......
........1.....2.....3....4........5....16.....7....38......583.16..9....2........;........1.....2.....3....4........5....16.....7....83......538.16..9....2........
........1.....2.....3....4........5....16.....7....38......583.16.9.....2........;........1.....2.....3....4........5....16.....7....83......538.16.9.....2........
........1.....2.....3....4........5....16.....7....83......538.16..9....2........;........1.....2.....3....4........5....16.....7....38......583.16..9....2........
........1.....2.....3....4........5....16.....7....83......538.16.9.....2........;........1.....2.....3....4........5....16.....7....38......583.16.9.....2........


Cheers,
MD