The New Sudoku Players' Forum

[coloin]

I dont think a new standard is needed. The minlex [ with a significant bug ] has been used as the standard and works for the purpose when a puzzle needs to be identified
The true min lex [ as referenced] is technically superior in may ways although needs a clean line end of string to function.
The solution grid min lex has the drawback that any manual solver wont be able to unsee the initial clues in the first line to aid solving !!!
But it does allow for comparing non-minimal puzzles [ of the same expanded stem] from the same solution grid.

My observation would be that we have two groups of puzzles
1 the original minimal puzzles with 20-25 clues which have a hard early initial step
2 the loki puzzles with triagdon pattern which typically have 25-29 clues, which tend to expand with singles to 30-35 clues.

Some of recently found puzzles with high BnB tend to not expand as much and have therefore have less minimal puzzles from the expand.

Looking for 21 and lower clue puzzles.... I even found 19 clue puzzles with the clue pattern.

Code: Select all

+---+---+---+                         +---+---+---+
|8..|.4.|...|                         |89.|.4.|.67|
|...|7..|.9.|                         |...|7.6|.9.|
|.6.|5..|4..|                         |76.|598|4..|
+---+---+---+                         +---+---+---+
|.4.|.5.|..6|                         |.48|.57|9.6|
|...|.8.|...|                         |.7.|.89|...|
|..9|...|.7.|                         |..9|...|.7.|
+---+---+---+                         +---+---+---+
|.8.|9..|...|                         |.8.|97.|3..|
|...|.6.|...|  19 clues               |...|.65|789|
|..7|...|.12|  ED=7.2                 |957|834|612|
+---+---+---+  Expands to 43 clues    +---+---+---+

Here is a diamond 21 clue puzzle with the necessary clue distribution [1 and 2 only in box 9], so it is possible !

Code: Select all

+---+---+---+
|8..|...|...|
|9.4|..7|..8|
|.6.|...|.5.|
+---+---+---+
|...|85.|.69|
|...|...|.45|
|...|...|...|
+---+---+---+
|5..|9..|...|
|48.|.6.|...|
|..7|...|.12|  21 clues
+---+---+---+  ED=8.4/8.4/8.3

Finding a puzzle which doesnt have singles to start but has the triagadon pattern remains elusive.

EDIT - The [expanded] B10B and B13B puzzles morphed to show the clue distribution and the thors hammer [!] are wildly different from the 21 clue of course.

Code: Select all

+---+---+---+       
|45.|.79|6..|       
|6.7|8.4|...|       
|.89|56.|7..|       
+---+---+---+       
|.46|..5|...|       
|5.8|49.|...|       
|97.|.86|...|       
+---+---+---+       
|895|...|47.|       
|...|...|.2.|       
|...|...|..1|       
+---+---+---+   B10B
                   
+---+---+---+       
|45.|.69|...|       
|6.7|4.8|5..|       
|.89|57.|6..|       
+---+---+---+       
|.75|69.|...|       
|8.6|.45|...|       
|94.|8..|.56|       
+---+---+---+       
|7..|...|..5|       
|...|9..|..3|       
|...|...|.21|       
+---+---+---+   B13B


[coloin]

There are so far 298 minimal puzzles found with B13B,B10B and B9B

Hidden Text: Show

Code: Select all

B13B
..3.......571...3669.7..51..76...3..3.9..1.6.51....97.....28.......4..9...5......
..3.....9.571...3669.7..51..76...3..3.9..1.6.51.....7.....28.......4..9...5......
1.3.......57....3669.7..5...76...3.13.9..1.6.51....97.....28.......4..9...5.1....
1.3.......57....3669.7..51..76...3..3.9..1.6.51....97.....28.......4..9...5.1....
..3.......571...3669.7..51..76...3.13.9....6.51....97.....28.......4..9...5.1....
1.3.......571...3669.7..5...76...3.13.9....6.51....97.....28.......4..9...5.1....
1.3.....9.57....3669.7..5...76...3.13.9..1.6.51.....7.....28.......4..9...5.1....
1.3.....9.57....3669.7..51..76...3..3.9..1.6.51.....7.....28.......4..9...5.1....
..3.....9.571...3669.7..51..76...3.13.9....6.51.....7.....28.......4..9...5.1....
1.3.....9.571...3669.7..5...76...3.13.9....6.51.....7.....28.......4..9...5.1....
1.3.......571...3669.7..5...76...3.13.9..1.6.51....97.....28.......4..9...5......
..3.......571...3669.7..51..76...3.13.9.7..6.51....97.....28.......4..9...5......
1.3.......571...3669.7..5...76...3.13.9.7..6.51....97.....28.......4..9...5......
1.3.....9.571...3669.7..5...76...3.13.9..1.6.51.....7.....28.......4..9...5......
..3.....9.571...3669.7..51..76...3.13.9.7..6.51.....7.....28.......4..9...5......
1.3.....9.571...3669.7..5...76...3.13.9.7..6.51.....7.....28.......4..9...5......
B10B
1.3..67...57..9.36.9....15..16....93......5.19.5....7....8.....7316.5.......4....
1..4.67..4..18...66...72.142.5......7......28.3...........1487....6.8.42...7..6.1
1..4.678.4..18...66...72.142.5......7......28.3...........14.7....6.8.42...7..6.1
....56.89...1.92.6....2.51...961..5...52.8.91..1.956.23.8.......7.........2....68
1.3.....945.....36.69...15..95.1..633...6.5.161..3.94.54..9.......84.........7...
....56.89...1.92.6....2.51...691..5...1.659.2..52.8.613.8.......7.........2....98
1.3..67...57..9.36.9....15..36....9171....5.39.5....7.3716.5......8.........4....
1.3..67...57..9.36.9....15..16....9373....5.19.5....7.3716.5......8.........4....
12.....89.5....2.68.6....5.28.6..51..612.....9.58...6....9.4.......7.......5...91
12.....89.5....2.68.6...15.28.6..5...612.....9.58...6....9.4.......7.......5...91
....56.89...1.92.6....2.51...561......92.8..1..1.956.23.8.......7.........2....68
1.3.....945.....36.69...15..95.1..63.1..6.94.....3.5.154..9.......84.........7...
....56.89...1.92.6....2.51...591......1.659.2..62.8..13.8.......7.........2....98
........945....2........51.2.48.36..6...253.....64.8..3.2.64...5..3.8....682.....
........945....2........51.2.43.86..6...253.....64.8..3.2.64...5..8.3....682.....
...4.6.......8.2.6...72..45.9.......3........5.6...874..524..68....67.2...25.8..7
...4.67......8.2.6...72..45.9.......3........5.6...874..524..68....67.2...25.8...
...4.6.......8.2.6...72..45.9.......3........5.6...874..254..68....67.2...5..8..7
...4.67......8.2.6...72..45.9.......3........5.6...874..254..68....67.2...5..8...
1...5...9..71....669.37...1......8.353......7.......2.36.5.1....7569....9.1..7...
1...5...9.571....669.37...1......8.353......7.......2.36.5.1....7.69....9.1..7...
....56.89...1.92.6....2.51...16...5...52.8.91..9..56.23.8.......7.........2....68
....56.89...1.92.6....2.51...19...5...6..59.2..52.8.613.8.......7.........2....98
B9B
.2345...945.......7.9.23...23..95.....5.4.2..9.4..7...3..............817....7..6.
.2345...945.......7.9.23...23..95.....5.4.2..9.4..7...3.7............81.....7..6.
.2345...945.7.....7.9.23...23..95....75.4.2..9.4......3..............817....7..6.
.2345...945.7.....7.9.23...23..95....75.4.2..9.4......3.7............81.....7..6.
.2345...945.7.....7.9.23...23..95.....5.4.2..9.4..7...3.7............817.......6.
.2.4...8....18...6....23.41...36....5......6.79..........8.4......61..23..1.328.4
.2.4.6.8....18........23.41...3.....5......6.796.........8.46.....61..23..1.328.4
.2.4...8....18...6....23.41...36....5........796.........8.46.....61..23..1.328.4
.2.4.6.8....18...6....23.41...3.....5........796.........8.46.....61..23..1.328.4
.2.4.6.8....18........23.41...36....5......6.79..........8.46.....61..23..1.328.4
.2.4.6.8....18...6....23.41...3.....5......6.796.........8.4......61..23..1.328.4
1...567.9.....9.3.6..37.15.....176.3........5.1.5.39..........7..89......42......
....567.9...1.9.3.6..37.15......76.3.......15.1.5.39....1.....7..89......42......
....567.9...1.9.3.6..37.15.....176.3........5.1.5.39....1.....7..89......42......
....567.9...1.9.3.6..37.15.....176.3.......15...5.39....1.....7..89......42......
1...567.9.....9.3.6..37.15.....176.3.......15...5.39....1.....7..89......42......
1...567.9...1.9.3.6..37.15......76.3.......15.1.5.39..........7..89......42......
.....6.89.5.1.92.6......15...851.9.....9.8.21....62..53..2...........6..74.......
....56.89.5.1.92.6......1....851.9.....9.8.21....62..53..2...........6..74.......
......7.94.7...23...9..2.41..16.............3...8.5...31.....2.7.4...19..92.7...4
1.....7.94.7...23...9..2.41..16.............3...8.5...3......2.7.4...19..92.7...4
...4..7.....18.2.6.8..27.1.2......4.3...6....9.5.........6...78...81.4.2..2.7.1..
.2.4..7.....18.2.6.8..27.1........4.3...6....9.5.........6...78...81.4.2..2.7.1..
...4.67.....18.2.6.8..27.1.2......4.3...6....9.5.............78...81.4.2..2.7.16.
.2.4.67.....18.2.6.8..27.1........4.3...6....9.5.............78...81.4.2..2.7.16.
.2.4..7.....18.2.6.8..27.1........4.3...6....9.5.........6.2.78...81.4.28...7.1..
.2.4..7.....18.2.6.8..27.1.2......4.3...6....9.5.........6.2.78...81.4.2....7.1..
.2.4.67.....18.2.6.8..27.1........4.3...6....9.5...........2.78...81.4.28...7.16.
.2.4.67.....18.2.6.8..27.1.2......4.3...6....9.5...........2.78...81.4.2....7.16.
1.3.5.7...57....36.9.....1...13...7..6....1.5.75....93..6..2........39.....8.4...
1.3.5.7...57....36.9..3..1...13...7..6....1.5.75....93..6..2.........9.....8.4...
1.3.5.7...57....36.9..3..1...1....7.36....1.5.75....93..6..2........39.....8.4...
1.3.5.7...57....3669.....1...13..67.......1.5.75....93..6..2........39.....8.4...
1.3.5.7...57....36.9..3..1...1..5.7.36....1.5.75....93..6..2.........9.....8.4...
1.3.5.7...57....3669..3..1...13..67.......1.5.75....93..6..2.........9.....8.4...
1.3.5.7...57....3669..3..1...1...67.3.....1.5.75....93..6..2........39.....8.4...
1.3.5.7...57....3669..3..1...1..567.3.....1.5.75....93..6..2.........9.....8.4...
1...56..9.571.9...6.972....2.....34.7.....8.....2........5.....5.2.17.6..619.2...
12..56..9.571.9...6.972..........34.7.....8.....2........5.....5.2.17.6..619.2...
1...56..9.571.9...6.972....2.....34.7.....8.....2........56....5.2.17.6...19.2...
12..56..9.571.9...6.972..........34.7.....8.....2........56....5.2.17.6...19.2...
1.3...7.9.5.....3.69..7.15..165..39.53.......7.9...6.......2.6...1.........8.4.1.
1.3...7.9.5.....3.69..7.15..165..39.53......17.9...6.......2.6...1.........8.4...
1.3...7.9.5.....3.69..7.1...165..39.53.......7.9...6.5.....2.6...1..5......8.4.1.
1.3.5.7.9..7....3.69..7.1...16...39.53.......7.9...6.5.....2.6...1..5......8.4.1.
1.3.5.7.9.5.....3.69..7.1...16...39.53.......7.9...6.5.....2.6...1..5......8.4.1.
1.3.5.7.9..7....3.69..7.1...165..39.53.......7.9...6.5.....2.6...1.........8.4.1.
1.3.5.7.9.5.....3.69..7.1...165..39.53.......7.9...6.5.....2.6...1.........8.4.1.
1.3.5.7.9..7....3.69..7.15..165..39.53.......7.9...6.......2.6...1.........8.4.1.
1.3...7.9.5.....3.69..7.1...165..39.53......17.9...6.5.....2.6...1..5......8.4...
1.3.5.7.9..7....3.69..7.1...16...39.53......17.9...6.5.....2.6...1..5......8.4...
1.3.5.7.9.5.....3.69..7.1...16...39.53......17.9...6.5.....2.6...1..5......8.4...
1.3.5.7.9..7....3.69..7.1...165..39.53......17.9...6.5.....2.6...1.........8.4...
1.3.5.7.9.5.....3.69..7.1...165..39.53......17.9...6.5.....2.6...1.........8.4...
1.3.5.7.9..7....3.69..7.15..165..39.53......17.9...6.......2.6...1.........8.4...
1.3.5.7.9.......36.9..7.15.....38...3.6.........2.4...5.9....677.....91..61...5..
1.3.5.7.9.......36.9..7.15.....386..3...........264...5.9.....77.....91..61...5..
1.3.5.7.9.......36.9..7.15.....386..3.6.........2.4...5.9.....77.....91..61...5..
1.3.5.7.9.......3.69..7.15.....386..3...........264...5.9.....773....91..61...5..
1.3.5.7.9.......3.69..7.15.....386..3.6.........2.4...5.9.....773....91..61...5..
1.3.5.7.9.......3.69..7.15.....386..3...........264...5.9....677.....91..61...5..
1.3.5.7.9.......3.69..7.15.....386..3.6.........2.4...5.9....677.....91..61...5..
1.3.5.7.9.......3.69..7.15.....386..3.6.........2.4...5.9....6773....91...1...5..
1.3.5.7.9.......3669..7.15.....38...3.6.........2.4...5.9....6773....91...1...5..
1...56..9.571.....69.73.........7.4..3.............82.3.6.95...57...16...19......
1...56..9.571.9...6..73.........7.4..3.............82.3.6.95...57...16...19......
1...56....5718..3.68.7.3....3587......63.1....1...5..8......4.....6.7.........962
1...56....5718..3.68.7.3....3587.......3.1....1..65..8.6....4.......7.........962
1...56....5718..3.68.7.3....3587.......3.1....1..65..8.6....4.....6.7.........9.2
1...56....5718..3.68.7.3....3587......63.1....1...5..8.6....4.....6.7.........9.2
1..4....9.....923.....73.14..67............728.5..........4.9...3.9.214....31..27
1.34....9.....923.....7..14..67............728.5..........4.9...3.9.214....31..27
1..4....9...1.923.....73..4..67............728.5..........4.9...3.9.214....31..27
1.34....9...1.923.....7...4..67............728.5..........4.9...3.9.214....31..27
1..4....9.....923.....73.14..67............728.5..........4.9.3.3.9.214.....1..27
1.34....9.....92......73.14..67............728.5..........4.9.3.3.9.214.....1..27
1..4....9...1.923.....73..4..67............728.5..........4.9.3.3.9.214.....1..27
1.34....9...1.92......73..4..67............728.5..........4.9.3.3.9.214.....1..27
1..4....9.....923.....73.14..6.............72875..........479...3.9.214....31..27
1.34....9.....923.....7..14..6.............72875..........479...3.9.214....31..27
1..4....9...1.923.....73..4..6.............72875..........479...3.9.214....31..27
1.34....9...1.923.....7...4..6.............72875..........479...3.9.214....31..27
1..4..7.9.....923.....73.14..67.............2875..........4.9...3.9.214....31..27
1.34..7.9.....923.....7..14..67.............2875..........4.9...3.9.214....31..27
1..4..7.9...1.923.....73..4..67.............2875..........4.9...3.9.214....31..27
1.34..7.9...1.923.....7...4..67.............2875..........4.9...3.9.214....31..27
1..4....9.....923.....73.14..6.............72875..........479.3.3.9.214.....1..27
1.34....9.....92......73.14..6.............72875..........479.3.3.9.214.....1..27
1..4....9...1.923.....73..4..6.............72875..........479.3.3.9.214.....1..27
1.34....9...1.92......73..4..6.............72875..........479.3.3.9.214.....1..27
1..4..7.9.....923.....73.14..67.............2875..........4.9.3.3.9.214.....1..27
1.34..7.9.....92......73.14..67.............2875..........4.9.3.3.9.214.....1..27
1..4..7.9...1.923.....73..4..67.............2875..........4.9.3.3.9.214.....1..27
1.34..7.9...1.92......73..4..67.............2875..........4.9.3.3.9.214.....1..27
1..4....9.....923.....73.14..6.............2.875..........479...3.9.214....31..7.
1.34....9.....923.....7..14..6.............2.875..........479...3.9.214....31..7.
1..4....9...1.923.....73..4..6.............2.875..........479...3.9.214....31..7.
1.34....9...1.923.....7...4..6.............2.875..........479...3.9.214....31..7.
1..4....9.....923.....73.14..67............2.875..........4.9...3.9.214....31..7.
1.34....9.....923.....7..14..67............2.875..........4.9...3.9.214....31..7.
1..4....9...1.923.....73..4..67............2.875..........4.9...3.9.214....31..7.
1.34....9...1.923.....7...4..67............2.875..........4.9...3.9.214....31..7.
1..4....9.....923.....73.14..67............278.5..........4.9...3.9.214....31..7.
1.34....9.....923.....7..14..67............278.5..........4.9...3.9.214....31..7.
1..4....9...1.923.....73..4..67............278.5..........4.9...3.9.214....31..7.
1.34....9...1.923.....7...4..67............278.5..........4.9...3.9.214....31..7.
1..4....9.....923.....73.14..6.............2.875..........479.3.3.9.214.....1..7.
1.34....9.....92......73.14..6.............2.875..........479.3.3.9.214.....1..7.
1..4....9...1.923.....73..4..6.............2.875..........479.3.3.9.214.....1..7.
1.34....9...1.92......73..4..6.............2.875..........479.3.3.9.214.....1..7.
1..4....9.....923.....73.14..67............2.875..........4.9.3.3.9.214.....1..7.
1.34....9.....92......73.14..67............2.875..........4.9.3.3.9.214.....1..7.
1..4....9...1.923.....73..4..67............2.875..........4.9.3.3.9.214.....1..7.
1.34....9...1.92......73..4..67............2.875..........4.9.3.3.9.214.....1..7.
1..4....9.....923.....73.14..67............278.5..........4.9.3.3.9.214.....1..7.
1.34....9.....92......73.14..67............278.5..........4.9.3.3.9.214.....1..7.
1..4....9...1.923.....73..4..67............278.5..........4.9.3.3.9.214.....1..7.
1.34....9...1.92......73..4..67............278.5..........4.9.3.3.9.214.....1..7.
1..4..7.9.....923.....73.14..6.............27875..........479...3.9.214....31....
1.34..7.9.....923.....7..14..6.............27875..........479...3.9.214....31....
1..4..7.9...1.923.....73..4..6.............27875..........479...3.9.214....31....
1.34..7.9...1.923.....7...4..6.............27875..........479...3.9.214....31....
1..4..7.9.....923.....73.14..67............2.875..........479...3.9.214....31....
1.34..7.9.....923.....7..14..67............2.875..........479...3.9.214....31....
1..4..7.9...1.923.....73..4..67............2.875..........479...3.9.214....31....
1.34..7.9...1.923.....7...4..67............2.875..........479...3.9.214....31....
1..4..7.9.....923.....73.14..67............278.5..........479...3.9.214....31....
1.34..7.9.....923.....7..14..67............278.5..........479...3.9.214....31....
1..4..7.9...1.923.....73..4..67............278.5..........479...3.9.214....31....
1.34..7.9...1.923.....7...4..67............278.5..........479...3.9.214....31....
1..4..7.9.....923.....73.14..6.............27875..........479.3.3.9.214.....1....
1.34..7.9.....92......73.14..6.............27875..........479.3.3.9.214.....1....
1..4..7.9...1.923.....73..4..6.............27875..........479.3.3.9.214.....1....
1.34..7.9...1.92......73..4..6.............27875..........479.3.3.9.214.....1....
1..4..7.9.....923.....73.14..67............2.875..........479.3.3.9.214.....1....
1.34..7.9.....92......73.14..67............2.875..........479.3.3.9.214.....1....
1..4..7.9...1.923.....73..4..67............2.875..........479.3.3.9.214.....1....
1.34..7.9...1.92......73..4..67............2.875..........479.3.3.9.214.....1....
1..4..7.9.....923.....73.14..67............278.5..........479.3.3.9.214.....1....
1.34..7.9.....92......73.14..67............278.5..........479.3.3.9.214.....1....
1..4..7.9...1.923.....73..4..67............278.5..........479.3.3.9.214.....1....
1.34..7.9...1.92......73..4..67............278.5..........479.3.3.9.214.....1....
1...5.7.9...1.9.3.6..37.15....96..1....7.539.......6.5.48........6....7...2..3...
1...5.7.9...1.9.3.6..37.15....96..1..6.7.539.......6.5.48.............7...2..3...
1...567.9...1.9.3.6..37.15....9...1..6.7.539.......6.5.48.............7...2..3...
1...5.7.9...1.9.36...37.15....96..1..6.7.539.......6.5.48........6....7...2..3...
1...567.9...1.9.36...37.15....9...1..6.7.539.......6.5.48........6....7...2..3...
..3.56....571...3.96.73..5..1539....6.9..15...7.6.......1...4.....9.73..........8
1.3.56....571...3.96.73..5...539....6.9..15...7.6.......1...4.....9.73..........8
.2.45........89.......3..4.2.4...36..31....7.67....1.23.7...62..12...4.7.6.....13
.2..........78........32.6..9....45.6.4..5.91.1....2.6.41......5.2...91.96.5...4.
.2..........78........32.6..9....4..6.4..5.91.15...2.6.41.....55.2...91.96.5...4.
.2..5.......78........32.6..9....45.6.4....91.15...2.6.41......5.2...91.96.5...4.
.2..5.......78........32.6..9....4..6.4..5.91.15...2.6.41.....55.2...91.96.....4.
.2..5.......78........32.6..9....45.6.4..5.91.1....2.6.41.....55.2...91.96.....4.
..3..678....18..36...7..5.12.5....1.3..5.....94............1..87..8.516....63..75
..3.5678....18..36...7..5.12.5....1.3........94............1..87..8.516....63..75
..3.5678....18..36...7..5.12.5....1.3..5.....94............1..87..8..16....63..75
..3..678....18..36...7..5.12.5....1.3..5.....94...........71..87..8.516....63...5
..3.5678....18..36...7..5.12.5....1.3........94...........71..87..8.516....63...5
..3.5678....18..36...7..5.12.5....1.3..5.....94...........71..87..8..16....63...5
..3..678....18..36...7..5.12.5....1.3..5.....94.....5......1..87..8.516....63..7.
..3.5678....18..36...7..5.12.5....1.3........94.....5......1..87..8.516....63..7.
..3..678....18..36...7..5.12.5....1.3..5.....94.....5.....71..87..8.516....63....
..3.5678....18..36...7..5.12.5....1.3........94.....5.....71..87..8.516....63....
..3..678...718..36.....35.12.5....1.3..5.....94...........71..8...8.516....63..75
..3..678...718..36...7..5.12.5....1.3..5.....94...........71..8...8.516....63..75
..3.5678...718..36.....35.12.5....1.3........94...........71..8...8.516....63..75
..3.5678...718..36...7..5.12.5....1.3........94...........71..8...8.516....63..75
..3.5678...718..36.....35.12.5....1.3..5.....94...........71..8...8..16....63..75
..3.5678...718..36...7..5.12.5....1.3..5.....94...........71..8...8..16....63..75
..3..678...718..36.....35.12.5....1.3..5.....94...........71..87..8.516....63...5
..3.5678...718..36.....35.12.5....1.3........94...........71..87..8.516....63...5
..3.5678...718..36.....35.12.5....1.3..5.....94...........71..87..8..16....63...5
..3..678...718..36.....35.12.5....1.3..5.....94.....5.....71..8...8.516....63..7.
..3..678...718..36...7..5.12.5....1.3..5.....94.....5.....71..8...8.516....63..7.
..3.5678...718..36.....35.12.5....1.3........94.....5.....71..8...8.516....63..7.
..3.5678...718..36...7..5.12.5....1.3........94.....5.....71..8...8.516....63..7.
..3..678...718..36.....35.12.5....1.3..5.....94.....5.....71..87..8.516....63....
..3.5678...718..36.....35.12.5....1.3........94.....5.....71..87..8.516....63....
1.3..67...5..8....68.3.7..........5.....6..92....1..4...8......73.5.1....61.38..5
1.3..67...5..8....68.3.75...............6..92....1..4...8......73.5.1....61.38..5
1.3.567...5..8....68.3.7................6..92....1..4...8......73.5.1....61.38..5
1.3.567...5..8....68.3.7................6..92....1..4.5.8......73...1....61.38..5
1.3..67...5..8....68.3.7.....6....5........92....1..4...86.....73.5.1.....1.38..5
1.3..67...5..8....68.3.75....6.............92....1..4...86.....73.5.1.....1.38..5
1.3.567...5..8....68.3.7.....6.............92....1..4...86.....73.5.1.....1.38..5
1.3.567...5..8....68.3.7.....6.............92....1..4.5.86.....73...1.....1.38..5
1.3..67....7.8....68.3.75...............6..92....1..4.5.8......73.5.1....61.38..5
1.3.567....7.8....68.3.75...............6..92....1..4.5.8......73...1....61.38..5
1.3..67....7.8....68.3.75....6.............92....1..4.5.86.....73.5.1.....1.38..5
1.3.567....7.8....68.3.75....6.............92....1..4.5.86.....73...1.....1.38..5
1.3..67....7.8....68.3.75.........5.....6..92....1..4.5.8......73.5.1....61.38...
1.3..67...5..8....68.3.75.........5.....6..92....1..4.5.8......73.5.1....61.38...
1.3..67....7.8....68.3.75....6....5........92....1..4.5.86.....73.5.1.....1.38...
1.3..67...5..8....68.3.75....6....5........92....1..4.5.86.....73.5.1.....1.38...
1.3..6.8..57......68...31.5......5.7....97......24....3.......1.65...3.88.1...67.
1.3..6.8..57......68...31.5........7....97......245...3......51.65...3.88.1...67.
1.3..6.8..57......68...31.5........75...97......245...3......51.6....3.88.1...67.
1.3..6.8..57......68...31.5......5.75...97......24....3......51.6....3.88.1...67.
1.3..678..57......68...31.5........7....97......245...3......51.65...3.88.1...6..
1.3..678..57......68...31.5......5.7....97......24....3......51.65...3.88.1...6..
1.3..678..57......68...31.5........75...97......245...3......51.6....3.88.1...6..
1.3..678..57......68...31.5......5.75...97......24....3......51.6....3.88.1...6..
1.3.5.78...7...2.3.......15......87....94....8..6.....3.2...1..51...2.37.78...52.
1.3.5.78...7...2.3.8.....1.......87....94....8..6.....3.2...1..51...2.37.78...52.
1.3.5.78..57...2.3.......1.......87....94....8..6.....3.2...1..51...2.37.78...52.
1.3.5.78...7...2.3.8.....1.......87....948......6.....3.2...1..51...2.37.78...52.
1.3.5.78...7...2.3.8.....1.......87.7..94.......6.....3.2...1..51...2.37.78...52.
1.3.5.78...7...2.3.......15.......7....948...8..6.....3.2...1.851...2.3..78...52.
1.3.5.78...7...2.3.8.....1........7....948...8..6.....3.2...1.851...2.3..78...52.
1.3.5.78..57...2.3.......1........7....948...8..6.....3.2...1.851...2.3..78...52.
1.3.5.78...7...2.3.......15......87....94....8..6.....3.2...1.851...2.3..78...52.
1.3.5.78...7...2.3.8.....1.......87....94....8..6.....3.2...1.851...2.3..78...52.
1.3.5.78..57...2.3.......1.......87....94....8..6.....3.2...1.851...2.3..78...52.
1.3.5.78...7...2.3.8.....1.......87....948......6.....3.2...1.851...2.3..78...52.
1.3.5.78...7...2.3.8.....1.......87.7..94.......6.....3.2...1.851...2.3..78...52.
1.....7...57....6368.3..5...36....1.51....3.77.8..1..6....92.....5.1........4...8
1.3...7...57....6.68.3..5...36....1.51....3.77.8..1..6....92.....5.1........4...8
..3...7...571...6.68.3..5.1.36....1.51....3.77.8.....6....92.....5.1........4...8
1.....7...571...6368.3..5...36....1.51....3.77.8.....6....92.....5.1........4...8
1.3...7...571...6.68.3..5...36....1.51....3.77.8.....6....92.....5.1........4...8
..3...7...571...6.68.3..5.1.36....1.51....3.77.8..1..6....92.....5..........4...8
1.....7...571...6368.3..5...36....1.51....3.77.8..1..6....92.....5..........4...8
1.3...7...571...6.68.3..5...36....1.51....3.77.8..1..6....92.....5..........4...8
..3...7...571...6.68.3..5.1.36...8..51....3.77.8..1..6....92.....5..........4...8
..3...78..571...6.68.3..5.1.36......51....3.77.8..1..6....92.....5..........4...8
..3...7...571...6.68.3..5.1.36....1.51....3.77.8.3...6....92.....5..........4...8
1.....7...571...6368.3..5...36....1.51....3.77.8.3...6....92.....5..........4...8
1.3...7...571...6.68.3..5...36....1.51....3.77.8.3...6....92.....5..........4...8
1.....7...57....6368.3..5.1.36...8..51....3.77.8..1..6....92.....5.1........4...8
1.3...7...57....6.68.3..5.1.36...8..51....3.77.8..1..6....92.....5.1........4...8
1.....78..57....6368.3..5.1.36......51....3.77.8..1..6....92.....5.1........4...8
1.3...78..57....6.68.3..5.1.36......51....3.77.8..1..6....92.....5.1........4...8
1.....7...571...6368.3..5.1.36...8..51....3.77.8..1..6....92.....5..........4...8
1.....78..571...6368.3..5.1.36......51....3.77.8..1..6....92.....5..........4...8
1...567.9.....9...6..72..51.38...........5....4......2....67.2...19.2..7...51..96
1...567.9.....92..6..72..51.38...........5....4......2....67.....19.2..7...51..96
....567.9...1.9...6..72..5..38.......1...5....4......2....6712...19.2..7...51..96
1...567.9...1.9...6..72..5..38...........5....4......2....6712...19.2..7...51..96
....567.9...1.9...6..72..51.38.......1...5....4......2....67.2...19.2..7...51..96
....567.9...1.9.6.6..72..5..38.......1...5....4......2....671....19.2..7...51..96
....567.9...1.92..6..72..5..38.......1...5....4......2....671....19.2..7...51..96
1...567.9.....9.6.6..72..51.38...........5....4......2....671....19.2..7...51..96
1...567.9...1.9.6.6..72..5..38...........5....4......2....671....19.2..7...51..96
1...567.9...1.92..6..72..5..38...........5....4......2....671....19.2..7...51..96
....567.9...1.92..6..72..51.38.......1...5....4......2....67.....19.2..7...51..96
1...567.9.....9...6..72..51.38...........5....4......2....6712..6.9.2..7...51..96
1...567.9...1.9...6..72..5..38...........5....4......2....6712..6.9.2..7...51..96
1...567.9.....9.6.6..72..51.38...........5....4......2....671...6.9.2..7...51..96
1...567.9.....92..6..72..51.38...........5....4......2....671...6.9.2..7...51..96
1...567.9...1.9.6.6..72..5..38...........5....4......2....671...6.9.2..7...51..96
1...567.9...1.92..6..72..5..38...........5....4......2....671...6.9.2..7...51..96
1...567.9.....9...6..72..51.38.......1...5....4......2....6712....9.2..7...51..96
1...567.9...1.9...6..72..5..38.......1...5....4......2....6712....9.2..7...51..96
1...567.9.....9.6.6..72..51.38.......1...5....4......2....671.....9.2..7...51..96
1...567.9.....92..6..72..51.38.......1...5....4......2....671.....9.2..7...51..96
1...567.9...1.9.6.6..72..5..38.......1...5....4......2....671.....9.2..7...51..96
1...567.9...1.92..6..72..5..38.......1...5....4......2....671.....9.2..7...51..96

The B8B max expands reduce to 59 minimal puzzles

Hidden Text: Show

Code: Select all

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
1..4.6.8....18.2..6...27.4......8.67....4.82....6..1...61...47..952..............
1..4.6.8....18.2.6....27.4......8.67..6.4.82....6..1...61...47..952..............
1...5...945....13..89.....4..4....938....34.1.3....85..1.6.7...............3.59.8
1...5...945....13..89.3...4..4....938.....4.1.3....85..1.6.7...............3.59.8
1.3.5...945....1...89.3...4..4....938.....4.1.3....85..1.6.7...............3.59.8
1...5..8945....13..89.....4..4....938....34.1.3....85..1.6.7...............3.59..
1...5..8945....13..89.3...4..4....938.....4.1.3....85..1.6.7...............3.59..
1.3.5..8945....1...89.3...4..4....938.....4.1.3....85..1.6.7...............3.59..
..3.56......18....68.7.3.1..36..8...7.5.3...881.67...........7457..............52
..3.56.8....1.....68.7.3.1..36..8...7.5.3...881.67...........7457..............52
..3.56.....718....68.7.3.1..36..8...7.5.3...881.67...........745.............7.52
..3.56.8...71.....68.7.3.1..36..8...7.5.3...881.67...........745.............7.52
12.....89.5..8..3...8...1.52.59...18.31...5..98....3.2...27...........23...34....
12.....89.5..8..3...8...1.52.59...18.318..5..9.....3.2...27...........23...34....
12.....89.5..8.23...8...1.52.59...18.31...5..98....3.2...27............3..234....
12.....89.5..8.23...8...1.52.59...18.318..5..9.....3.2...27............3..234....
1...56.......892...........27.6..51.3.5.....7.165...235.2...36.73......2.61....7.
12..56.......892............7.6..51.3.5.....7.165...235.2...36.73......2.61....7.
12..56.......892...........27.6..51.3.5.....7.165...235.....36.73......2.61....7.
1...56.......892...........27....51.3.5...6.7.165...235.2...36.73..6...2.61....7.
12..56.......892............7....51.3.5...6.7.165...235.2...36.73..6...2.61....7.
12..56.......892...........27....51.3.5...6.7.165...235.....36.73..6...2.61....7.
1...56.......892...........27.6..51.3.5.....7.6.5...235.2...36.73......2.16....7.
12..56.......892............7.6..51.3.5.....7.6.5...235.2...36.73......2.16....7.
12..56.......892...........27.6..51.3.5.....7.6.5...235.....36.73......2.16....7.
1...56.......892...........27....51.3.5...6.7.6.5...235.2...36.73..6...2.16....7.
12..56.......892............7....51.3.5...6.7.6.5...235.2...36.73..6...2.16....7.
12..56.......892...........27....51.3.5...6.7.6.5...235.....36.73..6...2.16....7.
.2..5..89...18.23......25.1...8.531.3...91.25...32..........89.86.......94.......
.2..5..89...18.23......25.12..8.531.3...91..5...32..........89.86.......94.......
.2..5..89...18.23......25.12..8.531.3...91.25...3...........89.86.......94.......
.2..5..89...18.23......25.1...8.531.3...91.25...32...8.......9.86.......94...8...
.2..5..89...18.23......25.12..8.531.3...91..5...32...8.......9.86.......94...8...
.2..5..89...18.23......25.12..8.531.3...91.25...3....8.......9.86.......94...8...
12....7..4.7.....6..9...41.2.6.7..4..1..9..67....4.1.2....65.9.6.2.1.........8...
12....7..4.7.....6.69...41.2.6.7..4..1..9..67....4.1.2....65.9...2.1.........8...
12....7.94.7.......69...41.2.6.7..4..1..9..67....4.1.2....65.9...2.1.........86..
12....7..4.7.....6..9...41.2.4.7..6..16.9...7....4.1.2....65.9.6.2.1.........8...
12....7..4.7.....6.69...41.2.4.7..6..16.9...7....4.1.2....65.9...2.1.........8...
12....7.94.7.......69...41.2.4.7..6..16.9...7....4.1.2....65.9...2.1.........86..
1.3..6....57......69.....1..1.5...93..9...67.73..9.1..............9.1357...82....
1.3..6....57......69.....1..1.5...935.....67.73..9.1..............9.1357...82....
1.3..6....57..9...69.....1..1.5...93..9...67.73....1..............9.1357...82....
1.3..6..9.57..9...6......1..1.5...93..9...67.73....1..............9.1357...82....
1.3...78945...................37..6...6.98.71...6.1..3.....739....91.6..8....3.1.
1.3...78945..................137..6...6.98.71...6....3.....739....91.6..8....3.1.
1.3...78945...................37..6...6.98.71...6.1..3.1...739....9..6..8....3.1.
1.3...78945..................637........98......6.1..3.1...739....9..6..8....3.71
1.3...78945..................637......1.98......6.1..3.....739....91.6..8....3.71
1.3...78945..................637..1...1.98......6....3.....739....91.6..8....3.71
1.3...78945...................37..6...6.98.1....6.1..3.....739....91.6..8....3.71
1.3...78945..................137..6...6.98.1....6....3.....739....91.6..8....3.71
1.3...78945...................37..6...6.98.1....6.1..3.1...739....9..6..8....3.71

And to complete
Here is the B7B expands from the files, which reduce to 547 minimal puzzles
Top of the list presumably are the 3 B7B puzzles found a long time ago
Sorted by -q2 which just about sorts the twin puzzles conveniently

Hidden Text: Show

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.....6.....718........2...5..85....13.....9...6.....4...2.7...8.4.....6.9.....3.. # 97868 FNBP C20.m/M2.3.63423
..3..6....5.18....6....2...2...6...4......9...7.8...1.....1.89...4.....3.9..7.45. # 97723 FNBP C23/M2.6.9837
.2...67..4...8......9.......3.....7.5.8...34..1.3....2....9..5....6.1..3...2..6.7 # 97625 FNBP C23/M2.7.5622
.23..6..945.....366.9...5..23...........37.......283..36..4.95..45.9.6.29.2....43 # 97050 FNBP C32/M2.11.1788 # twins8
.2..5..89...18.2.3.....251....89.35.3...25.915..3.18.2......9.886.......94...8... # 97005 FNBP C32/M2.11.1788
1.3.5.78..57.8..3686....1.5...96.......21..6..16......38.....7.6.17..8...75...6.3 # 97003 FNBP C32/M2.11.1788
1.3.5.78..57.8.3.668.....15...96.......21.6...16......37....8..8.17...6..65....73 # 97003 FNBP C32/M2.11.1788
12.....89.5..8.23...8...1.52.15...98.859..31.93....5.2...27...........23..234.... # 96997 FNBP C32/M2.11.1788
12.....89.5..8.23...8...1.52.59...18.815..39.93....5.2...27...........23..234.... # 96997 FNBP C32/M2.11.1788
1..45.7.94..7.913.....13.54....719.....94..75..73.5.1.3.8...5..5.2.........53.... # 96994 FNBP C32/M2.11.1788
12..56.8..5718..6.6.82.7...21.7....8.85.2....7.6.18...57....8.6..............13.4 # 96976 FNBP C32/M2.11.1788
12....78..571..2.66.827..15....4........9.8.......1...5.2..7..878...562..61....57 # 86762 FNBP C32/M2.40.328 # twins2
12.....89.5.1..2.66.82..15....9..........4.....5..7....86.9..125.2...96.91..628.5 # 84280 FNBP C32/M2.40.328
...45.7.9..71.92....9.72.51.4.79.51.71.2.59.4....41.723..........4......8......2. # 50786 FNBP C32/M2.50.262
1.3..678..57....3686...31.5....683.75..9.7......2.....3......616.531.87....6..5.3 # 13845 FNBP C34/M2.80.82 # twins16
..3.567.9..71.9.36...37.51..85..1...3.6....57.4............739..3.....7197..136.5 # 13589 FNBP C34/M2.80.82
1...567.9...1.9.366..37.51..7196.35...6...9.1....1..673.4.9....56....1.3..2...... # 13582 FNBP C34/M2.80.82
..3.5678...718..36...3.75.1..1...6..7.5.31...94....31....81.......7.38..8...651.3 # 13487 FNBP C34/M2.80.82
..3.5678...718..36...7.35.1..1...6..7.5.31...94....31....81.......3.78..8...651.3 # 13487 FNBP C34/M2.80.82
..3.567.9..71.9.36...37.51.2.........79.13...8.1.....536.9.1.577...35......76...3 # 13224 FNBP C34/M2.80.82
..3.567.9..71.9.36...73.51.2.........79.13...8.1.....53...75...76.9.1.53...36...7 # 13224 FNBP C34/M2.80.82
1.3....89.57.89...8...2..........84...489..12....4.9.33..2.849....91.3.89...34.21 # 13222 FNBP C34/M2.80.82
12.4.67..4.718.2...68.27...28.6.1.47...87...27...42......26.17.........38.....6.5 # 13217 FNBP C34/M2.80.82
12.4.6...4.718...6.68.27..42.6...4.1...26.95....7....2.82......64.8.....7.16.28.. # 13215 FNBP C34/M2.80.82
...4.6...4...89...68.37..4..786.49..3.479.8..96..38......86.39.7.....6..8.6....15 # 13210 FNBP C34/M2.80.82
...4.6...4...89...68.37..4..786.49..36..98...9.473.8.....86.39.7.....6..8.6....15 # 13210 FNBP C34/M2.80.82
...4.6...4...89...68.73..4..786.49..36..98...9.437.8.....86.39.7.....6..8.6....15 # 13210 FNBP C34/M2.80.82
12.4.6.8.4.718.....68.72.1.24.7.86.1.71.....88.6..1....14...82......7.43........5 # 13208 FNBP C34/M2.80.82
12...67.9.57..926.6.9....512......96......52.9.5.2.1.759.83....7....5.......619.5 # 12853 FNBP C34/M2.80.82
1.3...7.9.571...3669.7..51...5...1.7......95.9.1..5.63.19.24......3.7.91..69..... # 12851 FNBP C34/M2.80.82
..3.567.9..71.9.36..637.15.241..7.....9..1...63....9173..7.5.91......5.3.....367. #  1911 FNBP C36/M1.1.64 # twins4
1..4.678.4..18..366...731.4.167.8.43......6.7...6..81.3.58.....8.2.......41...368 #  1911 FNBP C36/M1.1.64
12..567...571.92..6.972.1..26........7569..129.12.....592....71......9.4...9..5.3 #  1911 FNBP C36/M1.1.64
12..56..9.571.9..66.927...126.5.719..95..1...7.1......512...96.......3.5.....58.2 #  1900 FNBP C36/M1.1.64
.23.56......18.23......24..29.......3.5...9...46.9.3.253.....24.64..359.9.2..56.3 #  1434 FNBP C34/M1.1.40 # twins5
.23.56......18.23......24..29.......3.5...9...64.9.3.253.....24.46..359.9.2..56.3 #  1434 FNBP C34/M1.1.40
.23.56......18.23......34..2.5...9..39........46.9.3.253.....24.64..259.9.2..56.3 #  1434 FNBP C34/M1.1.40
.23.56......18.23......34..2.5...9..39........64.9.3.253.....24.42..569.9.6..25.3 #  1434 FNBP C34/M1.1.40
.23.56......18.23......34..2.5...9..39........64.9.3.253.....24.46..259.9.2..56.3 #  1434 FNBP C34/M1.1.40
....5678....18..366..3.71.5...56..73...7.851..7..316....2......8.4...3.....81.... #  1270 FNBP C31/M1.2.36 # twins3
...4.6.....7....36.......5.24.6.7...7.8.14..2.6182......274.1...14.68...87.2.1... #  1270 FNBP C31/M1.2.36
1.3.567...5718....68.3.7......81....5.....8.2........431..68...7..5.1.6..6573.... #  1270 FNBP C31/M1.2.36
12..56....571.9..66.927...127.69.....917.5.....6.12.9.......8.2...52......2...3.5 #  1070 FNBP C33/M1.1.39 # twins6
12..56....571.9..66.927...127.96.....917.5.....6.12.9.......3.2...52......2...8.5 #  1070 FNBP C33/M1.1.39
12..56....571.9..66.927...129.76.....719.5.....6.12.9.......3.2...52......2...8.5 #  1070 FNBP C33/M1.1.39
.23....894...8.2.398....14.2..7.1......6.2..........2139...481..14...3.28.2..3.94 #  1070 FNBP C33/M1.1.39
1.3...78..57.8..3668..3.5.1.......17.7..14.......72...56....1.37.8....65.3.5..87. #  1070 FNBP C33/M1.1.39
12..567...5718.2..6.87.2...21..6....7.582.....865.1..2.....8..........93.61....27 #  1070 FNBP C33/M1.1.39
..3.567.9..71.9.63...73.15..3.51.69.....93......6.73.........1..7..6....84....5.. #   603 FNBP C30/M2.77.85

These groupings, minimizing and twinning all performed with gridchecker by dobrichev

[denis_berthier]

.
Happy New Year and best wishes to all

Regarding the way "harderst" puzzles are published, there are three points. They have already been discussed in different places, but some summary may be useful.

1) min-expands (i.e. expansions of minimals by Singles):
This has been discussed long ago with mith in the context of the search for T&E(3) puzzles, but this applies indeed to any puzzles after using expansion has become a standard in the search techniques for the hardest puzzles: one needs to have both minimals and min-expands.
min-expands are essential in the search itself and in how results can be used; they avoid lots of redundancy; just as an example, there are 847,778 minimal puzzles in mith's latest release of T&E(3) puzzles, but only 158,276 min-expands, i.e. 5.36 times fewer.
As another example, Hendrik has found 16 minimals in B13B, but they make only 1 min-expand.
For any player but the most novice ones, two puzzles with the same min-expand are the same puzzle for all practical purposes.

2) solution (min or max)-lex:
With mith, we had come to the conclusion that using the solution in the lexical ordering was the right thing to do, because it made it much simpler to compare various puzzles.
Coloin's argument that using solution-(min or max)lex will be bad for human solvers is not convincing: if anyone wants to propose a puzzle for solution, he can always shuffle it before posting it; that doesn't even require any software.

3) (min or max)-lex:
minlex or maxlex is an arbitrary choice.
However, with mith, we had also come to the conclusion of using minlex (i.e. finally solution-minlex). Because all of mith's puzzles are published in this format and because he has the largest database as of now, I think we should stick to this.

(I don't have any software able to produce solution-minlex forms, but it doesn't matter as I'm not creating puzzles myself).
.

[coloin]

My last batch for a while in minlexsolution grid form ... not easy to get above B6B now.

Code: Select all

B10B
....567.9.5.1.9.36.9.73.15.23...7.....4..3...961...375.....159.........7..9.756.3 # 97771 FNBP C34/M2.14.1404
..3...78.4.7.8.2.6........4..46.5.....6.1.......23864764.8..37.7.8...4.2.327...68 # 97777 FNBP C34/M2.14.1404

B8B
12.4..7.94.....23........412.16.8......39.1.27...1....31....92..74.2..139.2.3.4.7 # 88918 FNBP C34/M2.55.119
1.3.56....5718...668.3.7..5...5.36.153....92.7.......33.57.18..8...65......83.... # 13224 FNBP C34/M2.79.83
...4.6...4...89...69.73...4.793.48..36..98...8.467.9.....96.3.87.....6..9.6....51 # 13211 FNBP C34/M2.79.83
...45..894...8923.8..3.25.4.71...8.55.......39.45.8.......25......84...2..29.3.58 # 13586 FNBP C34/M2.79.83
...45678..5....2.6......1.5.745.3..83.6.48..758.67...4....34....4.7.5....3586.47. #  1893 FNBP C36/M1.1.64
1..4.678.4..18..366...731.4.467.8.13......6.7...6..84.3.58.....8.2.......14...368 #  1906 FNBP C36/M1.1.64
12..56..9.571.9..66.927...129.5.716..65..1...7.1......512...69.......3.5.....58.2 #  1893 FNBP C36/M1.1.64
..3...78.4.7.832.6....7..34..469........1.......2.86.764.8..37.7.8...4.2.327...68 #  1420 FNBP C34/M1.2.41
....567.9.5.1.9.36.9.73.15..38..7.....4......96....3.5.....159...5....171.9.756.3 #  1420 FNBP C34/M1.2.41
.23.56......18.23......34..2.5...9..39........46.9.3.256.....24.34..259.9.2..56.3 #  1434 FNBP C34/M1.1.40

B7B
1.3....89.57.89...8...2..........84...489..21....4.9.33..2.849....91.3.29...34.18 #   965 FNBP C34/M1.2.40
12....78..571..2.66.82...1526......18.1..2....75.618.2...7.4..8.....3...7.251.... #  1421 FNBP C34/M1.2.40
12.4.6.8.4.718.....68.27.1.28....3.5...2.814.7......2.....62...6..81....8.27.46.. #  1421 FNBP C34/M1.2.40
12..5.7.9.57...26.6.9.7..5126...159..75...1..9.1..........9.6..59..27......3.89.5 #   965 FNBP C34/M1.2.40
...4.6...4...89...68.37..4..687.49..3.469.8..97..38......86.39.7.....6..8.6....15 #  1421 FNBP C34/M1.2.40
...4.6...4...89...68.37..4..687.49..37..98...9.463.8.....86.39.7.....6..8.6....15 #  1421 FNBP C34/M1.2.40
....567.9.5.1.9.36.6.37.15.29.7......35...96.8...........6..5.15.....67.6.15.7.93 #  1421 FNBP C34/M1.2.40
...45...9...1.9....9..72.15..49.715...5.419.2...52..74..1.....7.42.15...86....5.1 #   965 FNBP C34/M1.2.40
....567.9.5.1.9.36.9.37.15.26.7......35...69.8...........5..9.15.19.7.639.....57. #  1421 FNBP C34/M1.2.40
1.3.56.8....18......83.2.....6.....1.31...97.....31.2531.86...26.52.3....82.15..3 #   965 FNBP C34/M1.2.40


[denis_berthier]

.
Hi Coloin

First batch of the year.

Unsurprisingly, they all have a non-degenerate tridagon.
They also all have the same number of guardians: 2. But it may only be a matter of chance or proximity.
.

[hendrik_monard]

.
Hi Coloin

First batch of the year.

Unsurprisingly, they all have a non-degenerate tridagon.
They also all have the same number of guardians: 2. But it may only be a matter of chance or proximity.
.

Could it be that the twinning (inverting) process keeps those (and perhaps other) characteristics of the original?
BTW, nice work coloin. Did you also expand beyond the min-expands?
.

[denis_berthier]

Could it be that the twinning (inverting) process keeps those (and perhaps other) characteristics of the original?

Indeed, vicinity search has "good chances" of not destroying the tridagon pattern. As for the number of guardians, I haven't thought much about it, but I think vicinity search doesn't change it much either.
It's difficult to be more precise than saying "good chances". And obviously, the chances decrease as you iterate vicinity search.
.

[coloin]

Could it be that the twinning (inverting) process keeps those (and perhaps other) characteristics of the original?
BTW, nice work coloin. Did you also expand beyond the min-expands?
.

The twinning process keeps the solving situation the same for the puzzles …. But they do have different non-essential clues
But the main thing it does is that it gives you a different 4-box for the tridagon .

Yes I did expand further than Sudoku -E does but keeping the BnB at 6 - I surmised this gave more twin puzzles .

However there is a chance that a higher BnB is found with a repeat minimise and re expand - at least that is how I found the latest puzzles


I use Sudoku Architect ( in software)
1 to do the -1+1 and generate new puzzles
2 its easy to subtract known puzzles reliably - without any conversion !

Will be interesting to hear how you get on - my pc is off for a bit as I am enjoying winter sun

[hendrik_monard]

sudoku-64 is gsf's software
sudoku-64 -E file.txt > fileexpand.txt gives you a singles expansion ....

As I am considering to make use of min_expands to avoid for my possible new lists of puzzles that they contain many minimals covered by the same min_expand, I tested gsf's expander with the command line given by coloin. When I compared the results with those obtained by my own expander (basic solver limited to naked and hidden singles), it appeared that for some puzzles, gsf's expander went further than mine. In order to obtain gsf's results, I had to remove the limitation to singles in my basic solver. I guess therefore that in gsf's expander the full potential for (basic) expansion is used: besides singles, also pairs, triples, quads, pointing and claiming.
Some questions:
- what are the consequences of extending the expansion above singles? For instance, does it affect the BpB rating?
- could there be a good reason for extending the expansion?
- did mith use gsf's software or did he limit the expansion to singles? If there is no ready answer to this question, I could engage in examining this in mith's T&E(3) list of min_expands.
- is there perhaps a possibility to limit gsf's expansion to singles?

Anyway, if we proceed with min_expands, there should be a unequivocal definition of its meaning.

PS: I just discovered a B14B totally unrelated to the previously published B7B+'s. After some checks and vicinity searches I'll publish it soon.

[denis_berthier]

Hi Hendrik

Some questions:
- what are the consequences of extending the expansion above singles? For instance, does it affect the BpB rating?

First, you have to define what it means to expand beyond Singles. Most rules other than Singles eliminate candidates but don't assert values; as a result, what you get is a Sukaku, not a Sudoku. You could say that you keep only the asserted values, but that sounds very arbitrary, because in cases the extra rules have been applied, some cases will be taken into account and some cases will not be.
Moreover, you need to expand by only sets of resolution rules that have the confluence property (W1, S2, S3, S4 are OK); otherwise, the result is not well defined.

And yes, of course, it can affect the BpB classification (decrease it). The problem is, it can affect it in drastic ways. A puzzle in T&E(2), i.e. in some BpB, can be in T&E(1) after applying Quads - it's rare, but it happens.

- could there be a good reason for extending the expansion?

It depends on the purpose of the expansion:
- if it is to avoid redundancies in published collections of puzzles, I can't see any useful and consistent purpose;
- it it is an internal step in some extended form of vicinity search, why not? It's similar to Coloin's expansion by twins.

- did mith use gsf's software or did he limit the expansion to singles? If there is no ready answer to this question, I could engage in examining this in mith's T&E(3) list of min_expands.

Mith used his own expansion software - which is restricted to Singles. Note that SudoRules trivially allows to do the expansion.
Also, it shouldn't be too difficult to add this functionality to SHC. I'll see with François.

- is there perhaps a possibility to limit gsf's expansion to singles?

This, I don't know.

Anyway, if we proceed with min_expands, there should be a unequivocal definition of its meaning.

It has been unequivocal ever since Mith has introduced it: expansion by Singles. All his min-expand T&E(3) puzzles are expansions by Singles. And all my analyses of T&E(3) puzzles have used only these expansions.

PS: I just discovered a B14B totally unrelated to the previously published B7B+'s. After some checks and vicinity searches I'll publish it soon.

Wow. Great! Those are real monsters. Even the Boojums are afraid of them.
.

[hendrik_monard]

Hi Hendrik

- did mith use gsf's software or did he limit the expansion to singles? If there is no ready answer to this question, I could engage in examining this in mith's T&E(3) list of min_expands.

Mith used his own expansion software - which is restricted to Singles. Note that SudoRules trivially allows to do the expansion.
Also, it shouldn't be too difficult to add this functionality to SHC. I'll see with François.

Right. This was also my understanding. So gsf's software should not be used for a reference database. And if it"s not too much trouble for François, why not include in SHC an expansion mode restricted to singles.

[denis_berthier]

if it"s not too much trouble for François, why not include in SHC an expansion mode restricted to singles.

It should be done in a week or so.
In the meantime, I posted the relevant SudoRules function on GitHub (for details, see here: http://forum.enjoysudoku.com/csp-rules-sudorules-kakurules-t38200-96.html)
.

[hendrik_monard]

Code: Select all

12.4.......718...6.68..7..42.17.8....76..4...84.26.....1............2.51......39.   11.2/1.2/1.2   28c   B14B_1
12.4.6...4.718...6.68.27..42.17.8....76..4...84.26.....1............2.51......39.   11.2/11.2/3.4   31c   min_expand

1...5.7.9.....9.366..7..51.....13.65...6..17....5.79.3.42.............9.98.3.....   11.2/1.2/1.2   28c   B14B_2
1...567.9...1.9.366..73.51.....13.65...6..17....5.79.3.42.............9.98.3.....   11.2/11.2/3.4   31c   min_expand


Both B14B's are closely related but have different solutions. They share many characteristics such as:
- clue count
- min_expand with three singles
- unique minimal of their min_expand
- invert has a unique solution
- SER (11.2/1.2/1.2)
- BpB (p = 14)
- .....
A further examination of their 'internal structures' by experts may perhaps show why they are in a certain way identical.

I found B14B_1 (p in BpB = 14) in a batch of 29K puzzles produced by the same generation process that also produced my 50K batch that contained only puzzles with SER >= 11.6, and in which Denis discovered a substantial number of B7B+'s.
This 29K batch contains puzzles with 11.2<=SER<=11.5 and was not published.
B14B_1 was the only puzzle in this batch with p > 6.
Given the large numbers of puzzles in both batches, a first prudent conclusion could be that the occurrence rate of p > 6 decreases rapidly with SER < 11.6.
This doesn't exclude that high BpB values can still occur in the 'lower' SER regions as was demonstrated with B14B_1.
As the number of puzzles with SER 11.2 in the 29K batch is close to 60% of the total number of puzzles in that batch, it is not a surprise that B14B_1 has SER 11.2.

Code: Select all

Composition of the 29K batch:
p = 14    1
p = 6   4231
p = 5   20991
p = 4   3432
p = 3   418

11.5   1340
11.4   5714
11.3   4990
11.2   17029

[denis_berthier]

Hi Hendrik

Very nice example of a tridagon-preserving "near-isomorphism".

Code: Select all

12.4.......718...6.68..7..42.17.8....76..4...84.26.....1............2.51......39.   11.2/1.2/1.2   28c   B14B_1
12.4.6...4.718...6.68.27..42.17.8....76..4...84.26.....1............2.51......39.   11.2/11.2/3.4   31c   min_expand

1...5.7.9.....9.366..7..51.....13.65...6..17....5.79.3.42.............9.98.3.....   11.2/1.2/1.2   28c   B14B_2
1...567.9...1.9.366..73.51.....13.65...6..17....5.79.3.42.............9.98.3.....   11.2/11.2/3.4   31c   min_expand

Both B14B's are closely related but have different solutions. They share many characteristics

Both puzzles have the same tridagon with a single guardian. Starting from each of the two min_expands, it's easy to find such a tridagon. Then it's easy to find an isomorphism from the first to the second that preserves the previous mappings and that maps the cells of the first tridagon to those of the second in a unique possible way. Then, it's easy to find a second unique isomorphism that maps the remaining cells to cells with the same numbers of candidates.

Code: Select all

Here are the commands in SudoRules:
(permute-towers-9x9
    "12.4.6...4.718...6.68.27..42.17.8....76..4...84.26.....1............2.51......39."
    3 2 1)
"...4.612...618.4.7..4.27.68...7.82.1.....4.76...26.84........1..51..2...39......."

(permute-columns-in-nth-tower-9x9
    "...4.612...618.4.7..4.27.68...7.82.1.....4.76...26.84........1..51..2...39......."
    2
    3 2 1)
"...6.412...6.814.7..472..68...8.72.1...4...76....6284........1..512.....39......."

(permute-rows-in-nth-floor-9x9
    "...6.412...6.814.7..472..68...8.72.1...4...76....6284........1..512.....39......."
    2
    3 2 1)
"...6.412...6.814.7..472..68....6284....4...76...8.72.1.......1..512.....39......."

(permute-rows-in-nth-floor-9x9
    "...6.412...6.814.7..472..68....6284....4...76...8.72.1.......1..512.....39......."
    1
    2 1 3
)
"..6.814.7...6.412...472..68....6284....4...76...8.72.1.......1..512.....39......."

(permute-columns-in-nth-tower-9x9
    "..6.814.7...6.412...472..68....6284....4...76...8.72.1.......1..512.....39......."
    3
    3 2 1)
"..6.817.4...6.4.21..472.86.....62.48...4..67....8.71.2.......1..512.....39......."

(permute-columns-in-nth-tower-9x9
    "..6.817.4...6.4.21..472.86.....62.48...4..67....8.71.2.......1..512.....39......."
    1
    3 2 1)
"6...817.4...6.4.214..72.86.....62.48...4..67....8.71.2.......1.15.2......93......"

(permute-rows-in-nth-floor-9x9
    "6...817.4...6.4.214..72.86.....62.48...4..67....8.71.2.......1.15.2......93......"
    3
    3 1 2)
"6...817.4...6.4.214..72.86.....62.48...4..67....8.71.2.93.............1.15.2....."

Starting from the 1st min-expand, this leads to:

Code: Select all

+----------------------+----------------------+----------------------+
! 6      23     259    ! 359#   8      1      ! 7      359#   4      !
! 35789  378    5789   ! 6      359#   4      ! 359#   2      1      !
! 4      13     159    ! 7      2      359#   ! 8      6      359#   !
+----------------------+----------------------+----------------------+
! 3579   137    1579   ! 1359#@ 6      2      ! 359#   4      8      !
! 23589  1238   12589  ! 4      1359   359#   ! 6      7      359#   !
! 359    46     46     ! 8      359#   7      ! 1      359#   2      !
+----------------------+----------------------+----------------------+
! 278    9      3      ! 15     1457   568    ! 245    58     567    !
! 278    46     24678  ! 359    34579  35689  ! 23459  1      35679  !
! 1      5      4678   ! 2      3479   3689   ! 349    389    3679   !
+----------------------+----------------------+----------------------+

The 2nd min-expand gives directly:

Code: Select all

+----------------------+----------------------+----------------------+
! 1      23     348    ! 248#   5      6      ! 7      248#   9      !
! 24578  257    4578   ! 1      248#   9      ! 248#   3      6      !
! 6      29     489    ! 7      3      248#   ! 5      1      248#   !
+----------------------+----------------------+----------------------+
! 2478   279    4789   ! 2489#@ 1      3      ! 248#   6      5      !
! 23458  2359   34589  ! 6      2489   248#   ! 1      7      248#   !
! 248    16     16     ! 5      248#   7      ! 9      248#   3      !
+----------------------+----------------------+----------------------+
! 357    4      2      ! 89     6789   158    ! 368    58     178    !
! 357    16     13567  ! 248    24678  12458  ! 23468  9      12478  !
! 9      8      1567   ! 3      2467   1245   ! 246    245    1247   !
+----------------------+----------------------+----------------------+

Now, if you try to make a permutation of the digits so as to obtain a possible isomorphism from #1 to #2, it doesn't completely work. You can permute the digits so as to preserve the tridagon:
3 <-> 2
9 <-> 4
5 <-> 8
but you can't extend this to a permutation of the remaining digits that would map #1 to #2.
After applying the further permutations:
1 <-> 6
7 <-> 7
you get (compared to the second min-expand on second line):

Code: Select all

1...567.9...1.9.369..73.51.....13.95...9..17....5.76.3.42.............6.68.3.....
1...567.9...1.9.366..73.51.....13.65...6..17....5.79.3.42.............9.98.3.....

In terms of tridagons, we have the same tridagons, with resp.:

Code: Select all

+----------------------+----------------------+----------------------+
! 1      23     348    ! 248#   5      6      ! 7      248#   9      !
! 24578  257    4578   ! 1      248#   9      ! 248#   3      6      !
! 9      26     468    ! 7      3      248#   ! 5      1      248#   !
+----------------------+----------------------+----------------------+
! 2478   267    4678   ! 2468#@ 1      3      ! 248#   9      5      !
! 23458  2356   34568  ! 9      2468   248#   ! 1      7      248#   !
! 248    19     19     ! 5      248#   7      ! 6      248#   3      !
+----------------------+----------------------+----------------------+
! 357    4      2      ! 68     6789   158    ! 389    58     178    !
! 357    19     13579  ! 248    24789  12458  ! 23489  6      12478  !
! 6      8      1579   ! 3      2479   1245   ! 249    245    1247   !
+----------------------+----------------------+----------------------+

+----------------------+----------------------+----------------------+
! 1      23     348    ! 248#   5      6      ! 7      248#   9      !
! 24578  257    4578   ! 1      248#   9      ! 248#   3      6      !
! 6      29     489    ! 7      3      248#   ! 5      1      248#   !
+----------------------+----------------------+----------------------+
! 2478   279    4789   ! 2489#@ 1      3      ! 248#   6      5      !
! 23458  2359   34589  ! 6      2489   248#   ! 1      7      248#   !
! 248    16     16     ! 5      248#   7      ! 9      248#   3      !
+----------------------+----------------------+----------------------+
! 357    4      2      ! 89     6789   158    ! 368    58     178    !
! 357    16     13567  ! 248    24678  12458  ! 23468  9      12478  !
! 9      8      1567   ! 3      2467   1245   ! 246    245    1247   !
+----------------------+----------------------+----------------------+

The only differences are about digits 6 and 9 in some cells. They are unrelated to the tridagon pattern.
After applying the elementary tridagon elimination rule, both puzzles are solved in BC3, with very similar resolution paths (which explains why they have the same classifications, completely determined by their tridagon part).

Note that there are two independent groups of cells with digits 6 or 9: first group common to the two puzzles, in rows 1 and 2, columns 6 and 9, blocks 2 and 3; second group (where they are permuted in one puzzle wrt the other) in cells that don't "see" any of those of the 1st group.
.

[coloin]

Interesting that these 11.2 rated puzzles should be rated BnB 14 ... my cut off for BpB > 6 was SE 11.7 !!
Maybe the SE with uniqueness removed is higher ?

It looked very much that these were twin related .... as the -q2 is identical

Starting from the first min_expand and adding the only clue which keeps the SE at 11.0 [B5B] we got an expand with 13 solutions of the converse
On minimizing this picked up the 2nd puzzle and one other.

Here is the progression of the working...

Hidden Text: Show

Code: Select all

12.4.6...4.718...6.68.27..42.17.8....76..4...84.26.....1............2.51......39.  ED=11.2/11.2/3.4
12.4.6...4.718...6.68.27..42.17.8....76..4...84.26.....1...........72.51......39.  ED=11.0/11.0/3.4

..3.5.789.5...923.9..3..51..9..3.6453..59.128..5..19735.29438676398..4..784615..2   49  13
xx.x.x...x.xxx...x.xx.xx..xx.xx.x....xx..x...xx.xx.....x...........xx.xx......xx.

13 solutions
123456789457189236968327514291738645376594128845261973512943867639872451784615392
123456789457189236968372514291738645376594128845261973512943867639827451784615392
123456789458179236967382514291738645376594128845261973512943867639827451784615392
123456789458179236976382514291738645367594128845261973512943867639827451784615392
163452789457189236928376514291738645376594128845261973512943867639827451784615392
163452789458179236927386514291738645376594128845261973512943867639827451784615392
263154789451789236978326514197238645346597128825461973512943867639872451784615392
423156789157489236968327514291738645376594128845261973512943867639872451784615392
423156789157489236968372514291738645376594128845261973512943867639827451784615392
423156789158479236967382514291738645376594128845261973512943867639827451784615392
423156789158479236976382514291738645367594128845261973512943867639827451784615392
463152789157489236928376514291738645376594128845261973512943867639827451784615392
463152789158479236927386514291738645376594128845261973512943867639827451784615392

13 nonminimal puzzles
12.4.6...4.718...6.68.27..42.17.8....76..4...84.26.....1...........72.51......39.   B5B
12.4.6...4.718...6.68.72..42.17.8....76..4...84.26.....1...........27.51......39.   B5B
12.4.6...4.817...6.67.82..42.17.8....76..4...84.26.....1...........27.51......39.   B5B
12.4.6...4.817...6.76.82..42.17.8....67..4...84.26.....1...........27.51......39.   B5B
16.4.2...4.718...6.28.76..42.17.8....76..4...84.26.....1...........27.51......39.   B5B
16.4.2...4.817...6.27.86..42.17.8....76..4...84.26.....1...........27.51......39.   B5B
26.1.4...4.178...6.78.26..41.72.8....46..7...82.46.....1...........72.51......39.   B5B
42.1.6...1.748...6.68.27..42.17.8....76..4...84.26.....1...........72.51......39.   B5B
42.1.6...1.748...6.68.72..42.17.8....76..4...84.26.....1...........27.51......39.   B5B
42.1.6...1.847...6.67.82..42.17.8....76..4...84.26.....1...........27.51......39.   B5B
42.1.6...1.847...6.76.82..42.17.8....67..4...84.26.....1...........27.51......39.   B5B
46.1.2...1.748...6.28.76..42.17.8....76..4...84.26.....1...........27.51......39.   B5B
46.1.2...1.847...6.27.86..42.17.8....76..4...84.26.....1...........27.51......39.   B5B

minimal puzzles
12.4.......718...6.68.....42.17.8....76..4...84.26.....1...........72.5.......39.   B5B
12.4.......718...6.68..7..42.1..8....76..4...84.26.....1...........72.5.......39.   B5B
12.4.......718...6.68..7..42.17.8....76..4...84.26.....1............2.51......39.   B14B #1
12.4.......718...6.68.72..42.1..8....76..4...84.26.....1...........27.5.......39.   B5B
12.4.......817...6.67.82..42.1..8....76..4...84.26.....1...........27.5.......39.   B5B
12.4.......817...6.76.82..42.1..8....67..4...84.26.....1...........27.5.......39.   B5B
1..4.2.....718...6.28.76..42.1..8....76..4...84.26.....1...........27.5.......39.   B5B
1..4.2.....817...6.27.86..42.1..8....76..4...84.26.....1...........27.5.......39.   B5B
2..1.4.......8...6.78..6..41.72.8....46..7...82.46.....1...........72.5.......39.   B5B
2..1.4......78...6.78..6..41.72.8....46..7...82.46.....1............2.51......39.   B14B #New
42.1.....1.7.8...6.68.....42.17.8....76..4...84.26.....1...........72.5.......39.   B5B
42.1.....1.7.8...6.68..7..42.1..8....76..4...84.26.....1...........72.5.......39.   B5B
42.1.....1.7.8...6.68..7..42.17.8....76..4...84.26.....1............2.51......39.   B14B #2
42.1.....1.7.8...6.68.72..42.1..8....76..4...84.26.....1...........27.5.......39.   B5B
42.1.....1.8.7...6.67.82..42.1..8....76..4...84.26.....1...........27.5.......39.   B5B
42.1.....1.8.7...6.76.82..42.1..8....67..4...84.26.....1...........27.5.......39.   B5B
4..1.2...1.7.8...6.28.76..42.1..8....76..4...84.26.....1...........27.5.......39.   B5B
4..1.2...1.8.7...6.27.86..42.1..8....76..4...84.26.....1...........27.5.......39.   B5B     

12.4.......718...6.68..7..42.17.8....76..4...84.26.....1............2.51......39.   B14B #1 
2..1.4......78...6.78..6..41.72.8....46..7...82.46.....1............2.51......39.   B14B #New
42.1.....1.7.8...6.68..7..42.17.8....76..4...84.26.....1............2.51......39.   B14B #2

min_expands

Code: Select all

12.4.6...4.718...6.68.27..42.17.8....76..4...84.26.....1............2.51......39. #   331 FNBP C31/M1.2.53  #  14 # 1
1...567.9...1.9.366..73.51.....13.65...6..17....5.79.3.42.............9.98.3..... #   331 FNBP C31/M1.2.53  #  14 # 2
.234..7.945.7...327.9...54.2.5...9.33......74.47...25.5..9.8..........9.....61... #   331 FNBP C31/M1.2.53  #  14 # NEW


The new one reduces to 27 clues ,

Code: Select all

12.4.......718...6.68..7..42.17.8....76..4...84.26.....1............2.51......39. #   331 FNBP C28.m/M1.2.54#  14
1...5.7.9.....9.366..7..51.....13.65...6..17....5.79.3.42.............9.98.3..... #   331 FNBP C28.m/M1.2.54#  14
.234.....4..7...327.9...5..2.5...9.33......74.47...25.5..9.8..........9.....61... #   331 FNBP C27.m/M1.2.54#  14