The BxB classification of T&E(2) puzzles

Everything about Sudoku that doesn't fit in one of the other sections

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

Postby coloin » Sun Jun 29, 2025 12:09 pm

Code: Select all
+---+---+---+
|..3|45.|.89|
|...|.89|23.|
|..9|3.2|4.5|
+---+---+---+
|...|...|8.3|
|...|...|95.|
|9..|8.5|.24|
+---+---+---+
|392|...|54.|
|.18|..4|...|
|7.4|...|...|
+---+---+---+

a new BxB 11, with SE 11.7.11.7/9.5
at any rate not a simple tridagon insertion....
edit
although if you guess that the 3 goes at r6c5 then this implies the 2 goes into r5c4 ..... is this assumptive technique valid ?
coloin
 
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Location: Devon

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

Postby denis_berthier » Sun Jun 29, 2025 12:37 pm

.
Not the simplest tridagon but the next simplest case: with 2 guardians.

As in many cases, replacement leads to an easy solution:
Code: Select all
Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 126    267    3      ! 4      5      167    ! 167    8      9      !
   ! 1456   4567   1567   ! 167    8      9      ! 2      3      167    !
   ! 168    678    9      ! 3      167    2      ! 4      167    5      !
   +----------------------+----------------------+----------------------+
   ! 12456  24567  1567   ! 12679  124679 167    ! 8      167    3      !
   ! 12468  234678 167    ! 1267   123467 1367   ! 9      5      167    !
   ! 9      367    167    ! 8      1367   5      ! 167    2      4      !
   +----------------------+----------------------+----------------------+
   ! 3      9      2      ! 167    167    1678   ! 5      4      1678   !
   ! 56     1      8      ! 25679  23679  4      ! 367    679    267    !
   ! 7      56     4      ! 12569  12369  1368   ! 136    169    1268   !
   +----------------------+----------------------+----------------------+
178 candidates.


Code: Select all
Trid-OR2-relation for digits 1, 7 and 6 in blocks:
        b2, with cells (marked #): r1c6, r2c4, r3c5
        b3, with cells (marked #): r1c7, r2c9, r3c8
        b5, with cells (marked #): r4c6, r5c4, r6c5
        b6, with cells (marked #): r4c8, r5c9, r6c7
with 2 guardians (in cells marked @): n2r5c4 n3r6c5
   +----------------------+----------------------+----------------------+
   ! 126    267    3      ! 4      5      167#   ! 167#   8      9      !
   ! 1456   4567   1567   ! 167#   8      9      ! 2      3      167#   !
   ! 168    678    9      ! 3      167#   2      ! 4      167#   5      !
   +----------------------+----------------------+----------------------+
   ! 12456  24567  1567   ! 12679  124679 167#   ! 8      167#   3      !
   ! 12468  234678 167    ! 1267#@ 123467 1367   ! 9      5      167#   !
   ! 9      367    167    ! 8      1367#@ 5      ! 167#   2      4      !
   +----------------------+----------------------+----------------------+
   ! 3      9      2      ! 167    167    1678   ! 5      4      1678   !
   ! 56     1      8      ! 25679  23679  4      ! 367    679    267    !
   ! 7      56     4      ! 12569  12369  1368   ! 136    169    1268   !
   +----------------------+----------------------+----------------------+


Trid-OR2-whip[2]: OR2{{n2r5c4 | n3r6c5}} - c2n3{r6 .} ==> r5c2≠2
Trid-OR2-whip[3]: OR2{{n2r5c4 | n3r6c5}} - c2n3{r6 r5} - r5n8{c2 .} ==> r5c1≠2
whip[1]: r5n2{c5 .} ==> r4c4≠2, r4c5≠2
Trid-OR2-whip[4]: OR2{{n2r5c4 | n3r6c5}} - c6n3{r5 r9} - r9n8{c6 c9} - r9n2{c9 .} ==> r8c4≠2
Trid-OR2-whip[4]: OR2{{n2r5c4 | n3r6c5}} - r5n3{c6 c2} - r5n4{c2 c1} - r5n8{c1 .} ==> r5c5≠2
hidden-single-in-a-block ==> r5c4=2
z-chain[3]: r9n2{c5 c9} - c9n8{r9 r7} - r7n6{c9 .} ==> r9c5≠6
z-chain[3]: r9n2{c5 c9} - c9n8{r9 r7} - r7n1{c9 .} ==> r9c5≠1
z-chain[4]: r9n2{c5 c9} - r9n8{c9 c6} - b8n3{r9c6 r8c5} - c5n2{r8 .} ==> r9c5≠9

***** STARTING ELEVEN_S REPLACEMENT TECHNIQUE *****
RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens.
Trying in block 6

AFTER APPLYING ELEVEN''S REPLACEMENT METHOD to 3 digits 1, 6 and 7 in 3 cells r6c7, r5c9 and r4c8,
the resolution state is:
Code: Select all
   +----------------------+----------------------+----------------------+
   ! 1672   2167   3      ! 4      5      167    ! 167    8      9      !
   ! 16745  45167  1675   ! 167    8      9      ! 2      3      167    !
   ! 1678   1678   9      ! 3      167    2      ! 4      167    5      !
   +----------------------+----------------------+----------------------+
   ! 167245 245167 1675   ! 1679   16749  167    ! 8      7      3      !
   ! 16748  341678 167    ! 2      16734  1673   ! 9      5      6      !
   ! 9      3167   167    ! 8      1673   5      ! 1      2      4      !
   +----------------------+----------------------+----------------------+
   ! 3      9      2      ! 167    167    1678   ! 5      4      1678   !
   ! 5167   167    8      ! 51679  231679 4      ! 3167   1679   2167   !
   ! 167    5167   4      ! 16759  23     16738  ! 1673   1679   16728  !
   +----------------------+----------------------+----------------------+

THIS IS THE PUZZLE THAT WILL NOW BE SOLVED.
RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens.

Code: Select all
Resolution state after Singles:
   +----------------------+----------------------+----------------------+
   ! 1267   1267   3      ! 4      5      167    ! 67     8      9      !
   ! 14567  14567  1567   ! 167    8      9      ! 2      3      17     !
   ! 1678   1678   9      ! 3      167    2      ! 4      16     5      !
   +----------------------+----------------------+----------------------+
   ! 12456  12456  156    ! 169    1469   16     ! 8      7      3      !
   ! 1478   13478  17     ! 2      1347   137    ! 9      5      6      !
   ! 9      367    67     ! 8      367    5      ! 1      2      4      !
   +----------------------+----------------------+----------------------+
   ! 3      9      2      ! 167    167    1678   ! 5      4      178    !
   ! 1567   167    8      ! 15679  123679 4      ! 367    169    127    !
   ! 167    1567   4      ! 15679  23     13678  ! 367    169    1278   !
   +----------------------+----------------------+----------------------+


whip[1]: r7n6{c6 .} ==> r9c6≠6, r8c4≠6, r8c5≠6, r9c4≠6
z-chain[3]: c3n7{r6 r2} - r3n7{c2 c5} - r6n7{c5 .} ==> r5c1≠7
z-chain[3]: c3n7{r6 r2} - r3n7{c1 c5} - r6n7{c5 .} ==> r5c2≠7
whip[4]: r5c3{n1 n7} - r6n7{c3 c5} - r3c5{n7 n6} - r7c5{n6 .} ==> r5c5≠1
z-chain[3]: r5n1{c3 c6} - r1n1{c6 c1} - c3n1{r2 .} ==> r4c2≠1
z-chain[3]: r5n1{c3 c6} - r1n1{c6 c2} - c3n1{r2 .} ==> r4c1≠1
whip[5]: r5c3{n7 n1} - r5c6{n1 n3} - r6c5{n3 n6} - r3c5{n6 n1} - r7c5{n1 .} ==> r5c5≠7
whip[5]: r4c6{n6 n1} - r1c6{n1 n7} - r5n7{c6 c3} - c3n1{r5 r2} - r1n1{c1 .} ==> r7c6≠6
z-chain[6]: b5n7{r6c5 r5c6} - c6n3{r5 r9} - c6n8{r9 r7} - r7c9{n8 n1} - r2c9{n1 n7} - c4n7{r2 .} ==> r7c5≠7
t-whip[5]: c6n6{r4 r1} - b3n6{r1c7 r3c8} - b3n1{r3c8 r2c9} - b2n1{r2c4 r3c5} - r7c5{n1 .} ==> r6c5≠6, r4c5≠6
whip[1]: b5n6{r4c6 .} ==> r4c1≠6, r4c2≠6, r4c3≠6
z-chain[5]: r3n7{c2 c5} - r6n7{c5 c3} - c3n6{r6 r2} - r2c4{n6 n1} - r2c9{n1 .} ==> r2c2≠7
z-chain[5]: r3n8{c2 c1} - r3n7{c1 c5} - r6c5{n7 n3} - c2n3{r6 r5} - c2n8{r5 .} ==> r3c2≠1, r3c2≠6
t-whip[5]: c5n6{r7 r3} - b3n6{r3c8 r1c7} - b3n7{r1c7 r2c9} - b2n7{r2c4 r1c6} - r7n7{c6 .} ==> r7c4≠6
hidden-single-in-a-block ==> r7c5=6
biv-chain[3]: r3c5{n7 n1} - r3c8{n1 n6} - r1c7{n6 n7} ==> r1c6≠7
naked-pairs-in-a-column: c6{r1 r4}{n1 n6} ==> r9c6≠1, r7c6≠1, r5c6≠1
whip[1]: r5n1{c3 .} ==> r4c3≠1
naked-single ==> r4c3=5
naked-pairs-in-a-block: b4{r4c1 r4c2}{n2 n4} ==> r5c2≠4, r5c1≠4
hidden-single-in-a-row ==> r5c5=4
hidden-pairs-in-a-block: b1{n4 n5}{r2c1 r2c2} ==> r2c2≠6, r2c2≠1, r2c1≠7, r2c1≠6, r2c1≠1
biv-chain[3]: r1c6{n1 n6} - r1c7{n6 n7} - r2c9{n7 n1} ==> r2c4≠1
biv-chain[3]: r6c3{n7 n6} - r2n6{c3 c4} - b2n7{r2c4 r3c5} ==> r6c5≠7
easy end in BC3
.
denis_berthier
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Posts: 4522
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Location: Paris

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

Postby Paquita » Wed Jul 16, 2025 12:56 pm

I got 2 specials

One is a number of puzzles with BxB = 0
Hidden Text: Show
987......6..95.....4....3..3..2.6.911......3....1..5.6.3.5.2....2..69.5....31...2;0;3052
987......6..95.....4....3..3..2.6.911...9.......1..5.6.3.5.2....2..69.5....31...2;0;3053
98.76.5..7.4....6..6.4.....59....4.6..6....75......98.4.9.78......3.9.54....2....;0;3066
98.76.5..7.4.9.....5....9..8.5....3......479.......8.26...59....4.8.7.6....64..5.;0;3067
98.76.5..7.4.9.........89..8.5....3......479.......8.26...59....4.8.7.6....64..5.;0;3068
98.76.5..7.54......64...9..8.7...63....8.64.5........2.7.64......95.8.......9..8.;0;3069
98.76.5..7.54......64..59..8.7...63....8.64.5........2.7.64......95.........9..8.;0;3070
9876.....54....93..2.......4...31.691..59.......4.6.5...3.....1...1..34.....6..95;0;3071
9876.....54....93..2.......4...31.691..59...3...4.6.5...3.....1...1...4.....6..95;0;3072
9876.....54....93..2.......4...31.691..59.4.....4.6.5...3.....1...1...4.....6..95;0;3073
98.76.5..7.54......64.8.9..8.7....32.....64.........1..7.64...5..95.........9...8;0;3074
98.76.5..7.4.9.....5....9..8.5....3......47.........216...59....4.8.7.6....64..5.;0;3075
98.76.5..7.58.4.........7..5.79.....49.....5..68.4..9...4...8.....6.5.3........21;0;3076
98.76.5..7.4.9.........89..8.5....3......47.........216...59....4.8.7.6....64..5.;0;3077
98.76.5..7.4....6..6.4.....59...74....6....75......98.4.9..8......32..54....1....;0;3078
9876.....5..84.....3.......4.....2..2....683....2...14.1....68....36..41...1.8..2;0;3079
987......6..85.....4....3..5......322....34.8...2..15..1..........43.51....1.8.24;0;3080
987......6..95.....4....3..2...........23.56....1.6.29.3.5.1....1..69..5...32..1.;0;3081
9876.....5...4.....3....8..4......2.2....6.83...2..4.1.4.1.82...1...4.6....36.1..;0;3082
9876.....5...4.....3....8..4......2.2....6.83...2..4.1.4.1.82...1.....68...36.1..;0;3083
987......6..95.....4....3..3..2...911....5.3....1..5.6.3...2....2..69.5....31...2;0;3084
987......6..95.....4....3..3..2...911...95......1..5.6.3...2....2..69.5....31...2;0;3085
98.76.5..7...4.....6.....7.85....4..4.6...89...7....65..86.9......3.........28.54;0;3088
98.76.5..7...4.....6.....7.85....4.74.....89...7....65..86.9......3.........28.54;0;3089
98.76....7.59..8...64.5....6..57..4...8.4.......8...9..96...73......75.4........2;0;3090
98.76.5..7.54......64.8.9..8.7...63......64.5........2.7.64......95.........9..8.;0;3091
98.76.5..7...4.....6.....7.85....4....7....65..6...89..486.9......3.........28.54;0;3092
98.76....7.5...64..3.......2......97...2..48.....47..6..8.79..4..6..2......68..2.;0;3093
98.76....7.5...64..3.......2..8...97...2..48.....47..6..8.79..4..6..2.......8..2.;0;3094
98.76....7.5...64..3.......8...47..6...2..48........97.2..79..4..6..2......68..2.;0;3095
98.76....7.5...64..3.......8...47..6...8...97...2..48..2..79..4..6..2.......8..2.;0;3096
98.76....7.5...64..3.......8...47..62......97...2..48...6..2......68..2.....79..4;0;3097
98.76....7.5...64..3.......8...47..62..8...97...2..48...6..2.......8..2.....79..4;0;3098
9876.....5.....94..3.......2..59.......1.6.5.....42.69..4.....2..1.6..95...2..41.;0;3099
9876.....5.....94..3.......2..59...4...1.6.5.....42.69..4.....2..1.6..95...2...1.;0;3100
9876.....5.....94..3.......2..59.1.....1.6.5.....42.69..4.....2..1.6..95...2...1.;0;3101
9876.....5.....94..3.......2...4..69...59.......2.61...12.6..95..4.....1...1..42.;0;3102
9876.....5.....94..3.......2...4..69...59...4...2.61...12.6..95..4.....1...1...2.;0;3103
9876.....54....93..2.......4...3..69...59.......4.61...1..6..95..3.....1...1..34.;0;3104
9876.....54....93..2.......4...3..69...59...3...4.61...1..6..95..3.....1...1...4.;0;3105
9876.....54....93..2.......4...3..69...59.4.....4.61...1..6..95..3.....1...1...4.;0;3106
9876.....54....93..2.......4...3..691..59.......4.61....3.....1...1..34.....6..95;0;3107
9876.....54....93..2.......4...3..691..59...3...4.61....3.....1...1...4.....6..95;0;3108
9876.....54....93..2.......4...3..691..59.4.....4.61....3.....1...1...4.....6..95;0;3109
98.76.5..7...4.....6.....7.85...64..4.....89...7....65..8..9......32..54...1.....;0;3113
98.76....7.54..........87..56.....3....58.9.........214..67......8.95.4......4.6.;0;3114
98.76.5..7...4.....6.....7.85....4....7....65..6...89..48..9......32..54...1.....;0;3116
98.76....5..........4...73..7......2.1...63.4....2.17...2.43......61..2......76.3;0;3117
98.76....7.54..6.......87..56.....3.....8.9.........214..67......8.95.4......4.6.;0;3118
98.76....5..........4...73..7......2.1...63.4....2.1....2.43.1....61..2......76.3;0;3119
987......6..85.....4....3..5......2.2....348....2..1.5.1.....3....43.5.1...1.8..2;0;3123
9876.....5...4.....3....8..4......2.2....6.83...2..4.1.1.....6....36.1.4...1.82..;0;3125
987......6..95.....4....3..2....5......23.56....1...29.3...1....1..69..5...32..1.;0;3126
98.76....7.54..........87..56.....3.....8.97.......5.24..67......8.95.4......4.6.;0;3128
98.76....7.54..........87..8.....53..6......2...5..9.74..67......8.95..4.....4..6;0;3129
98.76....7.54..........87..4..67......8.95.4......4.6..6.....3....58.97.......5.2;0;3130
9876.....5.....94..3........21.6..95..4.....2...2...1....59.1.....1.62......4..69;0;3131
9876.....5.....94..3.......2..59.......1.62......4..69..4.....2..1.6..95...2..41.;0;3132
9876.....5.....94..3.......2..59...4...1.62......4..69..4.....2..1.6..95...2...1.;0;3133
9876.....5.....94..3.......2..59.1.....1.62......4..69..4.....2..1.6..95...2...1.;0;3134
9876.....54....93..2.......4...91.631..53...9...4.6.5...3.....1...1...4.....6..95;0;3150
9876.....5.....94..3........21.6..95..4.....2...2...1....54.1.9...1.62......9..64;0;3151
9876.....5.....94..3.......2..54...9...1.6.5.....92.64..4.....2..1.6..95...2...1.;0;3152
9876.....5.....94..3.......2...9..64...54...9...2.61...12.6..95..4.....1...1...2.;0;3153
9876.....54....93..2.......4...9..63...53...9...4.61...1..6..95..3.....1...1...4.;0;3154
9876.....54....93..2.......4...9..631..53...9...4.61....3.....1...1...4.....6..95;0;3155
98.76.5..7.54.......4.8.9..6.7....32.....84.........1..7.84...5..95.........9...6;0;3157
98.76.5..7...4.....6.....7.8.6....9.45....8....7....65.48..9......32..54...1.....;0;3158
98.76.5..7.4.59.........9..8.5....3......47.........216...9.....4.8.7.6....64..5.;0;3159
9876.....5..84.....3.......4.....2..2....683....2....1.1....68....36..14...1.8..2;0;3160
987......6..85.....4....3..5......322....34.8...2...1..1..........43.15....1.8.24;0;3161
987......6..95.....4....3..2...........32.56....1.6.29.3.5.1....1..69..5...2...1.;0;3162
98.76.5..7...4.....6.....7.8.6....9.45....8....7....65..86.9......3.........28.54;0;3163
98.76.5..7...4.....6.....7.8......9.45....8.7..7....65..86.9......3.........28.54;0;3164
98.76....7.54.......4.8.9..6.7...83......84.5........2.7.84..5...95.........9..6.;0;3165
98.76.5..7.54.......4.8.9..6.7...83......84.5........2.7.84......95.........9..6.;0;3166
9876.....5.....94..3.......2..54...9...1.62......9..64..4.....2..1.6..95...2...1.;0;3167
98.76.5..7...4.....6.....7.8......9.45...68....7....65..8..9......32..54...1.....;0;3169
98.76....7.5.4.........87..56.....3....85.9.........214...7......89.5.4......4.6.;0;3170
98.76....7.5.4.6.......87..56.....3....8..9.........214...7......89.5.4......4.6.;0;3172
987......6..85.....4....3..5......2.2....348....2....1.1.....3....43.1.5...1.8..2;0;3174
9876.....5...4.....3....8..4......2.2....6.83...2..1...1.....6....36.4.1...1.82..;0;3176
987......6..95.....4....3..2....5......32.56....1...29.3...1....1..69..5...2...1.;0;3177
98.76....7.5.4.........87..56.....3....8..97.......5.24...7......89.5.4......4.6.;0;3179
98.76....7.5.4.........87..8.....53..6......2....5.9.74...7......89.5..4.....4..6;0;3180
98.76....7.5.4.........87..4...7......89.5.4......4.6..6.....3....85.97.......5.2;0;3181
9876.....54....93..2.......4...9.6.3...5.641....43...5.1..6.5.9..3.....1...1...4.;0;3194
9876.....54....93..2.......4...9.6.31..43...5...5.641...3.....1...1...4.....6.5.9;0;3195
9876.....54....93..2.......4...916.31..43...5...5.64....3.....1...1...4.....6.5.9;0;3197
9876.....5.....94..3........21.6.5.9..4.....2...2...1....5.612....14...5....9.6.4;0;3198
9876.....5.....94..3.......2..14...5...5.612.....9.6.4..4.....2..1.6.5.9...2...1.;0;3199
9876.....5.....94..3.......2..14...5...5.61......926.4..4.....2..1.6.5.9...2...1.;0;3201
98.76.5..7...4......6....7.8......6.45...69...67....85.9...8......32..54...1.....;0;3202
98.76....7.5..49....6.9.8..6.4..7.9..9..8......8....5.4.....6.....57..32........1;0;3203
98.76.5..7.45.......5.4.9..6.7....32...8..4.........1..7.48...5..9..5.......9...6;0;3205
98.76.5..7...4......6....7.8......6.45....9...67....85.94..8......32..54...1.....;0;3206
98.76....7.5..4.....6.9.8..6.4..7.9..9..8......8....5.45....6.....57..32........1;0;3207
98.76....7.54.......4.5.9..6.7....32...8.65.........1..7.58...4..9..4.......9...6;0;3209
9876.....5..84.....3.......4.....2..2....638....2....1.1.3..8.2...16..34.....86..;0;3210
987......6..85.....4....3..5......2.2....384....2....1.1.4...82...13.4.5.....8.3.;0;3211
987......6..85.....4....3..5......322....38.4...2...1..1.4...28...13.45......8...;0;3213
9876.....5...4.....3....8..4......2.2....6.38...2..1...1.3..28....16.4.3.....8.6.;0;3214
987......6..95.....4....3..2..1.9.6....36.52......5..9.3...1....1..96..5...2...1.;0;3215
987......6..95.....4....3..2..1.9.6....36.52.........9.3.5.1....1..96..5...2...1.;0;3217
98.76.5..7...4......6....7.8......6.45....9...67....85.9.6.8......3.........29.54;0;3218
98.76....7.5..4.....6.9.8..6.4..7.9..9..8......8....5.4.....6.9...57.43.........2;0;3219
98.76....7.54.......4.5.9..6.7...83....8..5.4........2.7.58..4...9..4.......9..6.;0;3220
98.76....7.5..49....6.9....6.4..7.8..9..8......8.....54.....69....57.4.3.......2.;0;3221
98.76....7.5..49....6.9.8..6.4..7....9..8......8....5.4.....6.9...57.43.........2;0;3222
98.76.5..7.45.......5.4.9..6.7...83....8..4.5........2.7.48......9..5.......9..6.;0;3223

Is that normal?

The other is a puzzle with -3 as BxB result. It is not -4 and it is not a T&E(3). So I wonder, is it maybe above 14?

98.76.5..5.74.8.....6..9...86..9....4.95......75.8..4.....764........3.2........1
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Re: The BxB classification of T&E(2) puzzles

Postby denis_berthier » Wed Jul 16, 2025 1:32 pm

Hi Paquita
Paquita wrote:I got 2 specials
One is a number of puzzles with BxB = 0
Is that normal?

BxB = 0 means the puzzle is in B0B = B; i.e. in T&E(1 or0)
I didn't check all the list, but the first puzzle is indeed in T&E(1).
In order to avoid such 0 results, I systematically compute the T&-depth before the relevant secondary classification - that's what "hierarchical classifications" means.
In the present case, it's not really a problem, but suppose you try to apply BxB to a puzzle in T&E(3): it will take a very long time (depending on <max-length>) to conclude with a value of -3 or -4.

Paquita wrote:The other is a puzzle with -3 as BxB result. It is not -4 and it is not a T&E(3). So I wonder, is it maybe above 14?
98.76.5..5.74.8.....6..9...86..9....4.95......75.8..4.....764........3.2........1

From the Manual: -3 means <buffer-size> is too small for this puzzle; try increasing it.
In order to avoid any such problems, I systematically increase the default values to: -max-length 36 -buffer-size 20000000.

Indeed, the BxB rating is 14. Congrats for extending the short list of B14B puzzles.
.
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Re: The BxB classification of T&E(2) puzzles

Postby Paquita » Wed Jul 16, 2025 2:11 pm

These are B14B also (lower rated puzzles will follow later)


98.76.5..7.59.4.....6.857..6.849....45.8.7.....7.56.....4...93......9..........21;14;16
98.76.5..7.54.98...64.8....64..97...5.9..8....7854......6...........463........21;14;17
98.76.5..7.58.4....64.9.7..8.....43....4............216.9.48...5..97.....785.6...;14;18
98.76.5..7.54.9....46.5....8.49...6..7...4....69.85......8.7.5........32........1;14;19
98.76.5..7.54.9....46.85...86..74.9.5..9.6....948......78....5........32........1;14;20
98.76.5..7.59.4.....6.859..6.847....45.8.9.....9.56.....4...73......7..........21;14;21
98.76.5..7.58.46....4.95...6.9.57....784.9....5.68.....9....43.....4...........21;14;22
98.76.5..7.54.9....46.85...8.49...6..7...4....69.5.......8.7.5........32........1;14;23
98.76.5..7.64..8...54..9...8.5.97....796.4....6.85.....9....43.....4...........21;14;26
98.76.5..7.6..58...54..9...8.5.97....796.4....6.85.....9....43.....4...........21;14;27
98.76.5..7.65.4.......897..6.8.75...57.9......948.6...4...........6..43........21;14;28
98.76.5..7.6.4......58.96..65..84...4.897......95.6.....4...73......7..........21;14;33
98.76.5..7.6.45....458.....6.497..8..985.6....7...4.......97.5........32........1;14;34
98.76.5..7.64.5....4..98...69..84.7.5.86.7.....49......69....5........32........1;14;35
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Re: The BxB classification of T&E(2) puzzles

Postby Paquita » Wed Jul 16, 2025 3:29 pm

Ok it seems these are 3 puzzles
98.76.5..7.59.4....46.857..6.849....45.8.7.....7.56.....4...93......9..........21
98.76.5..7.59.4....46.859..6.847....45.8.9.....9.56.....4...73......7..........21
98.76.5..7.65.4....45.897..6.8.75...57.9......948.6...4...........6..43........21
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Re: The BxB classification of T&E(2) puzzles

Postby denis_berthier » Wed Jul 16, 2025 3:48 pm

yes, 3 more B14B
.
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Re: The BxB classification of T&E(2) puzzles

Postby Paquita » Wed Jul 16, 2025 4:12 pm

I don't quite understand this
it is these different puzzles

12.4.6...4.718...6.68..7..42.17.8....76..4...84.26.....1............2.51......39.
12.4.....4.718...6.68.27..42.17.8....76..4...84.26.....1............2.51......39.
12.4.6.....718...6.68.27..42.17.8....76..4...84.26.....1............2.51......39.
12.4.......718...6.68..7..42.17.8....76..4...84.26.....1............2.51......39.
1...5.7.9...1.9.366..73.51.....13.65...6..17....5.79.3.42.............9.98.3.....
1...567.9...1.9.366..7..51.....13.65...6..17....5.79.3.42.............9.98.3.....
1...567.9.....9.366..73.51.....13.65...6..17....5.79.3.42.............9.98.3.....
1...5.7.9.....9.366..7..51.....13.65...6..17....5.79.3.42.............9.98.3.....
.234....945.7...327.9...5..2.5...9.33......74.47...25.5..9.8..........9.....61...
.234..7..45.7...327.9...5..2.5...9.33......74.47...25.5..9.8..........9.....61...
.234.....45.7...327.9...54.2.5...9.33......74.47...25.5..9.8..........9.....61...
.234..7.94..7...327.9...5..2.5...9.33......74.47...25.5..9.8..........9.....61...
.234....94..7...327.9...54.2.5...9.33......74.47...25.5..9.8..........9.....61...
.234..7..4..7...327.9...54.2.5...9.33......74.47...25.5..9.8..........9.....61...

These are 14 different puzzles as far as I can see, the expands are 3
12.4.6...4.718...6.68.27..42.17.8....76..4...84.26.....1............2.51......39.
1...567.9...1.9.366..73.51.....13.65...6..17....5.79.3.42.............9.98.3.....
.234..7.945.7...327.9...54.2.5...9.33......74.47...25.5..9.8..........9.....61...

but when I try to get minimals from the expands, I get only these 3, not all the 14 (or even more)
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Re: The BxB classification of T&E(2) puzzles

Postby denis_berthier » Wed Jul 16, 2025 4:40 pm

.
the other puzzles are not minimals
.
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Re: The BxB classification of T&E(2) puzzles

Postby Paquita » Wed Jul 16, 2025 4:41 pm

Of course! I got to that too
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Re: The BxB classification of T&E(2) puzzles

Postby coloin » Thu Jul 17, 2025 8:23 pm

Well done in finding the 14....

Ive found a few more puzzles ....and recently have found new TE2 expanded puzzles with BxB>6 which allow a clue to be removed to a give a TE3 puzzle ...

Code: Select all
.2..56...45.18.26.......5..24....378.8....9......486.1.62.14...5.482...681.6.5..2 # 8#   
.2..56....5.18.26.......5...4....378.8....9......486.1.62.14...5.482...681.6.5..2 #-4#TE3
....56......78.132...1.2.......4...8.34.28.17..8....4.3.7...82..128..4.384.2...71 #12#   
....56......78.132...1.2.......4...8.34.28.17..8....4.3.7...82..128..4.3...2...71 #-4#TE3
....56......78.132...1.2.......4...8.34.28.71..8....4.3.7...82..128..4.384.2...17 #12#   
....56......78.132...1.2.......4...8.34.28.71..8....4.3.7...82..128..4.3...2...17 #-4#TE3
1.3......45....123.89..1........5..7.35.172.4.7....5..3..57.4.15...2437....1.3.52 # 9#   
1.3......45....123.89..1........5..7.35.172.4.7....5..3.....4.15...2437....1.3.52 #-4#TE3
...45.........9...689.72...29.71.86..16......7.8....1...1..792.8.2....7197...16.8 # 7#   
...45.........9...689.72...29.71.86..1.......7......1..61..792.8.2....7197...16.8 #-4#TE3
...4.....4...89......37.154.317..64.5.46...7167....3.5.6....4.7......56..45.67.13 # 8#   
...4.....4...89......37.154.317..64.5.46...7167....3.5.6......7.......6..45.67.13 #-4#TE3
.2..5....45..891.2.....25.........4....81429..4....3.6.1492..5.5.2.48...89.5.1.2. #12#   
.2..5....45..891........5.........4....81429..4....3.6.1492..5.....48...89.5.1.2. #-4#TE3
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Re: The BxB classification of T&E(2) puzzles

Postby denis_berthier » Fri Jul 18, 2025 3:09 am

coloin wrote:Ive found a few more puzzles ....and recently have found new TE2 expanded puzzles with BxB>6 which allow a clue to be removed to a give a TE3 puzzle ...

Getting a T&E(3) puzzle by minimising a T&E(2) one is certainly a very interesting result - with extremely low probability in general.
Were the original B6B+ derived from T&E(3) puzzles?
Can you estimate how close the new T&E(3) puzzles are to the already known T&E(3) list (maybe in terms of {-p +q} search)?
.
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Re: The BxB classification of T&E(2) puzzles

Postby coloin » Tue Jul 22, 2025 3:59 pm

Another pair
Code: Select all
......7.9456....31......56..1......863.8.41.58..1.....36..18.5.5.134.....486.5.1. #12#
......7.9456....31......56..1......863.8.41.58..1.....36.....5.5.134.....486.5.1. #-4#TE3
......7.9456....31......56..1......836.8.41.58..1.....5.134....63..18.5..486.5.1. #12#
......7.9456....31......56..1......836.8.41.58..1.....5.134....63.....5..486.5.1. #-4#TE3

Yes I started vicinity search [-1+1} on BxB6 which were produced from TE3 puzzles.
I had a look back at my file of new TE3 puzzles, added one clue, but none were BxB>6.
It would be a long computation to do this on miths list .. but i agree they must be rare as none of the previous known BxB>6 expands reduced to a TE3 puzzle

One would expect these new TE3 puzzle to have [at least] the qualities of their BxB>6 expand
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Re: The BxB classification of T&E(2) puzzles

Postby coloin » Thu Jul 24, 2025 2:54 pm

Generating BxB6 and finding TE3 and BXB>6 .. seems that there is many more.
There is occasional overlap of twin expands in previous batches.
Here are new batches of max-expands 11-15 and a link to the 4248 new minimals

Hidden Text: Show
Code: Select all
Master 11                                                                                                           
                                                                                                                   
.23..678.4.6....3278...36.4..45.8......9.........62348......47..4237.8.6..7....23 #7 #   546 FNBP C34/M1.3.49    # 7
12..567...5678.1..7.81.2...215...8.7.......4....2..53.57.82..168.16......62...... #7 #   543 FNBP C34/M1.3.49    # 7
1.34...8945....13..891..5.4....7....5..96.......3.14953.5.489.18.....34........58 #7 #   547 FNBP C34/M1.3.49    # 7
.234.6...4.678...378..32..62.4.6783...83.4......82...........9...2....17...2736.4 #7 #   546 FNBP C34/M1.3.49    # 7
.234.6...4.678...378..32..62.4.7386...86.4......82......2....17.......9....2673.4 #7 #   547 FNBP C34/M1.3.49    # 7
.234..78.45.7...237.8...4.5.......383.....5.458..4327.....1....8..29.......5.7842 #7 #   540 FNBP C34/M1.3.49    # 7
.234..78.45.7...237.8...5.4.......383.....4.558..4327.....1....8..29.......5.7842 #7 #   540 FNBP C34/M1.3.49    # 7
....5678...6....32.......64.378.5...5.816..7.61...7.5.3.56.8..7....13..5..157.... #1 # 97078 FNBP C33/M2.39.168  # 7
.23......456...12..98..2.....1...49.6..9.1.52......6.1.6..1524....29..16.1.6.49.5 #1 # 91548 FNBP C34/M2.54.605  # 7
1.3.56....571.9.3.69.73.....3657.9......61..3.1.9.3....6.....74.7......2...6.735. #1 # 97159 FNBP C33/M2.30.654  # 7
1.34.6........9..3...327..5.158..6.438.6..5..6.4....3854..683.1..6..1...8.1.....6 #1 # 96215 FNBP C34/M2.34.192  # 7
1.......9...18.23.8.....1.52.16.73..37.81.6...86.32......7.8...6.8.21.7.7..36.... #2 #   914 FNBP C33/M1.3.4     # 7
...4...89..7....3.......1.527.3.4.9.3.9.28....4879..2..3487.9.2..29.3.......42... #1 # 95323 FNBP C32/M2.44.447  # 7
12..5678..57.8....8.6......26..75....7.6.1..55.182...7...51.94.........1.1.....72 #1 #  1105 FNBP C32/M1.1.47    # 7
12..56....5.....3.8.9.......7..615.3.1.5.762....23..17...7.3...7.1.2536....61..7. #2 #   914 FNBP C33/M1.3.4     # 7
12....7..4.678....79..........6.83...8..476.1.6.31........6481.6..8.34.78...7..36 #2 # 97109 FNBP C33/M2.39.168  # 8
....5678...6....32.......64.358.7...61...5.7.7.816..5.3.76.8..5....13..7..157.... #2 # 97085 FNBP C33/M2.39.168  # 8
.23.56......18.23......34..2.5...9...46.9.3.293.......3.4...52.59...26.4.62..5.93 #2 #  1434 FNBP C34/M1.2.40    # 8
.23.56......18.23......34..29...56.43.4...52..65..2.935.2...9...46.9.3.293....... #2 #  1434 FNBP C34/M1.2.40    # 8
1.3.567...571.9...69.37.1......3...83.9...51.....9.3.47.1.6.....3591..6.96......1 #2 #   747 FNBP C34/M1.4.4     # 8
...45...9.....9.3.69..72...26.71.39.3.1.......79....1.7.6..192..32....7191...76.3 #2 #   747 FNBP C34/M1.4.4     # 8
.2..56....571.9..6...27.....619.7....9.56.1..7.5.216..51.....48....15962......5.. #2 # 95802 FNBP C33/M2.44.149  # 8
..345..89....8923...92.35.4...93..5..3..48.92.9.5......12....4..64......9.83.4... #2 # 95765 FNBP C33/M2.44.149  # 8
12.456.......89..66...3....2...7.6.8.......727.682.91..71..8.9.8.2..7.6196....8.7 #2 # 97772 FNBP C35/M2.24.1911 # 8
1...56......18...668.2.71.521.7.....5.8.21....768.5.1.....78.217.......486....973 #2 # 97774 FNBP C35/M2.24.1911 # 8
.23.5..8945..8.23.8.9...4.5...73.9..3.8.45......6.....5.2...8...348.259.98.5..... #1 #   956 FNBP C34/M1.2.40    # 8
12.......4.6...132.89......2..6.7.136...214.7...34.62.....6..7..62.73.41..7.....6 #2 #  6824 FNBP C33/M2.235.27  # 9
12.......4.6...123.89......2...416.76..3.7.12...62.43.....6..7..62.73.41..7.....6 #2 #  6824 FNBP C33/M2.235.27  # 9
.2..5.......1.92366..27....29....36....9...21.163..9.4.4....69..62.94.13......4.2 #1 # 97767 FNBP C33/M2.46.142  # 9
12........571.92.66.92.....29.6.1.5..71......5.67...2....51.893......5.49.5....72 #3 # 95037 FNBP C33/M2.42.156  # 9
12........571.92.66.92.....2.67...5..71......59.6.1.2....51.893......5.49.5....72 #3 # 95032 FNBP C33/M2.42.156  # 9
1.34.678........36.....31.4245.68...37....4.89.8............67..3...78.1.8.6.1.43 #3 # 95040 FNBP C33/M2.42.156  # 9
1.3.5.78..57.8..3668....1.5.71......36.7...518.5....7.5.683........64.1....2...6. #1 #  3012 FNBP C33/M1.1.70    # 9
....56......78.132...1.2.......4...8.34.28.71..8....4.3.7...82..128..4.784.2...13 #2 #  2594 FNBP C33/M1.2.45    # 9
....56......78.123...1.2.......4...8.34.28.17..8....4.3.2...87..178..4.284.2...31 #2 #  2594 FNBP C33/M1.2.45    # 9
1.3.5.78..57.8..3668....1.5.7...5...36.....515......7.....1....816.37......264.1. #1 # 95090 FNBP C32/M2.32.1025 # 9
12..5678.....8.....8...1...247....6.8.5.27...93.....7...21.865.....628.7..857..21 #1 #  1924 FNBP C34/M1.4.15    # 9
...4567.9......12........64.9436....3.7.45..656.9.7....7...3....35.946......7.3.. #1 #   335 FNBP C31/M1.2.46    # 9
1.34.6......7....17....1......3486.73.....4........352.318.4...6.417.8..87..631.. #1 # 82692 FNBP C32/M2.16.2460 # 9
....5..8.457....36....7.1.5.34.9....56..4739.7.9......34..65....76..4..39.573...4 #1 # 16682 FNBP C34/M2.55.238  # 9
12.....89.5....23.......1.52.15..8.3.352...9198.3..52..1.94.....9...7......8.39.2 #1 #  6674 FNBP C33/M2.96.68   # 9
1...5678....18..636..7.31.5.......58.....56.1.658.137.3.6...817..2......79....... #1 #  8821 FNBP C33/M2.102.64  # 9
.2.45..89.5..8912..9.2.15.4.1..48...34....8....7..........249.8...89..51...1.52.. #7 #  1221 FNBP C33/M2.71.92   # 9
.2345....45...9...6.9.23...2.6...5.......261.........739..654..5.29.43...6423.9.. #7 #  1216 FNBP C33/M2.71.92   # 9
.2345....45...9...6.9.23...2.6...5.......261.........73.29.54..56..349...9426.3.. #7 #  1216 FNBP C33/M2.71.92   # 9
.2345....45...9...6.9.23...2.6...5.......261.........73.42.59..59..643...6293.4.. #7 #  1216 FNBP C33/M2.71.92   # 9
1.3.5.78..57.8..3668..3.1.5.61.7.........4......21..6.5.8....7.73....6.8.16...35. #7 #  1226 FNBP C33/M2.71.92   # 9
1.3.5.78..57.8..3668..3.1.5.16.7.........4......21..6.5.8....7.73....6.8.61...35. #7 #  1226 FNBP C33/M2.71.92   # 9
1.3.5.78..57.8..3668..3.1.5.16.7.........4......21..6.5.8....7.76....3.8.31...65. #7 #  1226 FNBP C33/M2.71.92   # 9
1.3..67.9.57..9.3696...715..9....67........91.71.9.5.3.3..4.......2.3......9653.7 #3 #   742 FNBP C34/M2.94.69   # 9
12...6.89.56..91.28.9..156.2.56..8.1.68......91......65.1962......3....5....45... #3 #   742 FNBP C34/M2.94.69   # 9
1.3.56.8..5718..3.68.7.3....685.7..3...61......1.38.........96...6....54...86537. #3 #   758 FNBP C34/M2.94.69   # 9
..3.56.....71.9.36..937.15..3..1567......3.91......5.3.415.7....96....1.8....1... #1 #  3199 FNBP C32/M2.57.115  #10
1...5678....18..366..7.31.5.......58.....56.1.658.137.3.6...817..2......79....... #1 #  8755 FNBP C33/M2.104.63  #10
.....67..4.7189......37....21........94...1..7.8..14.2.41.9..278.2.4.9.197..1.84. #2 # 21573 FNBP C34/M2.75.87   #11
..3.567.9..71.9.36..937.15..3.6.5.17...79...3....31...3965.7....4......58.5...... #2 # 22416 FNBP C34/M2.75.87   #11
123.56......18..3....7.3...2.6.1..93..5.9....9......5.36....91.5.1...3.2.92..1.65 #1 #   291 FNBP C32/M1.2.41    #12
1.3.......56...13278.........563..91..1.952.3...1.256....5..9..51.92.3.6.9......5 #2 #  2604 FNBP C33/M1.2.45    #12
1.3.......56...13278.........563..91..1.925.3...1.526....5..9..51.92.3.6.9......5 #2 #  2604 FNBP C33/M1.2.45    #12
......7.9456....31......56..1......836.84...58..1.....5.13.4...64..18.5..3856.... #2 #   338 FNBP C31/M1.2.46    #13
...4.6.......89132...23....2.1....98.95.2.3.183....25......59..51...28.39.......5 #2 #   330 FNBP C31/M1.2.46    #13
.2345..89.5.....3.....3...52...953.43..82.59....3.4.28.72......8.1......93....842 #1 #   332 FNBP C33/M1.4.42    #13
.2....7..45.7.9...7..2...........69.394...25....9...415.739.....325.4.7.94..72.3. #2 # 38659 FNBP C32/M2.63.208  #13
.23...7.9.5...9.....9.....5247.35.......71......62...753..9.2.4.72.4.59.9.4....73 #2 # 40046 FNBP C32/M2.63.208  #13
                                                                                                                   
Master 12                                                                                                           
.......8....189.36......5.4.316.8.7.76..93...9.871..6..7..61....1983.6.7...9.7... #3 #  3816 FNBP C33/M2.235.27  # 7
.......8....189.36......5.4.317.8.6.76..93...9.861..7..7..61....1983.6.7...9.7... #3 #  3816 FNBP C33/M2.235.27  # 7
...45.........9...689.72...29.71.86..18......7.6....1..61..792.8.2....7197...16.8 #3 #  3816 FNBP C33/M2.235.27  # 7
.2...6...4.7....3668...3........7.51..1.3546.......3.7....61.455..3.417....57.6.3 #1 # 96047 FNBP C32/M2.22.298  # 7
1..4..78.4.718.2.3.......1424.967...7....4......8.34..3.2..8..1.74..18.281....3.. #6 # 95445 FNBP C34/M2.32.205  # 7
1.3..6..945.1.9.36.96...........19......951729.....4.33...64...56.91.3...4.5.36.. #6 # 95436 FNBP C34/M2.32.205  # 7
1.3..6..945.1.9.36.69...........16..6.....4.3....651723...94...59.61.3...4.5.39.. #6 # 95436 FNBP C34/M2.32.205  # 7
....56......1.926...923..15.3.....96...9..13.91.36.5.2392...65..4.5......8569.... #6 # 95416 FNBP C34/M2.32.205  # 7
.234..7.94.7....6369.........9..8......724.96.469.5.....4....32.62.4397......26.4 #6 # 95452 FNBP C34/M2.32.205  # 7
...4.6...4.7.892.66..27...424..9.....76.28.4.9.8..4.2.....6..927......6.86....173 #6 # 95425 FNBP C34/M2.32.205  # 7
1.3.567...571.9...69..3.5......9.1.4......9.897....36551.......7.6.......39.61.5. #1 #   792 FNBP C32/M1.3.5     # 7
....56.8..5.18....68.3.7.1..167.8...37.51...88.5..3.......318.7.3.....4..6.....23 #1 #  1111 FNBP C32/M1.1.47    # 8
...45...9.....9...698.72...26.71.89..81......7.9....1..16..792.8.2....7197...16.8 #3 # 37045 FNBP C34/M2.94.69   # 8
...45...9.....9...698.72...26.71.89..81......7.9....1..76..192.8.2....7191...76.8 #3 # 37045 FNBP C34/M2.94.69   # 8
...4.....4...89......37.154.317..64.5.46...7167....3.5.6....4.7......56..45.67.13 #3 # 36791 FNBP C34/M2.94.69   # 8
...45..89..6.8.....982.3....14.9.86.8.5.4..9196....4.5..1...94........166.91..5.8 #1 # 13199 FNBP C34/M2.77.255  # 8
.234.678.4.7......68.7.....24....8.3...6....2...24.19.3.48.2..787.36.....62.....8 #2 # 97254 FNBP C33/M2.26.252  # 8
.234.678.4.7......68.7.....24....8.3...6....2...24.19.37.86....8.43.2..7.62.....8 #2 # 97254 FNBP C33/M2.26.252  # 8
1.3....89.57.89...9...2..........49...489..21....4.3.83..91.84....2.8.138...349.2 #1 #   959 FNBP C34/M1.1.40    # 8
1.3..678..57....3668...75.1..8...67.5.687..13....6.8.5..5.21.......9.......6.3157 #2 #  2907 FNBP C35/M1.1.51    # 8
1.3.567...5718....68.7.35...3....1..71.....24....7185..6.5.7....71.38.6....61.... #1 # 13855 FNBP C34/M2.75.87   # 8
1.34...8945....13..891..5.4.14...8..3.8.4....59..184.3....7.......96.3..9315.4... #2 #  2907 FNBP C35/M1.1.51    # 8
12......94.71.9....8......1..6.14.97.7.69.......5.7..6....4597.5..76..147..9.16.5 #2 #   747 FNBP C34/M1.4.4     # 8
12..56.8..5718....8.67.2.1.2.5.671.871........68.1........7..6....6..9.36.2...85. #2 #   747 FNBP C34/M1.4.4     # 8
..3.5678...718..36......5.129.6.....346......7.5...6.3....7..6887..613.5......17. #1 #  4909 FNBP C33/M2.124.104 # 9
.23.5.7.945.....327.9.3.54..7.....53......4.7.345..92..4.89........25394....41... #2 #  6371 FNBP C34/M2.94.69   # 9
1.3..678..57....3668...75.1..8....675.6.7.1.3......85...5.91......2.5......7.3615 #2 #  6477 FNBP C34/M2.94.69   # 9
1.3...7...571...3668.3..15..75.3.86...1.6.....6..........842.7.....93....385..... #2 #  1025 FNBP C30/M1.1.39    # 9
......7.9.5.1.9.36.6.37.51.2.86.7...6.4.......35...69....5..9.1.......7...17..36. #2 #   777 FNBP C30/M1.1.39    # 9
12.....89.5....2.68.6...15...157.........4......9...1..182..96.56.8...219.26..8.5 #1 #  1606 FNBP C32/M2.74.88   # 9
.23.56...45......6..9.....5.1..658.3.3.8.1.52...23.61....6.8.......13..8..852..61 #2 # 20260 FNBP C33/M2.52.126  # 9
1.3..67.9.57..9.3696....15....6.53.7...2......1..43....9....67........91.7196.5.3 #2 # 19930 FNBP C33/M2.52.126  # 9
.23..678.4.7....3668...34.....3.7864...5.8.....8.94.....2...3.88.6.3..47......62. #1 #   742 FNBP C33/M2.97.67   # 9
1.3...789.57..9...6.9........189.4.7..8.41.93...7.381.........8.1.9.837......49.1 #1 # 17816 FNBP C33/M2.72.91   # 9
..34.....4......3.7.923.54.2.5.47......825.9....16..5.57...4.2..34..297.9.2...4.5 #1 #  2013 FNBP C34/M1.4.15    # 9
1.3..67.9.57..9.36......15..1684........21......9.7..1......9.55.139.67...9....13 #2 # 95136 FNBP C32/M2.65.100  # 9
1.3..67.9.57..9.36......15..1984........21......6.7..1......6.55.136.97...6....13 #2 # 95136 FNBP C32/M2.65.100  # 9
...4...89....8923....23.1.4.613.....7..........8...3.1..981..42..29.48.3..4.2391. #7 #  1221 FNBP C33/M2.66.99   #10
12.....89.5....26.6.9..21.521.8..95..96....288.52..6.1.....7......9.8516....4.... #7 #  1215 FNBP C33/M2.66.99   #10
12....7.9.571..26.6.92...15.....3.......4....96571....5.6.2..9771....62..92...5.. #7 #  1211 FNBP C33/M2.66.99   #10
12..5.........9......32..1.21.....477.5...6.1.64....5..72.4..6554..6.17.6.1.7.4.2 #7 #  1217 FNBP C33/M2.66.99   #10
1.3.56.8..5.18....68.2.3...26.53...88.5.61..2.318.2.........4.........7....615.23 #7 #  1221 FNBP C33/M2.66.99   #10
1.3.56.8..5.18....68.2.3...2.5.61..886.53...2.318.2.........4.........7....615.23 #7 #  1221 FNBP C33/M2.66.99   #10
12.4..7.94.7...23...9....14.....8......32.971...6.....39..4.1.7.12...34.7.4.3..92 #7 #  1221 FNBP C33/M2.66.99   #10
.23...78.45.7...237.82..5.4.45..783.37....2.58......47.....1........2458....6.... #2 # 45717 FNBP C32/M2.32.205  #10
.2345..8.45..89.3.8.92.3.4.........7..5...62.....25...59..48.....493.....385.2... #2 # 45311 FNBP C32/M2.32.205  #10
..34.....4.718..36....3..4....86.3.4.4...3.18.3..4167..6.......5.2....6..14678... #1 #  1287 FNBP C32/M1.5.10    #12
......7.9456....31......56..1......836.8.41.58..1.....5.134....64..18.5..386.5.1. #1 #  2486 FNBP C33/M1.2.45    #12
.2..5....45..891.2.....25.........4....81429..4....3.6.1294..5.5.4.28...89.5.1.2. #2 #   800 FNBP C33/M1.2.45    #12
.2..5....45..891.2.....25.........4....81429..4....3.6.1492..5.5.2.48...89.5.1.2. #2 #   800 FNBP C33/M1.2.45    #12
.2.45.7.9.5.7.9.23.9..3254........75.....54.2..5.4793.5.2...39463...4....41...... #2 # 49393 FNBP C35/M2.36.182  #12
.2.45.7.9.5.7.9.23.9..3254........75.....54.2..5.4739.5.2...93463...4....41...... #2 # 49393 FNBP C35/M2.36.182  #12
.234..7.945.7...327.92..54.2.....4.3......29.93...2.573..5.8......31........24375 #2 # 39958 FNBP C35/M2.41.160  #12
.234..7.945.7...327.92..54.2.....4.3......29.93...2.753..5.8......31........24357 #2 # 39958 FNBP C35/M2.41.160  #12
12..56....5.1.9...6.923....2.....8.7...6.2.139.....42.3.29.16.......3......5..3.. #2 #  3741 FNBP C29/M2.108.60  #12
.2......945..89..39.............8.76.....48.183....59.3.28.5...54.2......89.43... #2 #  3169 FNBP C29/M2.108.60  #12
1.3456....56......78.........159.63.....43.51..56.19.4...9...1.51.36.49.9...1.... #1 #  2606 FNBP C33/M2.122.106 #13
......7.9...189.36......15..68.13...3.489...191.6.4..3.3..4.......3...4.84.96.3.. #4 #   306 FNBP C32/M1.3.13    #13
1...5678....18..366..3.71.5.6.5.837...5...6.....6...5.3.6...817.12......74....... #4 #   328 FNBP C32/M1.3.13    #13
12.4...894.6...1.2.892..64.2.....9......9..2.96...281....12.468...8.7.......34... #4 #   306 FNBP C32/M1.3.13    #13
..345.7.9...7.9.32..9.3254..4....3..3...742.5.....3..46.5.......32...95791....... #4 #   328 FNBP C32/M1.3.13    #13
.2..5.....5678.1.2...2..5.........6..6....9.3...61827..728.5...5.816..2.61..72.5. #2 #  2555 FNBP C33/M2.257.50  #13
.2..5.....5678.1.2...2..5.........6..6....9.3...16827..728.5...5.861..2.61..72.5. #2 #  2555 FNBP C33/M2.257.50  #13
....56......78.132...1.2...2.1...4.784.2...13.37...82.3.4.2..71....4...8..8....4. #1 #   331 FNBP C31/M1.2.46    #14
                                                                                                                   
Master 13                                                                                                           
12..56.8..5718....6.87.2.1.27.6..1.88.5.......168......62....71......9.4...5...2. #1 # 47737 FNBP C32/M2.60.436  # 7
...45.........9...689.72...29.71.86..16......7.8....1...1..792.8.2....7197...16.8 #1 # 95131 FNBP C32/M2.33.396  # 7
.23......4...8....69....1.4....7.9.8.79.1864........71...79.8.67..8..49.9...64.17 #3 # 15912 FNBP C32/M2.60.436  # 7
1..45.7.94..1.9.3.....7314.....314.....54.....149.75.3.62......7.1.95...9.....3.. #3 # 16161 FNBP C32/M2.60.436  # 7
1..45.7.94..1.9.3.....7341.....341.....51.....419.75.3.62......7.4.95...9.....3.. #3 # 16161 FNBP C32/M2.60.436  # 7
.......894..18.2.6.8....41....8.46.1..8.91.42..426.89..32.......71.2....946....28 #1 # 95042 FNBP C34/M2.55.595  # 7
1.3...7.9.571...3669.7..51..35.6.19.7.1......96...1...3.951.........83.....3.29.. #2 # 43172 FNBP C33/M2.78.84   # 7
.2.4.....4...89......73..142.13..46..746..3.163.....27......6.2.6.....43.4..6317. #2 # 45952 FNBP C33/M2.78.84   # 7
123...7.945.7.....78.......2..1.739.....92.149..34.2.7.9....42...29.4.71......9.3 #1 # 87876 FNBP C34/M2.58.565  # 7
12..567.9.5......6......15.29.6..57..61....927..2..6.1...96...7.72.48....1.7..... #1 #  5945 FNBP C32/M2.60.327  # 7
12.4...894.6...2.1.982..64.2.4...9...19..4...68..9241......7...84.62.......8.51.. #1 #   958 FNBP C34/M1.2.41    # 8
1.3....89.57.89...9...2..........49...489..21....4.3.83..21.84....9.8.138...349.2 #2 #   933 FNBP C34/M1.1.40    # 8
12..5.7.9.57...26.6.9.7..51.....4....6571........68..2.169.7.2559......77.2..5... #2 #   933 FNBP C34/M1.1.40    # 8
.2.45.7.9.5.7.9.32....3254..4..9....6.824.....35....24....7.2.5......47...7.24.93 #1 #  1395 FNBP C34/M1.2.40    # 8
.2.4.67..4.7.892..86.72..........4....4...82.....74.53.42.9....78.64..929.6...... #1 #  1093 FNBP C32/M1.1.46    # 8
1.345....45...91...89.315.....9.3..553..48.919..51....3.....8.7.....541.8.......6 #1 #   880 FNBP C33/M1.2.47    # 8
12..56.8..5718....6.87.2.1.27.6..1.88.5.......168......62....71....6.9.4...5...6. #1 # 44186 FNBP C33/M2.78.84   # 8
...45.........9.3.69..27...26.....1.3.1.......7921..6.71.....23.36..29.19.2..167. #2 # 50467 FNBP C32/M2.61.107  # 8
...45.........9.3.69..27...26.....1.3.1.......7921..6.73.....21.16..29.39.2..167. #2 # 50467 FNBP C32/M2.61.107  # 8
12...678..57...2.66.8..2.152.56......16....2.78.21.56....3........9.7.5..72.68... #2 #   962 FNBP C34/M1.1.40    # 8
12...678..57...2.66.8..7.1528.71.56..16....7.7.56........3........9.2.5..72.68... #2 #   962 FNBP C34/M1.1.40    # 8
.23...7.9.5...9.....9.....5247.35.......28..7...17....57..9.2.4.32.4.59.9.4....73 #2 #  6694 FNBP C32/M2.82.160  # 9
12....7.9.5.7.....7.....5..21..6..756.7...29..95.7.6.1...81.9......93...96152.... #2 #  6835 FNBP C32/M2.82.160  # 9
12..5678..5....1......1..5.24........17...6289.8.........6.821...2.718.5..152..67 #1 #   325 FNBP C33/M1.4.42    # 9
1...5678....18..636..3.7....658.137......5......67..5..42....17791....3.8.671.... #1 #  1098 FNBP C34/M1.4.39    # 9
.2...6...45.....366.9..7.........8.7.....8.53....7364.3..7.5.685..83.47.8...643.5 #2 #  2063 FNBP C33/M1.1.69    # 9
.23.5.7.945.....327.9.3.54..7.....53......4.7.345.792....89........25394.....1... #2 #  2063 FNBP C33/M1.1.69    # 9
.....67..4.7189......37....21........94...1..7.8..14.2.41.9.82.87..4.9.19.2.1..47 #1 # 22928 FNBP C34/M2.96.68   # 9
....5.......1.9.3.6.9.72...29.74.36.7.6....4..4.......3.2....74.64..792.97...46.3 #1 #   834 FNBP C32/M2.62.105  # 9
1..4.6.......892.66...3....2.1.7.96........717.....8.2.72..819.81...26.79.6....28 #1 #   828 FNBP C33/M1.1.42    # 9
.23.5.7.945.....327.9.3.54......3..539.5.72.45.....3......9........459279..1.8... #3 #   479 FNBP C33/M1.3.38    # 9
.234.6..94.6.89..389.23.......9..3..36.8.249.9....3......6249.86.....51.........6 #3 #   479 FNBP C33/M1.3.38    # 9
1.3..678..57....3668...71.5...94..1......1...8156.3...53.86..717......6..6.7..... #3 #   478 FNBP C33/M1.3.38    # 9
.2345..8.45..89.3.8.92.3.4.........7..5...62.....25...59..48.....893.....345.2... #2 # 53452 FNBP C32/M2.37.177  # 9
.2..5678..5.18.2.6.8.2.7.15...67....3.........74....6....7.862.....21.5....56.1.8 #2 # 52386 FNBP C32/M2.37.177  # 9
12..56....5718...66.82.7..5.......48.8....9.1...861.52.7.5.8...86..125.....6..... #1 #  5781 FNBP C33/M2.64.102  #10
....56..9...1......9..2....2.....37.3.9....54.74...9.2.35.7.42.7.2.4..9394..3.5.7 #1 #  1611 FNBP C32/M2.77.85   #10
1.3.5..8945..8.1.3.89.3.54..35...8..84.......9.1...3.439.51.......6..9......974.. #3 #   812 FNBP C33/M1.3.14    #10
......78.4.7...2.38......542..6........5.342.7...92...3.4..587.57...8.42.82..43.5 #3 #   812 FNBP C33/M1.3.14    #10
....5..89...18.32.......5.12.9...8.334..1......6.3....5...91.388..3.529.9..82.1.5 #3 #   812 FNBP C33/M1.3.14    #10
12.......4.7...2.3.89.2.....4.83.6.7.7.6.234..3..74.28....4.87...4.68.32......4.6 #3 # 51853 FNBP C34/M2.41.160  #10
..3.56....571.9..6...37.....91.65...53.71..6.7.69.3.1...5....98...5916.3......45. #3 # 50004 FNBP C34/M2.41.160  #10
..3.56....571.9..6...37.....96.15...53.76..1.7.19.3.6...5....98...5916.3......45. #3 # 50004 FNBP C34/M2.41.160  #10
1.3....8..5718..3668........65..18.331...8.757.8...61.53..17......9.5.6.....4.... #1 # 53031 FNBP C33/M2.54.121  #10
......7.94.7...236....7..5.27.84..6.3.4.6.....68.......3672.4..74.6.83..8.2.346.. #3 #  6543 FNBP C34/M2.94.69   #11
......7.94.7...236....7..5.27.84..6.3.4.6.....68.......4672.3..73.6.84..8.2.346.. #3 #  6543 FNBP C34/M2.94.69   #11
.23.5.78.45..8..237.8.3.5.42.7..543..45......83.....5.37.528........1.7....67.... #3 #  6842 FNBP C34/M2.94.69   #11
..345..89....8923...93.24.5......8.3......95.9..8.5.24392...54..18..4...7.4...... #1 # 70554 FNBP C33/M2.58.113  #11
.2345..8.45..89.3.8.93.2.5..9......7.4....69....93..25.3429.....8.5.3.......48... #1 #  9170 FNBP C33/M2.147.44  #11
123....8.4.7189...8...........69.84.6..7.8.919...146.7....6..7...6..7.......41.68 #2 # 18677 FNBP C32/M2.75.174  #12
123....8.4.7189...8...........69.84.6..7.8.919...416.7....6..7...6..7.......14.68 #2 # 18677 FNBP C32/M2.75.174  #12
1.3.567...571.9...69.37.1......9.34.379...56.......9.8..1.6.....3591.....6.....1. #1 # 62769 FNBP C32/M2.22.596  #12
....5..8....18..368.......521.......56....317.34.1........6187..8.37.5.1.7.5.8.63 #2 # 40036 FNBP C32/M2.64.204  #12
..3.567.9..71.9.36..9...51.2.15.....396....57.4............3.91.3..1567.......3.5 #2 # 39334 FNBP C32/M2.64.204  #12
...4.........892....837.4..2..8.3.973...948.28..72.34..82937...71....9..9.6...... #2 #   909 FNBP C33/M1.3.24    #12
...4.........892....837.4..2..8.3.973..72.84.8...943.2.82937...71....9..9.6...... #2 #   909 FNBP C33/M1.3.24    #12
.2.45..89.5..8923..8...24.52...4359........42......3.8.96......73..9....8.2...953 #2 #   483 FNBP C33/M1.1.49    #12
...45678..5....2.6.......15..83.4..734..75..8.7586...4....38....3654.8.....6.7... #2 #   486 FNBP C33/M1.1.49    #12
...4.678....18..36.8..374.1....4..1...4..1.....8.7364..31.68...862....7.9.5....6. #2 #  3456 FNBP C33/M2.96.68   #12
12..56....571.9...6.927..5..1....8.4.7....315...51.62..9172.5.....6..9...6..9.... #2 #  3446 FNBP C33/M2.96.68   #12
12.4.6...4.6.891...8921.6........4.....6249.8..4...273.419.2......8....1..8..1... #2 # 19153 FNBP C32/M2.57.575  #13
12.4.6..94.6.89..1.9821....2.....578........2...128.646..9.........6..9.9.284.... #2 # 19028 FNBP C32/M2.57.575  #13

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Master 14                                                                                                           
...4.6...4.7.892.66..72....2.4.97.6..7864..2.96.2.8.7.......1.3.....4.928........ #2 #  4200 FNBP C32/M2.62.315  # 7
...4.6...4.7.892.66..72....2.4.97.6..6824..7.97.6.8.2.......1.3.....4.928........ #2 #  4200 FNBP C32/M2.62.315  # 7
...4.67..4.718.2.6....27....15...6...69......8.4761....8..124.7.7.6.482..4.87..61 #19#   650 FNBP C36/M1.1.64    # 7
...4.67..4.718.2.6....27....15...6...69......8.4761....8..724.1.7.6.482..4.81..67 #19#   650 FNBP C36/M1.1.64    # 7
...4.67..4.718.2.6....72....15...6...69......8.4761....7..248.1.8.6.742..4.81..67 #19#   650 FNBP C36/M1.1.64    # 7
...45.789..7..9.....8327.....5...4.88.15...97......51..84..59.151...8.747.9..485. #19#   650 FNBP C36/M1.1.64    # 7
...45.789..7..9.....8327.....5...8.48.15...97......51..14..59.85.9..847.78...4.51 #19#   650 FNBP C36/M1.1.64    # 7
...45.789..7..9.....8327.....5...8.48.15...97......51..14..59.858...4.717.9..845. #19#   650 FNBP C36/M1.1.64    # 7
...45.789..7..9.....8327.....5...8.48.15...97......51..84..59.15.9..847.71...4.58 #19#   650 FNBP C36/M1.1.64    # 7
...45.789..7..9.....8327.....5...8.48.15...97......51..84..59.151...4.787.9..845. #19#   650 FNBP C36/M1.1.64    # 7
...45.789..7..9.....8327.....5...8.48.15...97......51..89..54.15.4..897.71...4.58 #19#   650 FNBP C36/M1.1.64    # 7
...45.789..7..9.....8327.....5...8.48.15...97......51..89..54.151...4.787.4..895. #19#   650 FNBP C36/M1.1.64    # 7
...45.789..7..9.....8327.....5...84.8.15...97......5.1.84..591.51...4.787.9..84.5 #19#   650 FNBP C36/M1.1.64    # 7
..3.567.9..71.9.36..637.15..3.69..15....3.6.7......39.37....561..5.1....841.6.... #19#   650 FNBP C36/M1.1.64    # 7
..3.567.9..71.9.36..937.15..3.96..15....3.9.7......36.37....591841.9......5.1.... #19#   650 FNBP C36/M1.1.64    # 7
..3.567.9..71.9.36..937.51..3.96..51....3.9.7......36.37....195841.9......5.1.... #19#   650 FNBP C36/M1.1.64    # 7
..3.567.9..71.9.36..973.51.246...3....5...6..97.563......37.9......91....9.6.51.3 #19#   653 FNBP C36/M1.1.64    # 7
1.3.5.78..57.8..3668..7.1.5....1.6.....9628..8167.5...53.......7.8...5...615..3.8 #19#   650 FNBP C36/M1.1.64    # 7
1.3.5.78..57.8..3668..7.1.5....1.6.....9628..8617.5...53.......7.8...5...165..3.8 #19#   650 FNBP C36/M1.1.64    # 7
12...67.9.57..926.6.9..2.51...847.9......5.7.79526....57..2.91..12......9.6....2. #19#   650 FNBP C36/M1.1.64    # 7
12..567...571.92..6.927.5...7..65....1692..57...7.1....6....9.8...697.25......6.4 #19#   650 FNBP C36/M1.1.64    # 7
12..56..9.571.9..66.927...52.57.1.9....92....9...65......51796.5.....3477.......1 #3 #  1900 FNBP C36/M1.1.64    # 7
12..56.8..5718..6.6.82.7.5.2.571...88...65......8.2......5718.65.....3747......1. #3 #  1900 FNBP C36/M1.1.64    # 7
1..4.678.4..18..368...731.4....31......84...1.1.6.78.3.41768...6.......7792.....8 #3 #  1903 FNBP C36/M1.1.64    # 7
...4.67..4.718.2.6....27....15...6...69......8.4671....7..648.1.8.7.246..4.81..27 #12#  1884 FNBP C36/M1.1.64    # 8
...45.789..7..9.....8327.....5...4.88.15...97......15..19..58.45.4..897.78...4.15 #12#  1884 FNBP C36/M1.1.64    # 8
...45.789..7..9.....8327.....5...8.48.15...97......15..14..59.85.9..847.78...4.15 #12#  1884 FNBP C36/M1.1.64    # 8
...45.789..7..9.....8327.....5...8.48.15...97......15..19..54.85.4..897.78...4.15 #12#  1884 FNBP C36/M1.1.64    # 8
..3.567.9..71.9.63..937.15..3.96..15....3.9.7......63.37....591841.9......5.1.... #12#  1879 FNBP C36/M1.1.64    # 8
.23.5..8945..8.23.8.9.3.5.4...8.3495..4.9......5741...5.2..894...8....53......8.2 #12#  1884 FNBP C36/M1.1.64    # 8
.23.5..8945..8.23.8.9.3.5.4...8.3945..4.9......5741...5.2..849...8....53......8.2 #12#  1884 FNBP C36/M1.1.64    # 8
12...6....571.926.6.9......2.17.5..6.7569...296..12..5.......41.....1.37716...52. #12#  1879 FNBP C36/M1.1.64    # 8
12..567...571.92..6.927.5...7..15....6192..57...6.7....1....9.8...791.25......1.4 #12#  1883 FNBP C36/M1.1.64    # 8
12..567...571.92..6.972.5.....6.7....6159..27.7..12....1....9.8...971.52......1.4 #12#  1879 FNBP C36/M1.1.64    # 8
12..567...571.92..6.972.5...7..15....6129..57...6.7....1....9.8...971.25......1.4 #12#  1883 FNBP C36/M1.1.64    # 8
12.4..78.4.71..2.6.682...1421.....4..74......8.6.4..72...8...6.682.14......693.2. #12#  1884 FNBP C36/M1.1.64    # 8
...45678..5....236........4.415.8...6.571...878..64..5....71...51.64.8...7.8.5... #5 #   695 FNBP C34/M2.90.72   # 8
...45678..5....236........4.418.5...6.571...878..64..5....71...51.64.8...7.5.8... #5 #   695 FNBP C34/M2.90.72   # 8
1.3.....9.571...3669........69..135.3.1...6.757...3.9173591.......245..3.....7... #5 #   685 FNBP C34/M2.90.72   # 8
1.3.5.78..57.8..3668..3.5.1.3....6.5.163..87........13...27.....7.96.......5.83.7 #5 #   685 FNBP C34/M2.90.72   # 8
12....78..571..2.66.82...1521....6...86......7.5.2.8.1571.62......5941.....7..... #5 #   692 FNBP C34/M2.90.72   # 8
1.34...8945....13..891..5.4...56.....389.1......32....39.....51.14.....88...1.... #1 # 95041 FNBP C31/M2.53.369  # 8
.2..56....571.92.6...27.....9156....76..21.5...59.7.6.....1569.51....8.3.7.....1. #1 #  3106 FNBP C34/M2.72.273  # 8
.23....8945...923.8.9...5.424.9..8.53..5......95.....35.2.94......7....2...6.2..8 #1 # 12595 FNBP C32/M2.39.168  # 8
1.3.......571.9.6369.3........7..9....5...1.6.......245.16.7...7..59.6...69.315.. #1 # 95242 FNBP C31/M2.46.426  # 8
123.56......189.3....2.....23....15.5.63...27.715..6.33.5....6.76........12..537. #2 # 54851 FNBP C34/M2.48.136  # 8
.2.456......18.236.....3...2.1..867.78...21.3.36....28.1....8.2.728..36........17 #2 # 53002 FNBP C34/M2.48.136  # 8
....56......78.123...1.2.......4...8.34.28.71..8....4.3.2...81..178..4.284.2...37 #1 #  2577 FNBP C33/M1.2.45    # 9
...4.678....18..63.8..734.1....4..1...4..1.....8.6734..61.38...832....7.9.5....3. #2 #  3444 FNBP C33/M2.96.68   # 9
12...678..57...2.66.8....1526.7.5......94...2...362..151.6...287..8......8......7 #2 #  3434 FNBP C33/M2.96.68   # 9
..34.6.....7.89.36..973..4.2.4..8....1..47....96...4.......3.94......3.893.8.467. #1 #   564 FNBP C32/M1.2.22    # 9
.2.4.67.9....89....9.72....26....5.1.8....623...26..47.42.97.6....8.2.7.87.64.... #1 #   329 FNBP C34/M1.1.47    # 9
.23...7.94571.....89.7.....2.....6.....2.71.3...6....2..297..61..9.623.7...3.192. #1 #  3890 FNBP C33/M2.70.279  # 9
1.3......45....123.89..1........5..7.35.172.4.7....5..3..57.4.15...2437....1.3.52 #1 #   468 FNBP C34/M1.3.38    # 9
1.3....894....9.....9.....4.18...9.539.5...415.49..83....8.2...8351.4......36...8 #2 # 40920 FNBP C32/M2.63.208  # 9
..3....8..5678.....8..3.....375.8..16.531...881..67..........47571....36....7.2.5 #2 # 38745 FNBP C32/M2.63.208  # 9
1.3...7.9.571...3669.7..51..7951........749.....9.83...6...1....35..719...1...6.. #1 #  1320 FNBP C33/M2.104.63  # 9
1.3...78..571...3668.7..1.5....9....365.1.........4...53......78.6.7.35..71...6.8 #6 #  2057 FNBP C32/M2.38.172  # 9
..34.678.....8..63....735.4..5...876.9.........1......3...47.585..83.6.7...6.534. #6 #  2090 FNBP C32/M2.38.172  # 9
1.3.56..9.571.9..669.37...5.6179....5.9.31....3.6.5.......17..........2..1....8.7 #6 #  2057 FNBP C32/M2.38.172  # 9
1..4.678.4..18.2.68...72.14.3.......7.5....6....76.......62.1.8....1764....8.4.2. #6 #  2090 FNBP C32/M2.38.172  # 9
.2345..8.45..89.3.8.92.3.5.........7..4...62.....24...39..45.....893.....458.2... #6 #  2057 FNBP C32/M2.38.172  # 9
12..5.78..57.8.2.66.8.2..15...3.......1.64.........16.71....82.8.5...6.1..2....57 #6 #  2090 FNBP C32/M2.38.172  # 9
1.3.5.7.9.57....3669..3.51....3.8.6.3.651.......264.7.7.19.365...5......9....5... #1 #   338 FNBP C34/M1.1.48    # 9
1.3.567...5718....68.7.35...3.....7.7........81.67..53....1.69456....8.7....6..25 #1 #  1130 FNBP C34/M1.1.48    # 9
1.3.567...5718....68.7.35...3.....7.7...3....81.67..53....1.69556....8.7....6..24 #1 #  1956 FNBP C35/M1.4.15    # 9
12..56..9.567.9..27.921...52.59......91...5..67....92.......4.....6..3.79.7...2.1 #4 # 97590 FNBP C33/M2.40.164  # 9
12..56.8..5678..2.7.82.1.6.21....65.......9.......741..71...2.65.2...8..86...2... #4 # 97594 FNBP C33/M2.40.164  # 9
.234......57....36.9.........136.5.4..5.4716...65.1.73.1....6.756....34....6...51 #4 # 97598 FNBP C33/M2.40.164  # 9
.234......57....36.9.........536.1.4..1.4756...65.1.73.1....6.756....34....6...51 #4 # 97598 FNBP C33/M2.40.164  # 9
1.3...78..567...3178.1..5.6....751686..8.4......62....36...781.5.....6.7.......53 #1 #  1346 FNBP C34/M1.1.67    #10
1.....7.94.7..9.36......41.....913676..72....7..6.5...3.6...94..149...7397.3..6.1 #10#   414 FNBP C35/M1.1.66    #10
.2..56......1.923....72....21..9.35..35.1.9.49.4.3..12.9....4.154.9.1.23......59. #10#   423 FNBP C35/M1.1.66    #10
.2..56......1.923....72....23..1.95..15.9.3.49.4.3..12.9....4.154.9.1.23......59. #10#   423 FNBP C35/M1.1.66    #10
.2..56......1.923....72....23..1.59..15.9.3.49.4.3..12.9....4.154.9.1.23......95. #10#   423 FNBP C35/M1.1.66    #10
1.3.5.78..57.8..3668..3.1.5.368.5......27..6.....64...36.5.8.178.1....5..75...... #10#   414 FNBP C35/M1.1.66    #10
1...56......18....86.2.75..2.6.71.5.57.82.....816.5.2....7621.56......737.....96. #10#   414 FNBP C35/M1.1.66    #10
....56...45.1.9......73..5.2.1....9.39........459.132.53..4.91..14.9.5.29.2.1..43 #10#   414 FNBP C35/M1.1.66    #10
....56...45.1.9......73..5.2.1....9.39........459.132.53..1.94..14.9.5.29.2.4..13 #10#   414 FNBP C35/M1.1.66    #10
..34.67.9...1...36......14..31...9676.57.....78.6.....3..96..71...3.749.9...146.3 #10#   420 FNBP C35/M1.1.66    #10
1.3.......571.....68.37..5..165.7..83.586....87..31..5...6..9.7768...51....7...26 #10#   423 FNBP C35/M1.1.66    #10
1.3.......571.....68.37.51..165.7..83.586....87..31..5...6..9.7768....5....7...26 #10# 97909 FNBP C35/M2.20.656  #10
...45..8..571.9........2.5..78.1..955.9.7.6.161..9.87..81......7.59.1.6896.....1. #10# 97898 FNBP C35/M2.20.656  #10
...45..8..571.9........2.5..18.9..755.9.7.6.167..1.89..81......7.59.1.6896.....1. #10# 97898 FNBP C35/M2.20.656  #10
1.3.5.78..57.8..3668..3.1.5.368.5......26..7......4.6.36.5.8.178.1....5..75...... #10# 97904 FNBP C35/M2.20.656  #10
1.3.5.78..57.8..3668..3.1.5.365.8......26..7......4.6.36.8.5.178.1....5..75...... #10# 97904 FNBP C35/M2.20.656  #10
1...56......18....86.7.21.52.6.71.5.57.82.....816.5.2....2675..6......737.....96. #10# 97915 FNBP C35/M2.20.656  #10
.2.4........1.92.6.8..23....1.....97.789.162.......1.8.91.6.8.27.2.1.96.86..9..71 #10# 97906 FNBP C35/M2.20.656  #10
..3456...4.7.....669......4.31.654.8...34...1...8.1...3..61..455...3481....5.86.3 #10# 97895 FNBP C35/M2.20.656  #10
.2345...945..89..38.93.2..42.5.3849...459.......2.4......8.394...8....7...2...6.8 #10# 97908 FNBP C35/M2.20.656  #10
.2.4........1.92.6.8..23....1.....97.789.162.......1.8.61.9.8.27.2.1.96.89..6..71 #10# 97906 FNBP C35/M2.20.656  #10
.234..78.45.7...237.82..5.428.374......89.........1..85.7.......42.....783...7.52 #1 #   789 FNBP C34/M2.102.64  #11
.2.45.7.9.5.7.9.23....3254.24.375...63........78....3....52..9....9.3.....2.4735. #1 #   742 FNBP C34/M2.89.73   #11
.2.45.7.9.5.7.9.23....3254.24.375....78......6...........9.3......52..9.9.2.4735. #1 #  8592 FNBP C33/M2.156.42  #11
1.34.6.8...7......68...7.........39......34.2.36...1.83.4.786...1864....76.3.18.. #1 # 96208 FNBP C32/M2.25.524  #11
....5..89.5.18.2.6......15...6...8.1..582.69...9.61.253........562...9.8.71..8... #1 # 31944 FNBP C32/M2.41.160  #12
.2.4.6.......8....86.73..4...6...5.8.......9....67.423.482.3..763..47..2...86...4 #1 #  2097 FNBP C31/M1.1.48    #12
1.3.56.8..5718..3.68.3.7........3..1.3..1....71..653.8.6....874.7....9.2....78.53 #2 #   333 FNBP C35/M1.4.15    #12
..3.567.9..71.9.36......51.27...1....36...1.78415.7...39..1567.......3.1.....3.95 #2 #   308 FNBP C35/M1.4.15    #12
                                                                                                                   
Master15                                                                                                           
                                                                                                                   
...4.6.894.....13.......45.21..94.6....62....6..8.1....42.689..8.19.26..96.14.8.. #2 #   694 FNBP C34/M2.91.72   # 7
...4.6.894.....13.......45.21..94.6....62....6..8.1....62.489..8.19.26..94.16.8.. #2 #   694 FNBP C34/M2.91.72   # 7
.2.45..89.5..8923..9.3.24.52...35.48...82.......9.4..2.3......47.6.....398.5.3... #1 # 28595 FNBP C34/M2.83.316  # 7
............189.3.......45.27.39.....918.2.7.8...71....127.3...7.891...393..28..7 #6 # 95268 FNBP C32/M2.26.252  # 7
..34.678...718..36..8.731.4....143.8...6.8.71...73..4.5............61...9.6....1. #6 # 95292 FNBP C32/M2.26.252  # 7
..34.678...718..36..8.731.42.1.6..........61.5...........63.8.1....4..73...8.746. #6 # 95281 FNBP C32/M2.26.252  # 7
.2.45..89....8926......24.5.........73........6....548..65.482...2.689.4...92..56 #6 # 95287 FNBP C32/M2.26.252  # 7
.2.45..89....8926......25.4.........73........6....845..65.842...2.649.8...92..56 #6 # 95287 FNBP C32/M2.26.252  # 7
1.3.5.78..57.8..6386....1.5.........371..5......2.4...5.6....3873...86.1.18....7. #6 # 95277 FNBP C32/M2.26.252  # 7
.2.45..89.5..8923..9.2.35.4.8..3....731......9.5...328......49.5...4.8.3.......52 #11#  3831 FNBP C33/M2.56.468  # 7
.2.45..89.5..8923..9.2.35.4.8..3....731......9.5...823......49.5...4.3.8.......52 #11#  3831 FNBP C33/M2.56.468  # 7
1.3.5...945........98.......1453.9..3.98.14..58..943......1.82.841....93......17. #11#  3829 FNBP C33/M2.56.468  # 7
1.3.5...945........98.......4153.9..3.98.14..58..943......1.82.814....93......17. #11#  3829 FNBP C33/M2.56.468  # 7
1.3.5...945........98.......4159.3..3.98.14..58..349......1.82.814....93......17. #11#  3829 FNBP C33/M2.56.468  # 7
1.3.56..9.571.9..669.37...5.39......5.1......76...1.9.375...96......74.3......8.7 #11#  3829 FNBP C33/M2.56.468  # 7
1.3.56..9.571.9..669.37...5.7..15.9....9.3......76..........4.1.1....8.3...63195. #11#  3829 FNBP C33/M2.56.468  # 7
1.3.56..9.571.9..669.73...5.7..15.9....9.3......67..........4.1.1....8.3...36195. #11#  3829 FNBP C33/M2.56.468  # 7
1.3.56.8..5718..3.68.7.3.1..61......3.8......57..6...8735...8.1......972....7..5. #11#  3829 FNBP C33/M2.56.468  # 7
....5.7..4571.9......372....49......57.9..6..6.1.......14.9.56.7.5.4.9.196..1..47 #11#  3829 FNBP C33/M2.56.468  # 7
....5.7..4571.9......372....49......57.9..6..6.1.......15.4.96.76..9..419.4.1.5.7 #11#  3829 FNBP C33/M2.56.468  # 7
..3.56.....71.9.63..937.51.28..9....7.6....5...5.1....3...61.95....3.67.......3.1 #1 # 95005 FNBP C31/M2.52.378  # 7
.23.5..8945..8.23...9.2.4.5....4.9....4.32......7.18..3.2...5..59........48..539. #1 # 95198 FNBP C32.m/M2.55.119# 7
12..56..9.571.9..66.972...5291...65.......4.1.....13.2.16..5...57.......9.2.1756. #8 #  1893 FNBP C36/M1.1.62    # 7
12..56..9.571.9..66.972...5291...56.......4.1.....13.2.16..5...57.......9.2.1765. #8 #  1893 FNBP C36/M1.1.62    # 7
...45.789..7..9.....9327.....5...4.77.15...98......15..78..49.551...8.749.4..581. #8 #  1889 FNBP C36/M1.1.62    # 7
...4.67..4.718.2.6....72....15...6..7.4618....69.......4..618.7.8.2.746..7.84..21 #8 #  1893 FNBP C36/M1.1.62    # 7
......7.9...18926...9...4.1...56.....95.1862...69.2...56..21..8.1289...69.86.5..2 #8 #  1893 FNBP C36/M1.1.62    # 7
...4..7.9457....36......4.1.68......3.46.....57.84..6373..685..8.65.43...4537.6.. #8 #  1888 FNBP C36/M1.1.62    # 7
......7.9...18926...9...4.1...56.....95.1862...69.2...56..21..8.1869...29.28.5..6 #8 #  1893 FNBP C36/M1.1.62    # 7
...4..7.9457....36......4.1.68......3.46.....57.84..6373..685..8.53.46...4657.3.. #8 #  1888 FNBP C36/M1.1.62    # 7
..3.567.9..71.9.36..937.51.24...3....91...6.3..6..5........79.1.7.5.136........75 #10#   540 FNBP C34/M1.3.49    # 8
.2.4.678....18.2.6.8..27.412.4.6187.....4.6.2.......14.68...1275........97..1.... #10#   546 FNBP C34/M1.3.49    # 8
.2.4.678....18.2.6.8..27.142.4.6187.....4.6.2.......41.68...1275........97..1.... #10#   546 FNBP C34/M1.3.49    # 8
12..5678..57.8....6.8......21.8.5..78.6.72..1.7561........6.4.2......3..762....15 #10#   541 FNBP C34/M1.3.49    # 8
12..5678..57.8....6.8......27.8.5..18.6.12..7.1567........6.4.2......3..762....15 #10#   541 FNBP C34/M1.3.49    # 8
12..5678..57.8....8.6......27.8.5..16.8.12..7.1567........6.4.2......3..762....15 #10#   541 FNBP C34/M1.3.49    # 8
..3.567.9..71.9.36..637.51.24......76.59.7.....9.....13..79.1.5....31......6.5..3 #10#   540 FNBP C34/M1.3.49    # 8
..3.567.9..71.9.36..937.51.24......7..6.....19.56.7...3..76.1.5....31......9.5..3 #10#   541 FNBP C34/M1.3.49    # 8
12..56.8..5718....6.82.7.5.21.......8.6.715.2.75.2........1.96.561....78......3.. #10#   540 FNBP C34/M1.3.49    # 8
12..56.8..5718....8.62.7.5.21.......6.8.715.2.75.2........1.96.561....78......3.. #10#   540 FNBP C34/M1.3.49    # 8
.2.45..89.5..8923....2.35.42.839.4.5....2.89........23.95....4264..3....7........ #2 #   762 FNBP C33/M1.2.40    # 8
.2.45..89.5..8923....2.34.52.839.5.4....2.89........23.95....4264..3....7........ #2 #   762 FNBP C33/M1.2.40    # 8
...4.6...4.7.892.66..27....2.89.4....64.27.9.97.86..2.......3.1....9..428......7. #1 # 98813 FNBP C32/M2.33.594  # 8
12...678..57...2.66.8..2.152.58..1.7.......58......62.5...37...7...4.......6.157. #1 # 23768 FNBP C32/M2.78.84   # 8
.2..56...45.18.26.......5..24....378.8....9......486.1.62.14...5.482...681.6.5..2 #1 # 95489 FNBP C35/M2.28.1872 # 8
.2..........18..36.8....54.2.1.37..876.8.1..3.3862...7...71.....12.6837..7.2.3... #1 # 58747 FNBP C34/M2.41.160  # 8
......7.9......13.789....642...6.....6.....2.94.82.67..946.2..767..48...8.297...6 #1 #  1638 FNBP C33/M1.2.45    # 9
...4..7.9457....36......41..68......3.46.....57.84..6373..685..8.53.46...4657.3.. #8 # 31279 FNBP C36/M2.56.117  # 9
...4..7.9457....36......41..68......3.46.....57.84..6373..685..8.65.43...4537.6.. #8 # 31279 FNBP C36/M2.56.117  # 9
...4..7.9457....63......41..68......3.46.....57.84..3673..685..8.53.46...4657.3.. #8 # 31279 FNBP C36/M2.56.117  # 9
...4..7.9457....63......41..68......3.46.....57.84..3673..685..8.65.43...4537.6.. #8 # 31279 FNBP C36/M2.56.117  # 9
1.3.56.8..5718..3.68.3.7.1..68......37.8.....5.167.3.8715...8.3......97....7...54 #8 # 31639 FNBP C36/M2.56.117  # 9
1.3.56.8..5718..3.68.3.7.1..68......37.8.....5.167.8.3715...3.8......97....7...54 #8 # 31639 FNBP C36/M2.56.117  # 9
...4.6.....678........31564.3.....9656.39.4.1......35.......6.561...394..95..4.13 #1 #   791 FNBP C33/M1.2.46    # 9
..3....8..5678.....8..3.....375.8..16.531...881..67...........7571....36....7.245 #2 #   957 FNBP C32/M1.3.23    # 9
1.3....894....9.....9.....4.18...9.539.5...415.49..83....8.....8351.4......362..8 #2 #   957 FNBP C32/M1.3.23    # 9
.2..5678..5.18.2.6...2.7.152897.....3.48......15...82.5.26.817...6....5....5..6.. #3 #   306 FNBP C35/M1.4.15    # 9
12..567...5718.2..6.82.7.....6...574..5....93....758.2.....2..15.1.68.27..2.1.... #3 #   329 FNBP C35/M1.4.15    # 9
.234...8945....23.8.92..5.4.4...8....35.4289...8...4......679.....9213...925.4... #3 #   305 FNBP C35/M1.4.15    # 9
1...56......1.....6..27.15.26....8933.....42.....32.1753..27..17.65.1..2...36.... #1 #  1819 FNBP C33/M2.116.56  # 9
1.3.....945.....3..98...14..81..4.533.5..19.494...381.....7.......6.8.9.8.9..5... #3 #  3184 FNBP C32/M2.51.128  # 9
12..5.78..57.8.2.66.8.2..15...9.........7.16...1.64.....2....578.5...6.1.1....82. #3 #  3200 FNBP C32/M2.51.128  # 9
12..56....5718...68.62.7..527..18.6..6.7.5.....862..........4.....872.51.......9. #3 #  3200 FNBP C32/M2.51.128  # 9
1.3.56.8..5718..3.68.3.7....36.75....1...3.......1...3.7....864.6....9.2....6835. #1 #  1818 FNBP C33/M1.3.23    # 9
12..56.8..5718....6.82.7.1....8.5973875....61...7......82......5.6......71...8..2 #5 #  2813 FNBP C33/M2.47.556  # 9
1.3.567...5718....68.3.75.....8156.78.5...142..1..........68...5..7.1..3...53.... #5 #  2819 FNBP C33/M2.47.556  # 9
12...6.89.56..91.28.9..156.21..98.......72..5....4....5.291.....61......98..6...1 #5 #  2812 FNBP C33/M2.47.556  # 9
1.3.5.7.9.57....3669..3.51..6.......73.864......51.3673..9..6.5.......93......17. #5 #  2816 FNBP C33/M2.47.556  # 9
.2345.7..45.7.92..7.9.325.........6......491.9.7...32.3.2..7.5.57........94....72 #5 #  2819 FNBP C33/M2.47.556  # 9
1.345...9.571.9.......37.....5..4...7.4.1359....5...4...1...96......14.3.79...821 #1 # 36937 FNBP C32/M2.62.315  # 9
12....789.57..9...6.9..7...2..7.4.98......4.2.....217...1.7892...29.18.4..824..17 #8 # 31984 FNBP C36/M2.56.117  # 9
12..56..9.571.9..66.972...5291...56........41.....13.2.16..5...57.......9.2.1765. #8 # 32827 FNBP C36/M2.56.117  # 9
12..567...5718.2..8.67.21...6....84.....285.7.8.....23.....7....7..1.....18.65.72 #2 #  1363 FNBP C34/M1.1.47    # 9
..3.567.9..71.9.36......51.2.5..7...74...5....39...17536.5.1.97......3.1.....365. #2 #  1363 FNBP C34/M1.1.47    # 9
..3.5678...718..36...7.31.524....8...3187....798...5..37.51.6.8.6.3.........6.3.. #1 #   291 FNBP C35/M1.4.15    # 9
...4.678...7.8.2.6...27..45.765.4...31......49.4.....25..6.24.7...7....87....8... #1 #   418 FNBP C31/M1.1.47    # 9
.234..7.94.67...2379.2..64.2......6736..2.9.4......23.....724966..9.5...9..61.... #8 # 31832 FNBP C36/M2.48.136  # 9
1..4.6...4..18........321452.....31........929.1.2.5.431.2..95.5.43...21.925..4.3 #8 # 33309 FNBP C36/M2.48.136  # 9
.234..7.94.67...2379.2..64.2......6736..2.9.4......23.....724966..91....9..6.5... #8 # 31832 FNBP C36/M2.48.136  # 9
1..4.6...4..18........321542.....31........929.1.2.4.531.5..92.5.23...41.942..5.3 #8 # 33309 FNBP C36/M2.48.136  # 9
....56..9...1.9..668932....2.8..364..34..8.9296...23.834........92.....38.6.3.9.4 #8 # 32444 FNBP C36/M2.48.136  # 9
1..4.6...4..18........321542.....31........929.1.2.4.53.25...4151.3..92..942..5.3 #8 # 33173 FNBP C36/M2.48.136  # 9
....56..9...1.9..668932....2.8..364..34..2.9896...83.234........92.....38.6.3.9.4 #8 # 32444 FNBP C36/M2.48.136  # 9
1..4.6...4..18........324152.....34........929.4.2.5.134.2..95.5.13...24.925..1.3 #8 # 33309 FNBP C36/M2.48.136  # 9
...4.........89..686..2....21..7.36.3.6.1.8.7.78.3..1263.....7.7.2.....1.81...6.3 #1 #  3405 FNBP C32/M2.52.126  #10
1.3.567...5678.1..78.1.3.........34.3.......2...83.5..51.6.8...6..37.....37.15... #5 # 95613 FNBP C32/M2.28.234  #10
.234.6.......8.........1...23..6..47.67...2..9.4...63.3.96...7267....49..429..3.6 #5 # 95604 FNBP C32/M2.28.234  #10
1.3.567...5678.1..78.1.3.........34.3.......2...83.5..57.6.8...6..31.....31.75... #5 # 95608 FNBP C32/M2.28.234  #10
........9.56...13........4..376.....5.83.1...61..75..337.1.8...8.5.673...6153.8.. #5 # 95595 FNBP C32/M2.28.234  #10
........9.56...13........4..376.....61..75..38.53.1...37.1.8...5.8.673...6153.8.. #5 # 95595 FNBP C32/M2.28.234  #10
12..56..9.567.9...7.912...5......8.6.......4.967....52.71......59..1....6.2.9751. #2 # 53908 FNBP C33/M2.58.113  #11
.2345....45.7.9.2.7.9.32.4.23..759.4...39....9..2.4.........6.....52347........51 #2 # 55231 FNBP C33/M2.58.113  #11
...45..894...8923.8..2.35.42.1.9.....6.......58.....42......39..3894..25....3.4.8 #1 #  1245 FNBP C33/M1.1.42    #11
....56......78.132...1.2.......4...8.34.28.17..8....4.3.7...82..128..4.384.2...71 #2 #   487 FNBP C33/M1.3.39    #12
....56......78.132...1.2.......4...8.34.28.71..8....4.3.7...82..128..4.384.2...17 #2 #   487 FNBP C33/M1.3.39    #12
12..567...567.9...7.921..........5.....56192........43..2.7.....17.95.6......2.7. #1 #   453 FNBP C30/M1.1.72    #13

BxB-Mastermins11-15.txt

The number of BxB6 minimals/min-expands is approaching mith file proportions ! But no real way of analysing !
coloin
 
Posts: 2617
Joined: 05 May 2005
Location: Devon

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

Postby denis_berthier » Thu Jul 24, 2025 4:28 pm

coloin wrote:The number of BxB6 minimals/min-expands is approaching mith file proportions ! But no real way of analysing !

What kind of analysis would you like to do?

I've had some delays in the development of my expansion scripts, due to unrelated activities. But I still plan to publish them, with the results obtained from them.

As for a first quick analysis of these new B7B+ puzzles:
- all the solution grids are new wrt Mastermins 1 to 10
- only 7 new solution grids are common with the T&E(3) ones:
Code: Select all
123456789457189263689372514245967138738514926961823475392748651574631892816295347
123456789457189236896237514275341968634895172981672453319764825562918347748523691
123456789457189263869237415234715896576928134918364572392841657641573928785692341
123456789457189263698237415219368547385724196746915328574691832862543971931872654
123456789457189236689237541238915674546872913971364825365721498714598362892643157
123456789457189236698732415245693178316875924789214563564321897831947652972568341
123456789457189236698237415289714563316825974745693128564371892831942657972568341

.
denis_berthier
2010 Supporter
 
Posts: 4522
Joined: 19 June 2007
Location: Paris

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