The New Sudoku Players' Forum

Website · by **denis_berthier** » Tue Feb 13, 2024 5:25 pm

Hi Coloin
Great finding.

coloin wrote: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 ?

Using FPGX with the -M option (no uniqueness) the 3 puzzles are indeed rated 11.6.
Generally speaking, eliminating uniqueness from the SER makes many things much simpler to understand.
Note however that if you continue to use SER (with or without uniqueness) as the value to maximise, and if you want to find high BpB values, you need to keep a low SER cutoff. It'd be simpler to directly maximise the BpB.

coloin wrote:
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 has the same kind of tridagon and the same kind of resolution path as the previous two. I don't have time to check now, but I'm quite sure that it can also be obtained from the 1st by a similar tridagon preserving near-isomorphism.
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Website · by **denis_berthier** » Thu May 02, 2024 6:49 am

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In order to avoid any confusion between the BpB classification and the BpB rating of a puzzle, the BpB classification has been renamed BxB classification. This is more consistent with the common usage that x is the unknown. Similar changes have been made to the BpBB classification (now BxBB classification).
Reminder:
- in "BxB classification", the "x" is the value to be found for the puzzle.
- in "BpB rating", p is fixed and what's to be found is the minimal length of Bp-braids necessary to solve the puzzle.
In any forthcoming post, I'll use this new notation. I'm too lazy to change the previous posts.
The changes have also been made in the SHC.
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by **hendrik_monard** » Tue May 07, 2024 8:30 pm

After examining new puzzles generated with my 'classic' scripts (limited to minimals) since the summer 2023, a significant number of new B7B+ puzzles were identified. Based on Denis' recommendations and thanks to the very interesting and transparent explanation given by coloin about the possible further development of derivative puzzles in the 'near isomorphism' (Denis' terminology) space, it was possible to significantly further expand the B7B+ list.
Since a reference list for testing novelty when searching for B7B+ min_expands was needed, I put all the min_expands in one list.
The word “min_expand” in this post means a singles-only expansion of a minimal puzzle.
Each puzzle in the list is the min_expand of at least one minimal puzzle.
The sources used to compile the list are as follows (chronologically):
- 3 B7B puzzles from the latest list published by Champagne (ph_2010) (3 grids)
- the puzzles identified as B7B+ by Denis in my previous posts until summer 2023 (38 grids)
- 2 B14B puzzles in my generated puzzles with SER < 11.6 (2 grids)
- the expanded puzzles obtained by coloin based on the above puzzles and some of his own puzzles (79 grids)
- the unpublished results of my scripts since the summer of 2023 (66 grids)
The total number of min_expands in the list is 478, grouped into these 188 different solution grids.
The fields of the lines in the following list are: min_expand | BxB | number of clues | SER | number of minimals | credits | publication date
If the min_expand equals its own minimal puzzle (and vice versa), the number of minimals is considered to be 0 to distinguish it from 1 for min_expands with 1 added single.
The records are sorted, first by BxB and then by solution grid. Empty lines separate the groups of puzzles sharing the same solution.
A small number of groups contain min_expands with different BxBs.
Min_expands not published previously carry the date 240507.
The list can best be viewed after copying it to a text file. The separator between the fields is a TAB.
I am looking forward to possible comments, questions, suggestions.... on the concept and the contents of the list.
A new generation of B7B+s produced by my scripts optimized for producing B7B+s min_expands should be ready in a couple of weeks.

Hidden Text: Show

Website · by **denis_berthier** » Wed May 08, 2024 5:17 am

Hi Hendrik
Great results again.
3 questions:
1) the sources you mention are not included in the list, right?
2) the list has no T&E-depth 3 puzzles for these seeds. Is it because they were already all in mith's T&E(3) list?
3) in the process of finding large BxBs, did you include the SHC in your scripts or did you use the SER as the filter? I'm asking because high BxB values can be obtained even with SER lower than 11.6.

No immediate comments on the format list; I can use it as such.
It's great to know which seeds you used.
I'll make further analyses before possibly deeper comments.
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Website · by **denis_berthier** » Thu May 09, 2024 3:36 am

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After further analysis, it appears all but 3 puzzles have a (non-degenerate) tridagon pattern.
The three exceptions are anterior to the discovery of Loki.

Code: Select all: .....6.....718........2...5..85....13.....9...6.....4...2.7...8.4.....6.9.....3.. 7 20 11.8/11.8/3.4 0 tax;m_b_metcalf 201000 .2...67..4...8......9.......3.....7.5.8...34..1.3....2....9..5....6.1..3...2..6.7 7 23 11.8/11.8/2.6 1 dob 201000 ..3..6....5.18....6....2...2...6...4......9...7.8...1.....1.89...4.....3.9..7.45. 7 23 11.9/11.9/9.9 1 OW 201000

Among these 3, one has a degenerate cyclic tridagon:

Code: Select all: ..3..6....5.18....6....2...2...6...4......9...7.8...1.....1.89...4.....3.9..7.45. 7 23 11.9/11.9/9.9 1 OW 201000

Also, 111 puzzles have a tridagon with only 1 guardian and can be solved using only the basic tridagon rule, Triplets and whips[≤2].

All this confirms my previous analyses: once you have a tridagon in a puzzle, vicinity search has a very strong tendency to preserve it.
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Website · by **denis_berthier** » Thu May 09, 2024 4:00 am

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T&E(2)-expands

The above results plus the previous ones obtained in the tridagon thread (http://forum.enjoysudoku.com/the-tridagon-rule-t39859.html) suggest that the following definition might allow to extend the search for puzzles in T&E(2):
Given a one-solution puzzle P in T&E(2), a T&E(2)-expand of P is an expansion of P that is still in T&E(2) but cannot be further expanded in T&E(2).
Obviously:
- a puzzle can have several T&E(2)-expansions,
- every such expansion is an expansion of min-expand(P),
- every such expansion has the same solution as P,
- every such expansion can have minimals that are not minimals of min-expand(P),
- every such expansion has at most the same BxB classification as P, but it can have minimals with a higher one.

Of course, similar definitions can be given for each T&E(n).
Note: this is the generalisation of mith's definition of a max-expand, when n=3.

In the n=3 case, I had shown previously that all the known minimal puzzles in T&E(3) have a tridagon (and also all their min-expands).
I've shown more recently that all the T&E(3)-expands (max-expands in mith's terminology) of known T&E(3) minimal puzzles also have a tridagon.
As a result, all the known puzzles in T&E(3) and all the puzzles in between them have a tridagon.

It is not true that for all the puzzles in T&E(2) having a tridagon, all their T&E(2)-expansions do have one also. But It is true in most known cases.

This suggests extending the search for T&E(2) puzzles, by modifying the expansion phase: replace Singles-expansion by T&E(2)-expansion.
In the results

Note that similar definitions can be given for BxB:
for any puzzle P in BpB for some finite p>0, one can define a BqB expansion of P for any q ≤ p as an expansion that is in BqB and cannot be further expanded in BqB.
This may be used if one wants to restrict the T&E(2) expansions to puzzles with a minimum BxB value.

All these definitions are meaningful due to the good properties of the T&E and BxB classification: they vary monotonously (decreasingly) with the addition of givens.

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by **hendrik_monard** » Thu May 09, 2024 2:22 pm

denis_berthier wrote:3 questions:
1) the sources you mention are not included in the list, right?

Instead of using "sources" I should have used "inputs". For instance the first input with 3 B7B puzzles in Champagnes's database ph_2010: you can find them in the list by searching "201000".

denis_berthier wrote:2) the list has no T&E-depth 3 puzzles for these seeds. Is it because they were already all in mith's T&E(3) list

in my generating scripts, T&E(3) puzzles and T&E(2) puzzles have been treated together. I only discriminated for evident reasons before BxB classification. However, the genealogy of the B7B+ puzzles has pointed out that only a small number of them started with a T&E(3) puzzle.

denis_berthier wrote:3) in the process of finding large BxBs, did you include the SHC in your scripts or did you use the SER as the filter? I'm asking because high BxB values can be obtained even with SER lower than 11.6.

All my published results until today came from the 'old' scripts. They were limited to SER >= 11.6. In my 'new' scripts, running since March, the focus is on methods resulting in grid (seed) changes with a much lighter filter resulting in a rapidly growing list of puzzles to be analysed at the end of the generation process. The purpose is to examine a much broader SER range. Including SHC in my generating scripts was therefore not needed as BxB was not used as a filter. SHC was of course very useful in the examination of the results.
The 'source' for the currently running 'new' scripts is my most recent generation of some 13 thousand 11.6+ puzzles. I expect to generate around 400K new minimal puzzles. That number will be drastically reduced after min_expanding, followed by the removal of duplicates and te3 before BxB classification.
To get an idea of the repartition per SER range in the future results from the 'new' scripts with higher output numbers due to the lighter filter, I tested it on an arbitrary group of 350 intermediate results. 57% were SER 8.5-10.4, 13 % 10.5-11.0, 8% 11.1-11.5 and 22% 11.6. There will thus be enough 'low' SER puzzles to demonstrate the presence (or absence or something in between) of B7B+ puzzles in the lower SER ranges. I expect to be able to publish the new results by the end of June.

by **coloin** » Sat May 25, 2024 2:13 am

New expanded puzzles with high BxB

Code: Select all: ..34.678....18..36..6.731.4.3..18.47...7..8.3...3.461..9.......5.........61...4.8 # 10 ...4.67.9....89.36...37..4.2.........4..98....81....9..3.86.97....9.3.64.6..473.8 # 10 ..34.6...4.7.89...68.37..4..6894....7.4.639..93.7.84.........2....6.789.........1 # 10 12..5.....571.92..8.9.72..........6.......4..91....8.7.8172....5.2.91..879.5.8..2 # 10 ..3.56....5718...6.6.7.3..5......9.........2.718....5338..175..6.15.8....75.3..1. # 10 ..3.567.9..71.9.36..9...15.....63.75...9.76.....51.39..4.....6.8.6.....7..56.1... # 10 .....6.89.5.1.9.....9.7....2.4...86..65...9.29......45.42..5.9859...26.48.6..4... # 10 1.3...7.94......36.69...14..94.3..7131..4.69.7.6.9........6..17..18......3..15... # 9 1.3..6..9.571.9..669.3........517.93.......2.......4..71..359...3.9.1.7.9.576.... # 9

43 minimal puzzles from these with similar BxB
No BxB 7 or 8 ....
Probably similar to the previous ones, however I did try to find a 25C or 26C with SE 11.6/11.7 but unsuccessful ...

Website · by **denis_berthier** » Sat May 25, 2024 2:46 am

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Always good to extend the collection of large BxB puzzles. We don't have thousands of them yet.
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by **coloin** » Fri May 31, 2024 3:35 pm

My last batches of 31 expanded minlex solution grid puzzles. BxB 10 seems to predominate ...
These are grouped in their twin related puzzles, which -q2 seems to identify
There are 620 minimal puzzles in these.

Hidden Text: Show

Code: Select all: 1........45....236..8......2...63.5...654.3.2...9.264.....954.....62.9.3.9.3.4..5 # 32735 FNBP C31/M2.75.87 ##1 #10 1.3...78..5718..3668.37.5.1....35618....4.......2.....5.6......73.....5..18....67 # 888 FNBP C32/M1.1.54 ##1 #10 1.3.56....571.9...69.37.....6179..5.....31.6..3.6.5.9....9.78.........1....5.3.74 # 741 FNBP C32/M1.1.54 ##1 #10 1.3.567...571.9...69.73.1.....9635.7.......2.........857.61.....3..97...9.63.5.7. # 30829 FNBP C33/M2.94.69 ##2 #10 1.3.5.....571.9.3.89..37.........6.........2.519...3.7.8537....7.19.8..393..15..8 # 30608 FNBP C33/M2.94.69 ##2 #10 ..3.567.9..71.9.36..6...51.2.....9.7.49...1....5.91.......63.9....9.73.1...51.67. # 4058 FNBP C33/M2.71.92 ##3 #10 ....567...5718.2..6.87.21.....81...3.86...5......6.84.56..71...8.162.....72..8... # 4086 FNBP C33/M2.71.92 ##3 #10 1.3.5.....57.8..3686..7.1.5....3..61.769.......1.62....18...6.76......587.5...31. # 4100 FNBP C33/M2.71.92 ##3 #10 1........4.7...236.9.......23..7846....24.3.884.6.3.27..4.6..7....7.48......3264. # 1994 FNBP C33/M2.81.81 ##3 #10 1........4.7...236.9.......23..7864....24.3.884.6.3.27..4.6..7....7.48......3246. # 1994 FNBP C33/M2.81.81 ##3 #10 1........4.7...236.9.......23.6.8.47...24.3.884..7362...4.6..7....7.48......3246. # 1994 FNBP C33/M2.81.81 ##3 #10 12...6....57..926.9.6..7.51.918......75.41........2...5.2...69.76......2.19....75 # 1085 FNBP C32/M1.2.26 ##6 #10 1.34.678.4.718..36....374.12..........5.......61...348...3.487......8.6....76.1.. # 1078 FNBP C32/M1.2.26 ##6 #10 1.34.678.4.718..36....371.42..........5.......64...318...3.187......8.6....76.4.. # 1073 FNBP C32/M1.2.26 ##6 #10 ..3.567.9..71.9.....637.51.2...31.....9.......41.65......6.7.9....59.3.7....1365. # 1061 FNBP C32/M1.2.26 ##6 #10 1.....7.9.57...2.6..8..........94.68...62.9.7...8..42...276..94..4...87...9.486.2 # 1057 FNBP C32/M1.2.26 ##6 #10 1.....7.9.57...2.6..8..........9486....62.9.7...8...24..276.49...4....78..9.486.2 # 1057 FNBP C32/M1.2.26 ##6 #10 1.3.5.....57.8..3686..7.1.5.86.14....719.........3....63.....587.5...3...18...6.7 # 1040 FNBP C32/M1.2.26 ##3 #10 ....567...5718.2..6.87.21........5.....82.69....61...35...71...8.126.....725.8... # 1039 FNBP C32/M1.2.26 ##3 #10 ..3.567.9..71.9.36..6...51.2.....1.7.81...9.3..5.........5..67....9.73.1....63.95 # 1036 FNBP C32/M1.2.26 ##3 #10 1.3.5.....571.9.3.89..3715.......6.........2.519...3.7.8.37....7..9.8..393..15..8 # 58209 FNBP C33/M2.107.61 ##1 # 9 ...45..8.4.......6......14.2.859.....94.78...7..2.4....7582..9.84.9.7.2.9.2.45.7. # 29195 FNBP C33/M2.94.69 ##1 # 9 ...45..8.4.7.....6..9...14.2.859.....94.78...7..2.4....7582..9.84.....2.9.2.45.7. # 46822 FNBP C33/M2.106.61 ##1 # 9 1.3...78..57....3668....5...365..8.771.8...53...3..16.....2..7....7.4..8.716..... # 345 FNBP C32/M1.2.36 ##1 # 9 ...4.678....18.2.6....27.41.3.....68..16.....9.6....72..2.418.7..4...61...8.6..24 # 3891 FNBP C33/M2.42.156 ##2 # 9 1.3...7.9.571.9.3696.7.315......4......8........96.31531....59.6.5.9.....79...6.. # 3911 FNBP C33/M2.42.156 ##2 # 9 1.3....8..571...3668.3....1..8.7..6337....15.5.6..38.7.....4.......9.......83.675 # 398 FNBP C32/M1.2.36 ##3 # 9 1.3...7.94......36.69...14..94.3..1731..4.69.7.6.9........6..71..18......4..15... # 398 FNBP C32/M1.2.36 ##3 # 9 1.3...7.94......36.69...14..94.3..7131..4.69.7.6.9........6..17..18......4..15... # 398 FNBP C32/M1.2.36 ##3 # 9 12....78..5.1..2.66..2...152.5...8.187...265...6....27.....15..5...43.7.78....... # 881 FNBP C32/M2.97.67 ##2 # 7 12....78..5.1..2.66..2...152.5...8.178...265...6....27.....15..5...43.7.87....... # 881 FNBP C32/M2.97.67 ##2 # 7

Website · by **denis_berthier** » Sat Jun 01, 2024 6:55 am

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Hi coloin
I checked your last two lists for tridagons.

It's interesting to note that all the newly found puzzles with BxB ≥ 7 have a (non-degenerate) tridagon.

If you don't mind publishing them, I'd like to have also the lists of minimals corresponding to your last two list of min-expands.
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by **coloin** » Sat Jun 01, 2024 1:03 pm

No problem as " gridchecker --similar --removeredundant <file.txt > filemins.txt " performs it in less than 2 sec
However i have re-expanded the 663 puzzles and re-checked that there were no higher BxB

These puzzles share the same solution grid, but expansion reduces the BxB

Code: Select all: ...45..8.4.......6......14.2.859.....94.78...7..2.4....7582..9.84.9.7.2.9.2.45.7. ...45..8.4.7.....6..9...14.2.859.....94.78...7..2.4....7582..9.84.....2.9.2.45.7. 1.3.5.....571.9.3.89..37.........6.........2.519...3.7.8537....7.19.8..393..15..8 1.3.5.....571.9.3.89..3715.......6.........2.519...3.7.8.37....7..9.8..393..15..8

620 plus 43 minimal puzzles

Hidden Text: Show

Website · by **denis_berthier** » Mon Jun 03, 2024 6:32 am

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Hi coloin
Thanks for the collection of minimals.
I can't use gridchecker on my Mac (ARM/Apple) processor. Last time I tried, I found it has x86 code. Maybe also misplaced libraries.
I tried gsf's software, but I still have problems using it to generate minimals.

by **hendrik_monard** » Thu Jun 13, 2024 4:50 pm

The following (hidden) list of new min-expands rated B7B or higher is the result of the procedure explained in my post of May 9.
My method(s) applied to previous high BxB generation(s) with, for the occasion, a 'softer' filter, produced some 575K puzzles. Around 70% are supposed to be in the SER range 8.5-11.0 (see explanation in previous post).
After removing duplicates before and after min-expanding, a list of 13.149 new min-expands remained. These were BpB rated (with SHC). The list contains the results (limited to B7B and higher).
The interesting thing is that, notwithstanding the high number of 'low' SER puzzles at the start, none reached the B7B threshold. All B7B+ puzzles are in the SER range 11.6-11.8. Does this prove something? Not necessarily, but I consider it as a serious indication that the chances for finding B7Bs or higher in the lower SER range are rather small.
In the list, 115 min-expands form 44 groups, each containing min-expands sharing the same grid (solution). Note that each line contains the min-expand of at least one minimal puzzle.
The layout is as follows (T = Tab):
min-expand T BxB T cc T SER T number of minimals.

Hidden Text: Show

Code: Select all: [code] 12..56..9.571.9..66.927...12..69.....76.21....1.7.5.........8..7......35...5....2 10 31 11.7/2.0/2.0 1 12..56....571.9..66.927...12..69.....76.21...91.7.5.........8..7......35...5....2 10 31 11.7/11.1/3.4 1 12..56..9.571.9..66.927...12..69.....76.21....1.7.5.........8..7......35...5.7..2 10 32 11.7/2.0/2.0 3 12..56....571.9..66.927...12..69.....76.21...91.7.5.........8..7......35...5.7..2 10 32 11.7/11.3/3.4 3 1...5678....18..636..7.31.5.6..75.....4.......9...........185.....6.731..1.53..78 10 31 11.8/11.8/9.1 4 1.3.567...5718....68.3.75.........4.361...8.7........251..3....7.8.65....368....5 10 32 11.8/2.0/2.0 2 1.3.567...5718....68.3.75.........4.36....8.7........251..3....7.8.65....368.1..5 10 32 11.8/11.3/3.4 2 1.3.5.78..57.8..6368..7.5.1.78...3..3.6....5751......6...9..6......64....61.3.... 10 32 11.7/2.0/2.0 10 1.3.5.78..57.8..6368..7.5.1.78...3..3.6....5751..........9..6......64....61.3.... 10 31 11.7/2.0/2.0 4 1.3.5.78..57.8..6368..7.5.1.78...3..3.6....5751....8.....9..6......64....61.3.... 10 32 11.7/2.0/2.0 6 12.4.67..4.718.2...68.27...2.1.6.....468....287..42..........9.614...82.........5 10 32 11.7/2.0/2.0 3 12.4.67..4.718.2...68.27...2.1.6.....468....287..4...........9.614...82.........5 10 31 11.7/2.0/2.0 1 12.4.67..4.718.2...68.27...2.1.6.....468.1..287..4...........9.614...82.........5 10 32 11.7/2.0/2.0 2 12.4.67..4.718.2...68.27..........5....8416.2........3.1267.....8.2.4...6...18.2. 10 32 11.7/2.0/2.0 5 12.4.67..4.718.2...68.27..........5....8416.2........3.1.67.....8.2.4...6...18.2. 10 31 11.7/2.0/2.0 2 12.4.67..4.718.2...68.27..........5....8416.2........3.1.67.....8.2.4...6.4.18.2. 10 32 11.7/2.0/2.0 3 .2.......45.189.....6........589..4....3.49.5....158..3...4159.5..9.8.13...53.4.8 10 32 11.7/2.0/2.0 20 .2.......45.189.....6........589..4....3.49......158..3...4159.5..9.8.13...53.4.8 10 31 11.7/2.0/2.0 8 .2.......45.189.....6........589..41...3.49......158..3...4159.5..9.8.13...53.4.8 10 32 11.7/2.0/2.0 12 ....5678...718..36...7.31.52..........5618....9..........36...1....758.3.3.8.156. 10 31 11.7/11.2/2.6 4 ..3.5678...718..36...7.3..52........3.5618....9..........36...1....758.3.3.8.156. 10 32 11.7/2.0/2.0 6 ..3.5678...718...6...7.31.52........3.5618....9..........36...1....758.3.3.8.156. 10 32 11.7/2.0/2.0 4 1..4.678.4..18.2.68...27.1429.........5......6.......7.....4.72...6..8......1264. 10 29 11.7/2.0/2.0 1 1..4.678.4..18.2.68...27.1429...8.....5......6.......7.....4.72...6.........1264. 10 29 11.7/3.4/2.6 1 1..4.678.4..18.2.68...27.1429.........5......6.......7.....4.7....6..8.1....1264. 10 29 11.7/2.0/2.0 1 1..4.678.4..18.2.68...27.1429.........5......6.......7...8.4.7....6....1....1264. 10 29 11.7/2.0/2.0 1 1..4.678.4..18.2.68...27.1429...8.....5..1...6.......7.....4.72...6.........1264. 10 30 11.7/3.4/2.6 2 1..4.678.4..18.2.68...27.1429.........5..1...6.......7...8.4.72...6.........1264. 10 30 11.7/11.2/2.6 1 1.3.56.8..5718..3.86.3.7.1.......97.7.......2...76..5..7.6.1...5..83.....81.75... 10 32 11.7/2.0/2.0 5 1.3.56.8..5718..3.86.3.7.1.......97.7.......2...76..5....6.1...5..83.....81.75... 10 31 11.7/2.0/2.0 2 1.3.56.8..5718..3.86.3.7.1.......97.7.......2...76..5.3..6.1...5..83.....81.75... 10 32 11.7/2.0/2.0 3 ..3.567.9..71.9.36...73.51..35...691.4.......8........3....516.....1.9.3...36..75 10 32 11.7/2.0/2.0 3 ..3.567.9..71.9.36...73.51..35...691.4.......8........3....516.....1.9.3....6..75 10 31 11.7/2.0/2.0 1 ..3.567.9..71.9.36...73.51..35...691.4.......8........3..9.516.....1.9.3....6..75 10 32 11.7/2.0/2.0 2 1.3.56..9.571.9..669.73...5..19.7....3..65...9.531.....1....8......71..3.......41 10 32 11.7/2.0/2.0 5 1.3.56..9.571.9..669.73...5...9.7....3..65...9.531.....1....8......71..3.......41 10 31 11.7/2.0/2.0 2 1.3.56..9.571.9..669.73...5.6.9.7....3..65...9.531.....1....8......71..3.......41 10 32 11.7/2.0/2.0 3 1.3.56..9.571.9..669.73...5.......43......8..7.......137.6......6139......5..1... 10 29 11.8/2.0/2.0 1 1.3.56..9.571.9..669.73...5.......43......8..7.......1.7.6......6139....9.5..1... 10 29 11.8/2.0/2.0 1 1.3.56..9.571.9..669.73...5.......43......8..7.......1.7.6.5....6139....9....1... 10 29 11.8/2.0/2.0 1 1.3.56..9.571.9..669.73...5...5...43......8..7.......137.6......6139.........1... 10 29 11.8/3.4/2.6 2 1.3.56..9.571.9..669.73...5...5...43......8..7.......137.6.5....6139.........1... 10 30 11.8/11.2/2.6 3 1.3.56..9.571.9..669.73...5...5...43...9..8..7.......137.6......6139.........1... 10 30 11.8/3.4/2.6 4 1.3.56..9.571.9..669.73...5...5...43...9..8..7.......137.6.5....6139.........1... 10 31 11.8/11.8/2.6 7 1.3.56..9.571.9..669.73...5.......43...9..8..7.......137.6.5....6139.........1... 10 30 11.8/11.2/2.6 1 1.3.56....571.9.3.69.73..5..1537....36.9.....7.9.61..3......8..........297......5 10 31 11.8/11.8/9.1 2 1...5678....18..366..7.31.5.1..37.58...5..31....8.16.7.4.........2......86....57. 10 32 11.7/11.3/3.4 2 1...5678....18..366..7.31.5.1..37.58...5..31......16.7.4.........2......86....573 10 32 11.7/9.2/2.6 4 1...5678....18..366..7..1.5.1..37.58...5..31....8.16.7.4.........2......86....573 10 32 11.7/2.0/2.0 2 ...4.678...718.2.6..8.72.41...81.4.7.8...412....2...68.74...612.3.......9........ 10 32 11.7/2.0/2.0 2 ...4.678...718.2.6..8.72.41...81.4.7.8..6412....2...68.74....12.3.......9........ 10 32 11.7/11.3/3.4 2 1..456.....7.......8...........9531....34.6...3.6.1.54....14.95...9.316.9..56.4.3 10 31 11.7/11.2/2.6 4 1.3456.....7.......8...........9531....34.6...3.6.1.543...14.95...9.316.9..56.4.. 10 32 11.7/2.0/2.0 4 1.3456.....7.......8...........9531....34.6...3.6.1.543...14.95...9.31..9..56.4.3 10 32 11.7/2.0/2.0 6 1..456.....7.......8...........9135....34.6...3.6.5.14....14.95...9.316.9..56.4.3 10 31 11.7/11.2/2.6 4 1.3456.....7.......8...........9135....34.6...3.6.5.143...14.95...9.316.9..56.4.. 10 32 11.7/2.0/2.0 4 1.3456.....7.......8...........9135....34.6...3.6.5.143...14.95...9.31..9..56.4.3 10 32 11.7/2.0/2.0 6 1..4.678.4..18.2.6....27.4129.7.......5......8......72....718.4...8..61....64..27 10 32 11.7/10.6/3.4 2 1..4.678.4..18.2.66...27.4129.7.......5......8......72....718.4...8..61.....4..27 10 32 11.7/2.0/2.0 2 1..4.678.4..18.2.6....27.4129.7.......5......8......72....418.7...8..61....67..24 10 32 11.7/10.6/3.4 2 1..4.678.4..18.2.66...27.4129.7.......5......8......72....418.7...8..61.....7..24 10 32 11.7/2.0/2.0 2 1..4.678.4..18.2.6....27.4129.7.......5......8......2.....718.4...8..61....64..72 10 31 11.7/10.6/3.4 1 1..4.678.4..18.2.66...27.4129.7.......5......8......2.....718.4...8..61.....4..72 10 31 11.7/2.0/2.0 1 1..4.678.4..18.2.6....27.4129.7.......5......8......27....718.4...8..61....64..72 10 32 11.7/10.6/3.4 3 1..4.678.4..18.2.66...27.4129.7.......5......8......27....718.4...8..61.....4..72 10 32 11.7/2.0/2.0 3 ...45.7.9...1.92....9.27.41.3.........6........57.2.......94.155..2.19.79..57.42. 10 31 11.8/11.8/9.1 2 1..4.678.4..18.2.6....27.1429.7.......5......8......72....748.1...8..64....61..27 10 32 11.7/10.6/3.4 2 1..4.678.4..18.2.66...27.1429.7.......5......8......72....748.1...8..64.....1..27 10 32 11.7/2.0/2.0 2 1..4.678.4..18.2.6....27.1429.7.......5......8......72....148.7...8..64....67..21 10 32 11.7/10.6/3.4 2 1..4.678.4..18.2.66...27.1429.7.......5......8......72....148.7...8..64.....7..21 10 32 11.7/2.0/2.0 2 1..4.678.4..18.2.6....27.1429.7.......5......8......2.....748.1...8..64....61..72 10 31 11.7/10.6/3.4 1 1..4.678.4..18.2.66...27.1429.7.......5......8......2.....748.1...8..64.....1..72 10 31 11.7/2.0/2.0 1 1..4.678.4..18.2.6....27.1429.7.......5......8......27....748.1...8..64....61..72 10 32 11.7/10.6/3.4 3 1..4.678.4..18.2.66...27.1429.7.......5......8......27....748.1...8..64.....1..72 10 32 11.7/2.0/2.0 3 ....5678...718.2.....2.7.152.1865....3.......9...........6.8..1....7182....52..6. 10 29 11.7/2.0/2.0 1 ....5678...718.2.....2.7.1.2.1865....3.......9...........6.8..15...7182....52..6. 10 29 11.7/3.4/2.6 1 ....5678...718...6...2.7.152.1865....3.......9...........6.8..1....7182....52..6. 10 29 11.7/2.0/2.0 1 ....5678...718...6...2.7.1.2.1865....3.......9...........6.85.1....7182....52..6. 10 29 11.7/2.0/2.0 1 ....5678...718.2.....2.7.1.2.1865....3.......9...........6.8..156..7182....52..6. 10 30 11.7/3.4/2.6 2 ....5678...718.2.....2.7.1.2.1865....3.......9...........6.85.1.6..7182....52..6. 10 30 11.7/11.2/2.6 1 .2345...945.7.9..27.9.32......54..9.......6.........1.3.5.74.2..4.32.....729.5... 10 31 11.8/11.8/9.1 1 1.345..8.45..89.3..891.3.4....91..5..9......7......6..53..41....4.89....9.83.5... 10 32 11.7/11.2/2.6 3 1.345..8.45..89.3..891.3.4.....1..5..9......7......6..53..41....4.89....9.83.5... 10 31 11.7/10.5/2.6 2 1.345..8.45..89.3..891.3.4....91..5..9......7......69.53...1....4.8.....9.83.5... 10 31 11.7/2.0/2.0 4 1.345..8.45..89.3..891.3.4....91..5..9......7......69.5....1....4.8.....9.83.5... 10 30 11.7/2.5/2.5 2 1.345..8.45..89.3..891.3.4....91..5..9......7......69.53...1....4.89....9.83.5... 10 32 11.7/2.0/2.0 6 1.345..8.45..89.3..891.3.4....91..5..9......7......69.5....1....4.89....9.83.5... 10 31 11.7/2.0/2.0 3 .23...7.945...9.327.9..354.23.....5..75.3.2.49.4....73...6.....54..9........1.... 10 31 11.8/11.8/9.1 2 ...4......57..9........2.1..31...5..56...3.717.9...63.31.....96.76.9.35.9.5.3.1.7 9 32 11.6/11.6/9.1 1 .2.45..89....892.6.....245.........83189.....7..8.......629.8.4...5.469.....68.25 9 32 11.7/11.1/4.1 8 .23....8.45..8.2.36.8....4528....4.63.68..52..456...3853..6........17..4........2 7 33 11.6/11.6/10.0 12 .23....8.45..8.2.36.8....4528....4.63.68..52..456...3853..6........17...........2 7 32 11.6/11.1/10.0 4 .23....8.45..8.2.36.8....4528....4.63.68..52..456...38534.6........17............ 7 32 11.7/11.7/2.6 4 ....56..9.5.1.926....32.5.1.48.......3.291............3...129.55..93..26...6.531. 7 32 11.7/11.7/2.6 2 1.3.5.7.9.57....3669..3.51.............2.8...9163.....3.9...65.57....1...615...97 7 32 11.7/11.7/2.6 2 1...5678..5718....6.82.7.........39.....12.75......4...627.1...5.18....778...5... 7 31 11.7/2.0/2.0 4 .23...7.945...923...9....452.49..5.737....49..957...23....61.................7352 7 32 11.7/11.7/2.6 8 .2..........1.9.3..8....45.2..97.....912.8.7.87..31....387.2...71.89...39.2.13..7 7 33 11.7/11.7/10.0 3 .2..........1.9.3.......45.2..97.....912.8.7.87..31....387.2...71.89...39.2.13..7 7 32 11.7/11.1/10.0 1 ............189.3.......45.2..97.....912.8.7.87..31....387.2...71.89...39.2.13..7 7 32 11.7/11.7/2.6 1 .2..........1.9.3..8....45.2..97.....912.8.7.87..13....387.2...71.89...39.2.31..7 7 33 11.7/11.7/10.0 6 .2..........1.9.3.......45.2..97.....912.8.7.87..13....387.2...71.89...39.2.31..7 7 32 11.7/11.1/10.0 2 ............189.3.......45.2..97.....912.8.7.87..13....387.2...71.89...39.2.31..7 7 32 11.7/11.7/2.6 2 ....5678..5.18..36.8.3.71.52.8.3......5...86.9.4..........1.65.5..76.3.8........1 7 31 11.7/10.6/2.6 2 ........9...18.....8....1.5.38.61.747.483.....6.7.4...37..486...416.73..8.631.... 7 33 11.7/11.7/10.0 12 ........9...18.....8....1.5.38.61.7.7.483.....6.7.4...37..486...416.73..8.631.... 7 32 11.7/11.1/10.0 4 ........9...18.....8....1.5.38.61...7.483.....6.7.4...37..486...416.73..8.631.4.. 7 32 11.7/11.7/2.6 4 .23...78.4.7.8..3668....4.....59.............734.2....37...284.8.6....27.42..86.3 7 32 11.7/11.7/2.6 1 .23...78.4.7.8..3668....4.....59..7.3.4.2...........6.73...284.8.6....27.42..86.3 7 33 11.6/11.6/10.0 3 .23...78.4.7.8..3668....4.....59....3.4.2...........6.73...284.8.6....27.42..86.3 7 32 11.6/11.1/10.0 1 .23...78.4.7.8..3668....4.....59....374.2.............73...284.8.6....27.42..86.3 7 32 11.7/11.7/2.6 1 ...4.6.89..6.891.2..921.64.....4.9.1....9286.9..8.1.2453.......6.....218......... 7 32 11.7/11.7/2.6 2 .2345...945.7.9..27.9.32...24.3.....3.5.74.2..972.5...5.4....9......3........761. 7 33 11.7/11.7/10.0 8 .2345...945.7.9..27.9.32...24.3.....3.5.74.2..972.5...5.4....9......3.........61. 7 32 11.7/11.1/10.0 4 .2345...945.7.9..27.9.32...24.3.....3.5.74.2..972.5...574....9................61. 7 32 11.7/11.7/2.6 4 [/code]

Website · by **denis_berthier** » Fri Jun 14, 2024 4:27 am

hendrik_monard wrote:The interesting thing is that, notwithstanding the high number of 'low' SER puzzles at the start, none reached the B7B threshold. All B7B+ puzzles are in the SER range 11.6-11.8. Does this prove something? Not necessarily, but I consider it as a serious indication that the chances for finding B7Bs or higher in the lower SER range are rather small.

Pre-tridagon Tables 11.2 and 11.4 of [PBCS] showed that the very few (i.e. 3) puzzles in B7B had high SER. Their extended versions in [HCCS2, forthcoming] confirm the old results to the whole (eleven and ph2010) collections, but that's still for pre-tridagon collections.
I can't say much more about the SER in recent collections. I've completely stopped using it: too slow (even the FPGX version), too many problems with uniqueness and with instability under isomorphisms). One can't exclude that a B7B+ puzzle could have a low SER but a much higher one when uniqueness is disabled. We have examples in T&E(3).

Maybe the most meaningful result as of now (I checked with your last puzzles) is: except the 3 pre-tridagon puzzles in B7B, all the known T&E(2) puzzles with BxB ≥ 7 have a non-degenerate tridagon.

Note that this doesn't imply much about the SER, as Paquita has generated (before the discovery of Loki) lakhs of puzzles with an unnoticed tridagon and SER ≤ 11.1.
.

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

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

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

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

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