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.
.

Website · by **denis_berthier** » Thu May 02, 2024 6:49 am

.
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.
.

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.
.

Website · by **denis_berthier** » Thu May 09, 2024 3:36 am

.
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.
.

Website · by **denis_berthier** » Thu May 09, 2024 4:00 am

.
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
.

The New Sudoku Players' Forum

The BxB classification of T&E(2) puzzles

Re: The BpB 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

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

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