The BxB classification of T&E(2) puzzles

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

The BxB classification of T&E(2) puzzles

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This thread has one and only one topic: the BpB classification of T&E(2) puzzles, with its possible correlations (or not) with other ratings, such as the SER.

1) INTRODUCTION
The discovery of the Loki puzzle by mith and my discovery that it was in T&E(3) (http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1048.html) have led to a sudden surge in the number of "potentially hard" puzzles.
- a new one dedicated to finding T&E(3) puzzles: http://forum.enjoysudoku.com/t-e-3-puzzles-split-from-hardest-sudokus-thread-t40514.html;
- the same old one with a now explicit goal of looking for SER-hardest puzzles and excluding puzzles in T&E(3), which turns it de facto into a thread dedicated to finding T&E(2) puzzles with highest SER.

In the same way as I introduced a thread (http://forum.enjoysudoku.com/the-tridagon-rule-t39859.html) to analyse the puzzles found in the T&E(3) one, I'm now introducing the present one to analyse the puzzles found in the T&E(2) one.

2) THE BpB SUB-CLASSIFICATION OF T&E(2)
The T&E(T, n) procedure and the BpB classification of T&E(2)=T&E(Singles, 2) puzzles were introduced in my book [CRT, 2011] and reproduced in all the subsequent editions of my book [PBCS].
The BpB classification relies on an easy theorem proven in [CRT]: a puzzle P can be solved in T&E(1) iff it can be solved by braids, i.e. by braids[≤p] for some maximal length p (depending on P).
This trivially implies the following theorem:
- a puzzle P can be solved in T&E(2) iff it can be solved by B-braids, i.e. by Bp-braids of any total length but for some maximal value of p (depending on P).

This defines a sub-classification of all the puzzles in T&E(2) - and the associated BpB rating (the smallest p such that P is in BpB).
T&E(2) is the disjoint union of all the T&E(Bp, 1) (also named BpB for obvious reasons), for p=1, 2....
(Note B0B=B=T&E(1)).

3) THE B7B CONJECTURE
I also showed in [CRT] that all the known puzzles in the currently "hardest" database were indeed in BpB, for some p ≤ 7. Which became my B7B conjecture. This was reproduced and updated in every edition of [PBCS].
With the discovery of Loki and it being in T&E(3), my T&E(2) and B7B conjectures (which had hold for more than 12 years) were falsified. From that time on, I also stopped checking systematically all the newly discovered high SER puzzles.
However, there remains a modified conjecture: all the puzzles in T&E(2) are indeed in BpB for some p ≤ 7.
[Notice that I've proven that all the known puzzles in T&E(3) are indeed in B2BB (BpBB defines a similar sub-classification of T&E(3) (see the T&E(3) thread).]

This doesn't imply that the modified T&E(2) conjecture is the topic of this thread, but it's clearly part of it. In any case, it'd be interesting to know how high p can be.

References:
[CRT, 2011]: https://www.researchgate.net/publication/280301602_Constraint_Resolution_Theories
[PBCS1, 2012]: https://www.researchgate.net/publication/280301697_Pattern-Based_Constraint_Satisfaction_and_Logic_Puzzles
[PBCS2, 2015]: https://www.researchgate.net/publication/280100555_Pattern-Based_Constraint_Satisfaction_and_Logic_Puzzles_Second_Edition
[PBCS3, 2021]: https://www.researchgate.net/publication/356313228_Pattern-Based_Constraint_Satisfaction_and_Logic_Puzzles_Third_Edition
Note that I gave many definitions on this forum before formally publishing them in the above references.

[Edit "2024 May 2"]:
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 post posterior to this date, I'll use this new notation. I'm too lazy to change all the posts.
The changes have also been made in the SHC.
[/edit]
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Last edited by denis_berthier on Thu May 02, 2024 6:46 am, edited 4 times in total.
denis_berthier
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Re: The BpB classification of T&E(2) puzzles

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Based on Paquita's current collection of hard puzzles http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1592.html, I computed the BpB rating of the 13 puzzles with SER=11.9 and 547 ones with SER=11.8 (after eliminating the T&E(3) puzzle in them).
(computations done in collaboration with François Cordoliani, alias Defise on this forum).

None of them is in BpB for p > 7.
The only ones in B7B are:
Code: Select all
`98.7..6.....9...7.....65...7.......443.....9...2...1...4.3...8...1.2.........65..;5.6...7...1.3.....8...5.9.....1...2.....8.6.7.....2.4.7...9...6.3...42....5......;11.90;1.20;1.20;OW;2015_08;1744614;22;98.7.....6.....5....4......7..8..9......3..4......2..1.5.9..6......4..3......1..2;5.......9.2.1...7...8...3...4.6.........5.......2.7.1...3...8...6...4.2.9.......5;11.80;11.80;3.40;tax;m_b_metcalf;22;20;98.7.....6..85......4..3...7..6..5....9...6....2....41.9..8.7.......1.2.........3;........1.....2.3...4.5.6...3.....72.4....8..6..8..9...7...1...4.56.....8..59....;11.80;1.20;1.20;dob;12_12_03;247964;22;98.76.5..7.5..9....645.8...8...75.9.5.649...7...8.....6.....4.3...6.4...........2;98.76.5..7.5..9....645.8...8...75.9.5.649...7...8.....6.....4.3...6.4...........2   11.8/1.2/1.2 monh98.76.5..7.58.49...46.5.....78.46.9...958.......9.7....6.........4....32.....8.5.;98.76.5..7.58.49...46.5.....78.46.9...958.......9.7....6.........4....32.....8.5.   11.8/1.2/1.2 monh98.76.5..7.5.496...4.......67.89....5..4.6.7..94.5........8..........8.3......4.2;98.76.5..7.5.496...4.......67.89....5..4.6.7..94.5........8..........8.3......4.2   11.8/1.2/1.2 monh98.76.5..7.4..98...56......8..5.6.9..67.8......9.74.......4..........6.3......4.2;98.76.5..7.4..98...56......8..5.6.9..67.8......9.74.......4..........6.3......4.2   11.8/1.2/1.2 monh98.76.5..7.4..98...56..8...8..5.6.9.5.9.74....679.........4..........6.3......4.2;98.76.5..7.4..98...56..8...8..5.6.9.5.9.74....679.........4..........6.3......4.2   11.8/1.2/1.2 monh98.76.5..7.5.496...4.5.....67.89....5..4.6.7..94..7.......8..........8.3......4.2;98.76.5..7.5.496...4.5.....67.89....5..4.6.7..94..7.......8..........8.3......4.2   11.8/1.2/1.2 monh98.76.5..7.5..89...645.9...59...4....486.5.7...7.8......6....9....4............32;98.76.5..7.5..89...645.9...59...4....486.5.7...7.8......6....9....4............32   11.8/1.2/1.2 monh`

The last 7 puzzles are new. B7B Is thus largely extended, but this old frontier within T&E(2) remains.
: note that all the new B7B puzzles have SER = 11.8, which shows once more that 11.9 vs 11.8 has no intrinsic meaning.
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Last edited by denis_berthier on Fri Sep 08, 2023 6:56 am, edited 1 time in total.
denis_berthier
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Re: The BpB classification of T&E(2) puzzles

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Considering that the T&E(2) Paquita's database is an intermediary version of a more stable one, I'm not going to do more calculations on it. It might be the case that new B7B puzzles will appear for SER=11.7, but we'll have to wait for the stable version for verification. In the old ph2010 database, this was not the case, but it can't be excluded.

Instead of more calculations, let me add a few words about T&E(n) and BpB. This is not new, as I must have written it many times in various forms and in many places. But it fits in this thread.

First of all, anything I'm saying below has a universal meaning for any finite binary CSP (Constraint Satisfaction Problem). (And I've shown in [PBCS] that many non-binary problems can be turned into binary ones by specific methods more efficient that the well-known universal one.)

The universal meaning of a puzzle being in T&E(n) is important to recall. It means that, in spite of being a binary problem, the puzzle at hand requires considering (indirect) contradictions between n candidates in the process of constructively eliminating candidates using only Singles and their direct implications.
The simplest case is T&E(1), where a candidate C can be proven false using only braids, a pattern-based way of proving an indirect contradiction implied by C alone. And the B rating provides the Bp sub-classification of T&E(1), by the maximal length of braids necessary to solve a puzzle in T&E(1).

Similarly, the universal meaning of being in BpB for a puzzle in T&E(2) is important. If the puzzle is in T&E(2), we know by the previous remark that we can solve it using indirect contradictions between at most 2 candidates. The value of p puts an upper bound on the complexity necessary to find these indirect contradictions. (Technically, this is the maximal length of inner braids in B-braids.)

Needless to say, these universal classifications are intrinsic to each puzzle (no arbitrary thresholds as in SER) and stable under isomorphisms.
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denis_berthier
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Re: The BpB classification of T&E(2) puzzles

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The Hunting of the B8B

You may seek it with thimbles - and seek it with care;
You may hunt it with forks and hope;
You may threaten its life with a railway-share;
You may charm it with smiles and soap;

But oh, beamish nephew, beware of the day,
If your Snark be a Boojum! For then
You will softly and suddenly vanish away,
And never be met with again!

For those of you who want to hunt a hypothetical B8B puzzle with the help of SudoRules, here is a non "perfect and absolute blank" map that should preserve you from the bad fate of meeting a Boojum.

1) The BpB classification applies only to puzzles in T&E(2). Your first step should always be to make sure your list of puzzles doesn't include ones in T&E(3). T&E(3) is where Boojums like to hide. They provoke very long and useless calculations (but nothing will vanish away, except maybe your patience and your processor time).

2) After the previous step, remember that it's generally faster to solve a puzzle than to reach a point were the current set of rules concludes that it is not enough to solve it. Knowing the SER of your puzzles, use table 11.2 of [PBCS] to choose the value of p for testing if they belong to T&E(Bp).

3) If you only want to find a Snark (the case p=8), instead of computing the detailed BpB distribution of your puzzles, always choose p=7. Anything not solved will be a Snark (possibly a Boojum if you overlooked the 1st recommendation).
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denis_berthier
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Re: The BpB classification of T&E(2) puzzles

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Based on calculations with SudoRules, Table 11.2 of [PBCS] proposed a classification of T&E(2) puzzles based only on a part of eleven's gotchi collection, defined here:
http://forum.enjoysudoku.com/the-making-of-a-gotchi-a-simple-way-to-find-extreme-sudokus-t30150.html

Using the faster Sudoku Hierarchical Classifier (SHC)
(http://forum.enjoysudoku.com/the-sudoku-hierarchical-classifier-shc-t42075.html,
https://github.com/denis-berthier/Sudoku_Hierarchical_Classifier))
I could run the calculations for the full collection of 26,370 puzzles.

General conclusions are unchanged, be it for the maximum value of p = 7 for the BpB classification or for the vague correlation between the SER and the BpB classification.

However, one more geenral conclusion is, the SHC allows much better computation times than the SER (or even its PGXplainer variant) and it could replace it in the search of the hardest T&E(2) puzzles.

The following table 4.2 form [HCCS] (https://www.researchgate.net/publication/374508822_Hierarchical_Classifications_in_Constraint_Satisfaction)
shows the respective times for the 3 softwares:
(the SER PGX part was already published here:
http://forum.enjoysudoku.com/pgexplainer-a-minimal-sudokuexplainer-in-56-712-bytes-t39049-45.html)

Code: Select all
`BpB =               2       3       4        5        6        7mean SER            11.09   11.45   11.63    11.78    11.76    11.8BpB mean time (s)   0.45    1.00    2.35     4.00     5.45     10.8SER mean time (s)   164.6   405.9   533.5    1240.6   888.8    635.4PGX mean time (s)   156.2   362.6   639.8    941.4    880.6    591.3`

Note that the times reported here are real total processor times, not apparent user times. Like the SER, the SHC has little parallelism (still less than SER) but PGX has much more than both of them, so that the PGX times below will appear lower, maybe 2 or 3 times lower than those for SER, if one considers only apparent user time; but run 3 or 4 instances of PGX in parallel in order to reduce parallelism and you’ll understand that real processor time is what really counts when you have to deal with large collections, e.g. then trying to find hard puzzles.

In any case, the comparisons speak by themselves: the BpB computation times are one or two orders of magnitude shorter than the SER or PGX ones.
The lower BpB cases (p = 2 or 3) with high SER are particularly noticeable: while using the SER would require long computation times, using the BpB classification instead allows to eliminate them from the BpB-hardest list in almost no time.

What this implies is, the SHC is the harpoon you needed to start hunting the Snark, without having to go through the SER optimisation.

[Edit 2022-11-03]: updated the SHC mean times to the most recent version of SHC.
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denis_berthier
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Re: The BpB classification of T&E(2) puzzles

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and I remarked that they have:
- unusually high proportions of non-degenerate tridagons (resp. 97.01%, 99.97% and 100%);
- unusually high proportions of puzzles in B6B;
- no puzzle in B7B.

It contains 55,088 puzzles, 46,079 of which are in T&E(2), the rest in T&E(3).
The puzzles in T&E(3) all have a non-degenerate tridagon pattern and they are all in B2BB=T&E(B2, 2), same as all the known T&E(3) puzzles.

Let's therefore concentrate on the T&E(2) sublist. This is where the main news are.

First big news is, it has 77 puzzles in B7B. (Until now, we knew only 10 different ones.)

Code: Select all
`puzzle  ER/EP/ED creation_date position_in_T&E(2)_list98.76.54.7.5.4.8....6....9.67...5...4.8...75..59....68...3....9...2..........4...    11.7/1.2/1.2    220515  #307998.76.5..7.4.8.....56...8..8.5..7.4.6..59.....79.48.6....9....3......4..........2    11.7/1.2/1.2    220515  #308098.76.54.7.5..4....6...8.9.85.9.6...4.6.87......45...8..7...3........2..........9    11.7/1.2/1.2    220515  #308198.76.54.7.5.9.....64..8.9.85.9.6...4.6.87......45...8..7...3........2..........9    11.7/1.2/1.2    220515  #323398.76.54.7.5.498...6.8.....49..87....579.6......45...9..6....3........2.........8    11.7/1.2/1.2    220515  #323498.76.54.7.5..4....6...8.9.8..9.6...4.6.87..5...45...8..7...3........2..........9    11.7/1.2/1.2    220515  #323598.76.54.7.5.9.....64..8.9.8..9.6...4.6.87..5...45...8..7...3........2..........9    11.7/1.2/1.2    220515  #323698.76.5..7.5.498...648......9..87....579.6.4....45..9...6.....3.......8.........2    11.7/1.2/1.2    220515  #323798.76.5..7.5..9....645.8...8...75.9.5.649...7...8.....6.....4.3...6.4...........2    11.8/1.2/1.2    220928  #574398.76.5..7.58.49...46.5.....78.46.9...958.......9.7....6.........4....32.....8.5.    11.8/1.2/1.2    220928  #574498.76.5..7.5.496...4.......67.89....5..4.6.7..94.5........8..........8.3......4.2    11.8/1.2/1.2    230514  #1534098.76.5..7.4..98...56......8..5.6.9..67.8......9.74.......4..........6.3......4.2    11.8/1.2/1.2    230514  #1534498.76.5..7.4..98...56..8...8..5.6.9.5.9.74....679.........4..........6.3......4.2    11.8/1.2/1.2    230514  #1534598.76.5..7.5.496...4.5.....67.89....5..4.6.7..94..7.......8..........8.3......4.2    11.8/1.2/1.2    230514  #1534698.76.5..7.5..89...645.9...59...4....486.5.7...7.8......6....9....4............32    11.8/1.2/1.2    230514  #1538298.76.5..7.6.4......58.....6.859..4.45..7.....9.6......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3441298.76.5..7.5.496...4.5.....67.89....5..4.6.7..94.7........8..........8.3......4.2    11.6/1.2/1.2    230514  #3715498.76....7.6..5....458.....6...98.....7..48.....57.9..5.4....98.....6..........32    11.6/1.2/1.2    230514  #3718898.76.5..7.5.496...4.......67.89....5....6.7..94.5........84.........8.3......4.2    11.6/1.2/1.2    230514  #3732598.76.5..7.5..96...4.......67.89....5..4.6.7..94.5........84.........8.3......4.2    11.6/1.2/1.2    230514  #3739698.76.5..7.6.4......58.....6.859..4.4...7.....9.6...5..7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3743398.76.5..7.4..98...5.......8..5.6.9..67.8......9.74...6.....4.3....4..........6.2    11.6/1.2/1.2    230514  #3743998.76....7.6..58...458.....6...98.....7..4......57..9.5.4...9.8.....6.........3.2    11.6/1.2/1.2    230514  #3747598.76.5..7.4..98...56......8..5...9..67.8......9.74......64..........6.3......4.2    11.6/1.2/1.2    230514  #3748598.76.5..7.6.45.....58.....6.8.9..4.45..7.....9.6......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3751798.76.5..7.6.4......58.....6.759..4.45..78....9.6......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3802898.76.5..7.4..98...56..8...8..5.6.9.5.7.94....6..7........4..........6.3......4.2    11.6/1.2/1.2    230514  #3883698.76.5..7.4..98...56..8...8..5.6.9.5.9.74....67.9........4..........6.3......4.2    11.6/1.2/1.2    230514  #3884498.76.5..7.4..98...5.......8..5...9..67.8......9.74...6.....4.3...64..........6.2    11.6/1.2/1.2    230514  #3889198.76.5..7.6.4......58.9...6..5...4.45..78....976......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3892298.76.5..7.6.45.....58.9...6......4.45..78....976......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3892798.76.5..7.5.496...4.5.....67.89....5..4.6.7..94..5.......8..........8.3......4.2    11.6/1.2/1.2    230514  #3893998.76.5..7.5.496...4.5.....69.87....5..4.6.7...4.9........8..........8.3......4.2    11.6/1.2/1.2    230514  #3894498.76.5..7.6.45.....58.....6...9..4.45..78....976......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3896798.76.5..7.4..98...56..8...8..5...9.5.9.74....679........64..........6.3......4.2    11.6/1.2/1.2    230514  #3900198.76.5..7.6.4......58.9...6.75...4.4...78....9.6...5..7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3904498.76.5..7.6.4......58.....6.759..4.4...78....9.6...5..7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3904598.76.5..7.6.4......58.....6..59..4.4...78....986...5..7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3904998.76.5..7.6.4......58.....6..59..4.45..78....976......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3905298.76....7.6.54....548.....64..98.....76.58......7.9..4.5....98.....6..........32    11.6/1.2/1.2    230514  #3905898.76.5..7.4..98...56..8...8..5.6.9..678.......9.74.......4..........6.3......4.2    11.6/1.2/1.2    230514  #3905998.76.5..7.5..96...4.5.....67.89....5..4.6.7..94..7.......84.........8.3......4.2    11.6/1.2/1.2    230514  #3908198.76.5..7.5.496...4.5.....67.89....5....6.7..94..7.......84.........8.3......4.2    11.6/1.2/1.2    230514  #3914098.76.5..7.5.496.....5.....69.87....5..4.6.7...4.9....4.....8.3....8..........4.2    11.6/1.2/1.2    230514  #3916298.76.5..7.6.45.....58.....6...9..4.45..78....986......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3916798.76.5..7.5..96...4.5.....69.87....5..4.6.7...4.9....4.....8.3....8..........4.2    11.6/1.2/1.2    230514  #3917098.76....7.6.54....548.....64..98.....7..58.....67.9..4.5....98.....6..........32    11.6/1.2/1.2    230514  #3919398.76.5..7.5.496...4.5.....67.89....5....6.7..94.7........84.........8.3......4.2    11.6/1.2/1.2    230514  #3919798.76.5..7.6.4......58.9...6.75...4.45..78....9.6......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3920098.76.5..7.4..98...5...8...8..5...9..678.......9.74...6.....4.3...64..........6.2    11.6/1.2/1.2    230514  #3921198.76.5..7.5.496...4.5.....69.87....5....6.7...4.9........84.........8.3......4.2    11.6/1.2/1.2    230514  #3922498.76.5..7.6.45.....58.....6.7.9..4.45..78....9.6......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3926198.76.5..7.5..96...4.5.....69.87....5..4.6.7...4.9........84.........8.3......4.2    11.6/1.2/1.2    230514  #3926598.76.5..7.5.496...4.5.....67.89....5....6.7..94..5.......84.........8.3......4.2    11.6/1.2/1.2    230514  #3931898.76.5..7.5..96...4.5.....67.89....5..4.6.7..94.7........84.........8.3......4.2    11.6/1.2/1.2    230514  #3933698.76.5..7.4..98...56..8...8..5...9..678.......9.74......64..........6.3......4.2    11.6/1.2/1.2    230514  #3942298.76.5..7.6.4......58.....6..59..4.45..78....986......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3943198.76.5..7.6.45.....58.9...6.7....4.45..78....9.6......7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3944398.76.5..7.4..98...5...8...8..5.6.9..678.......9.74...6.....4.3....4..........6.2    11.6/1.2/1.2    230514  #3944798.76....7.6..58...458.....65..98.....75.4.......7..9.5.4...9.8.....6.........3.2    11.6/1.2/1.2    230514  #3945598.76....7.6..5....458.....65..98.....75.48......7.9..5.4....98.....6..........32    11.6/1.2/1.2    230514  #3945898.76.5..7.5..96...4.5.....67.89....5..4.6.7..94..5.......84.........8.3......4.2    11.6/1.2/1.2    230514  #3946498.76.5..7.4..98...56..8...8..5.6.9..6.87......7.94.......4..........6.3......4.2    11.6/1.2/1.2    230514  #3968198.76.5..7.6.4......58.....6..59..4.4...78....976...5..7..........98.4.5......3.2    11.6/1.2/1.2    230514  #3979798.76.5..7.4..98...5...8...8..5...9..6.87......7.94...6.....4.3...64..........6.2    11.6/1.2/1.2    230514  #3995098.76....7.5...9...46..5...5..98.....6.5.7.8...8.46....7..........6.4.98.......32    11.6/1.2/1.2    230514  #3995298.76.5..7.4..98...56..8...8..5...9.5.7.94....6..7.......64..........6.3......4.2    11.6/1.2/1.2    230514  #3995398.76.5..7.4..98...5...8...8..5.6.9..6.87......7.94...6.....4.3....4..........6.2    11.6/1.2/1.2    230514  #3995598.76....7.5...9...46..58..5..98.....6.5.7.....8.46....7..........6.4.98.......32    11.6/1.2/1.2    230514  #3995798.76.5..7.4..98...56..8...8..5...9..6.87......7.94......64..........6.3......4.2    11.6/1.2/1.2    230514  #3995998.76.5..7.6..5....4..8....8..6...5.5...98.4..97.4....67....4.5...9...........3.2    11.6/1.2/1.2    230514  #3996098.76.5..7.6..5....45.8....8..6......9754........98.4.67....4.5...9...........3.2    11.6/1.2/1.2    230514  #3996198.76.5..7.6..5....4..8....8..6.....5...98.4..9754....67....4.5...9...........3.2    11.6/1.2/1.2    230514  #3996298.76.5..7.5.496.....5.....69.87....5....6.7...4.9....4.....8.3....84.........4.2    11.6/1.2/1.2    230514  #3996598.76....7.6..5....45.8....8..6..5...9754........984..67.....54...9............32    11.6/1.2/1.2    230514  #3996698.76.5..7.6.4......58.9...6..5...4.4...78....976...5..7..........98.4.5......3.2    11.6/1.2/1.2    230514  #4011898.76.5..7.4..98...56..8...8..5...9.5.9.74....67.9.......64..........6.3......4.2    11.6/1.2/1.2    230514  #40187`

Second big news is, it has puzzles beyond B7B. Indeed, it has 15 puzzles in B9B and 1 in B10B and they don't even have the highest SER.

Code: Select all
`puzzle  ER/EP/ED creation_date position_in_T&E(2)_list BpB_classif98.76.5..7.48......56......56..8..4.4.89.6....7945......7..........9...3....7.2.1   11.6/1.2/1.2   220515  #4706   B9B987......6...........85.....4.3..21....42..58....184.3..2..31.....54.32....1...84   11.6/1.2/1.2   220928  #15309  B9B987......65.9...........6..4..32.16.3..1.4..2....96......4...19...2.13......3.42.   11.7/1.2/1.2   230514  #19131  B9B987......65.9...........6..4..32.91.2..4.13.6....6.......2...93...13.4......942.1   11.7/1.2/1.2   230514  #21539  B9B987......65.9...........6..4..32.91.2..4.13.6....6.......2...93...13.46......42.1   11.7/1.2/1.2   230514  #22103  B9B98765.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....27......5.8   11.7/1.2/1.2   230514  #29398  B10B987......6...........85.....4.3.521....42..58....1.4.3..2..31.....54.32....1...84   11.6/1.2/1.2   230514  #31148  B9B987......6..8...........5...4.32..1....4.12.8....5834...32....1...13.45.....84.2.   11.6/1.2/1.2   230514  #31627  B9B98.76.5..7.58.49...64.9....64..78.5.5.8.......9.54.....7............6..3.......21   11.6/1.2/1.2   230514  #34255  B9B98.76.5..7.5.......64.8....8..5.7.4..9784.....5..96...6.9.........9....3......2.1   11.6/1.2/1.2   230514  #37229  B9B98.76.5..7.5.......64.9....6..5.7.4.5...89....7864.....9..........8....3......2.1   11.6/1.2/1.2   230514  #38797  B9B98.76.5..7.59.4.......8....6.95.....47.6.8.....8.7..4..6......3....96.........2.1   11.6/1.2/1.2   230514  #38898  B9B98.76.5..7.59.4.....6.8....6.95.....47.6.8.....8.7..4..9....3.2....96...........1   11.6/1.2/1.2   230514  #38903  B9B98.76.5..7.5..9....64.8....8..5.7.4..9784.....5..96...6.9.........6..3.2........1   11.6/1.2/1.2   230514  #38924  B9B98.76.5..7.59.4.....6.8....6.75.....49.6.8.....8.9..4..7....3.2....76...........1   11.6/1.2/1.2   230514  #39788  B9B98.76.5..7.59.4.......8....6.75.....49.6.8.....8.9..4..6......3....76.........2.1   11.6/1.2/1.2   230514  #39823  B9B`

In the same way as I couldn't believe my eyes when I found that Loki was not in T&E(2), I couldn't believe that these puzzles were not in B7B or lower and that they were not even in B8B. But all the checks I made lead to the conclusion that the results are correct.

Notice however that all these puzzles have a non-degenrate tridagon and they can be easily solved with short chains and Trid-ORk-chains when it is used (except 4 of the 77 B7B ones that require longer chains).

Note that all these results where made possible by the SHC:
(http://forum.enjoysudoku.com/the-sudoku-hierarchical-classifier-shc-t42075.html).
Without it, the computations could be done by SudoRules, but they would take so much more time as to become impractical.
.
denis_berthier
2010 Supporter

Posts: 4045
Joined: 19 June 2007
Location: Paris

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

Hi Denis Thank you for your program and I have used it on the puzzles I generated over the past couple of months....

Firstly ... I have expanded my minimal puzzles further than mini-expanding with singles, and its possible to get a maxi-expand to "pearl"

Your 16 puzzles with B9B and above originate from 8 solution grids, and here are the maxi-expands
Code: Select all
`98.76.5..7.48.5....56..9...56..87.4.4.89.6....7945......7..........9...3....7.2.1 ED=11.6/11.6/6.6987......6.....8.....85.....4.3.521....42..58....184.34.2.831.....54.32....1.2.84 ED=11.6/11.6/2.698765.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....277.9...5.8 ED=11.7/11.7/2.698.76.5..7.58.49...64.95...64..78.5.5.86......9754.....7......5.....6..3.....7.21 ED=11.6/11.6/2.698.76.5..7.5..9....64.85...8.65.7.4..9784....45..96...6.9.........9....3...6..291 ED=11.6/11.6/6.698.76.5..7.5..8....64.95...6.95.7.4.54..89....7864.....9..........8....3...9..2.1 ED=11.6/11.6/6.698.76.5..7.59.4.....6.85...6.754....49.6.8....58.97.4..7....362....76....6......1 ED=11.6/11.6/6.6987......65.9...........69.4..32.16.3..1.49.2....96......4...19...2.13.6....3942. ED=11.6/11.6/3.4`

These minimize to 50 minimal puzzles all presumably with same rating
Hidden Text: Show
Code: Select all
`98.76.5..7.48......56......56..8..4.4.89.6....7945......7..........9...3....7.2.1   2898.76.5..7.48.5.....6......56..8..4.4.89.6....7945......7..........9...3....7.2.1   2898.76.5..7.48......56......56..87.4.4.89.6....7945......7..........9...3......2.1   2898.76.5..7.48.5.....6......56..87.4.4.89.6....7945......7..........9...3......2.1   289.7......6.....8......5.....4.3..21....42..58....184.3..2.831.....54.32....1....4   279.7......6.....8......5.....4.3..21....42..58....184.34.2.831.....54.32....1.....   279.7......6.....8.....85.....4.3..21....42..58....184.3..2..31.....54.32....1...84   28987......6...........85.....4.3..21....42..58....184.3..2..31.....54.32....1...84   28987......6.....8......5.....4.3..21....42..58....184.3..2..31.....54.32....1...84   289.7......6.....8.....85.....4.3.521....42..58....1.4.3..2..31.....54.32....1...84   28987......6...........85.....4.3.521....42..58....1.4.3..2..31.....54.32....1...84   289.7......6.....8.....85.....4.3.521....42..58....1.4.3..2.831.....54.32....1....4   289.7......6.....8.....85.....4.3..21....42..58....184.34.2..31.....54.32....1...8.   28987......6...........85.....4.3..21....42..58....184.34.2..31.....54.32....1...8.   28987......6.....8......5.....4.3..21....42..58....184.34.2..31.....54.32....1...8.   289.7......6.....8.....85.....4.3.521....42..58....1.4.34.2..31.....54.32....1...8.   28987......6...........85.....4.3.521....42..58....1.4.34.2..31.....54.32....1...8.   289.7......6.....8.....85.....4.3.521....42..58....1.4.34.2.831.....54.32....1.....   2898765.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....27......5.8   28    only one minimal !98.76.5..7.58.49...64.9....64..78...5.8.......9.54.....7......5.....6..3.......21   2898.76....7.58.49...64.95...64..78.5.5.8.......9..4.....7......5.....6..3.......21   2898.76.5..7.58.49...64.9....64..78.5.5.8.......9.54.....7............6..3.......21   2898.76.5..7.58.49...64.95...64..78.5.5.8.......9..4.....7............6..3.......21   2898.76.5..7.........64.85...8....7.4..9784.....5..96...6...........9....3......291   2698.76.5..7.........64.85...8....7.4..9784.....5..96...6.9.........9....3......2.1   2698.76.5..7.5.......64.8....8..5.7.4..9784.....5..96...6...........9....3......291   2798.76.5..7....9....64.85...8....7.4..9784.....5..96...6.9..............3......291   2798.76.5..7....9....64.85...8....7.4..9784.....5..96...6.9..............3...6..2.1   2798.76.5..7.5.......64.8....8..5.7.4..9784.....5..96...6.9.........9....3......2.1   2798.76.5..7.5..9....64.8....8..5.7.4..9784.....5..96...6.9..............3......291   2898.76.5..7.5..9....64.8....8..5.7.4..9784.....5..96...6.9..............3...6..2.1   28.8.76.5..7.5.......64.9....6.95.7.4.5...89....7864.....9..........8....3......2.1   2698.76.5..7.5.......64.9....6..5.7.4.5...89....7864.....9..........8....3......2.1   2698.76.5..7.59.4.......8....6.75.....49.6.8.....8.9..4.......3.2....76....6......1   2698.76.5..7.59.4.......8....6.75.....49.6.8.....8.9..4.......362....7.....6......1   2698.76.5..7..9.4.......85...6.75.....49.6.8....58.9..4.......3.2....76....6......1   2798.76.5..7..9.4.......85...6.75.....49.6.8....58.9..4.......362....7.....6......1   2798.76.5..7.59.4.....6.8....6.75.....49.6.8.....8.9..4.......362....76...........1   2798.76.5..7.59.4.....6.8....6.75.....49.6.8.....8.9..4..7....3.2....76...........1   2798.76.5..7..9.4.....6.85...6.75.....49.6.8....58.9..4.......362....76...........1   2898.76.5..7..9.4.....6.85...6.75.....49.6.8....58.9..4..7....3.2....76...........1   28.87......65.............69.4..32.16.3..1.4..2....96......4...19...2.13......3942.   27.87......65.9...........69.4..32.16.3..1.4..2....96......4...19...2.13......3.42.   27987......65.9...........6..4..32.16.3..1.4..2....96......4...19...2.13......3.42.   27.87......65.............69.4..32.16.3..1.49.2....96......4...1....2.13.6....3942.   28.87......65.9...........69.4..32.16.3..1.49.2.....6......4...1....2.13.6....3942.   28.87......65.9...........69.4..32.16.3..1.49.2.....6......4...19...2.13......3942.   28987......65.9...........6..4..32.16.3..1.49.2.....6......4...19...2.13......3942.   28.87......65.9...........69.4..32.16.3..1.49.2.....6......4...19...2.13.6....3.42.   28987......65.9...........6..4..32.16.3..1.49.2.....6......4...19...2.13.6....3.42.   28`

Here are the puzzles that I found in T&E(2) greater than B6B. They are in minlexsolution grid format as this is easier to work with and visualise differences.
Code: Select all
`.23.56......18.23......24..3.5...9..29........64.9.3.253.....24.46..359.9.2..56.3##  ED=11.7/11.7/8.9 ##  B7B 12.4.6.8.4.718.....68.72.1.24.7.86.1.71.....88.6..1....14...82......7.43........5##  ED=11.7/11.7/8.9 ##  B7B 12..567...571.92..6.972.1..26........7569..129.12.....592....71......9.4...9..5.3##  ED=11.6/11.6/2.6 ##  B7B                                                                                                         123...7.9.56..9....89......2..6.139........21.1....6.7...96.21...12.3.76..2.179.3##  ED=11.7/11.7/2.6 ##  B8B   `

These too have many less minimal puzzles than the rest of my collection of maxi-expands
Hidden Text: Show
Code: Select all
`.23.56......18.........24..3.5...9...9........64.9.3.2........4.46..359.9.2..56.3u.2..56......18..3......24..3.5...9...9........64.9.3.2.3......4.46..359.9.2..56...23.56......18..3......24..3.5...9...9........64.9.3.2........4.46..359.9.2..56....3.56......18.........24....5...9..29........64.9.3.2.3.....24.46..359.9.2..56.3..3.56......18.........24....5...9..29........64.9.3.25......24.46..359.9.2..56.3..3.56......18.........24..3.5...9..29........64.9.3.2.......24.46..359.9.2..56.3..3.56......18.2.......24....5...9..29........64.9.3.2.3......4.46..359.9.2..56.3.23.56......18.........24....5...9..29........64.9.3.2.3......4.46..359.9.2..56.3..3.56......18.2.......24....5...9..29........64.9.3.25.......4.46..359.9.2..56.3.23.56......18.........24....5...9..29........64.9.3.25.......4.46..359.9.2..56.3..3.56......18.2.......24..3.5...9..29........64.9.3.2........4.46..359.9.2..56.3..3.56......18.2.......24....5...9..29........64.9.3.2.3.....24.46..359.9....56.3.23.56......18.........24....5...9..29........64.9.3.2.3.....24.46..359.9....56.3..3.56......18.2.......24....5...9..29........64.9.3.25......24.46..359.9....56.3.23.56......18.........24....5...9..29........64.9.3.25......24.46..359.9....56.3..3.56......18.2.......24..3.5...9..29........64.9.3.2.......24.46..359.9....56.3.23.56......18.........24..3.5...9..29........64.9.3.2.......24.46..359.9....56.3....56......18..3......24..3.5...9..29........64.9.3.2.3.....24.46..359.9.2..56....3.56......18..3......24....5...9..29........64.9.3.2.3.....24.46..359.9.2..56....3.56......18..3......24....5...9..29........64.9.3.25......24.46..359.9.2..56....3.56......18..3......24..3.5...9..29........64.9.3.2.......24.46..359.9.2..56......56......18.23......24..3.5...9..29........64.9.3.2.3......4.46..359.9.2..56....3.56......18.23......24....5...9..29........64.9.3.2.3......4.46..359.9.2..56...23.56......18..3......24....5...9..29........64.9.3.2.3......4.46..359.9.2..56....3.56......18.23......24....5...9..29........64.9.3.25.......4.46..359.9.2..56...23.56......18..3......24....5...9..29........64.9.3.25.......4.46..359.9.2..56....3.56......18.23......24..3.5...9..29........64.9.3.2........4.46..359.9.2..56...2..56......18..3......24..3.5...9..29........64.9.3.2.3.....24.46..359.9....56....3.56......18.23......24....5...9..29........64.9.3.2.3.....24.46..359.9....56...23.56......18..3......24....5...9..29........64.9.3.2.3.....24.46..359.9....56....3.56......18.23......24....5...9..29........64.9.3.25......24.46..359.9....56...23.56......18..3......24....5...9..29........64.9.3.25......24.46..359.9....56....3.56......18.23......24..3.5...9..29........64.9.3.2.......24.46..359.9....56...23.56......18..3......24..3.5...9..29........64.9.3.2.......24.46..359.9....56...2.4.6...4.7.8.....6..72.1.24.7..6...71.....88.6..1....14...82......7.43........512.4.6...4.7.8.....6..72.1.24.7..6...7......88.6..1....14...82......7.43........5.2.4.6.8.4.7.8.....6..72.1.24.7..6...71......8.6..1....14...82......7.43........512.4.6.8.4.7.8.....6..72.1.24.7..6.1.7.......8.6..1....14...82......7.43........512.4.6.8.4.718.....6..72...24.7..6.1.7.......8.6..1....14...82......7.43........512.4.6.8.4.7.8.....6..72.1.24.7.86...7.......8.6..1....14...82......7.43........512.4.6...4.718.....68.72...24.7..6...71.....88.6..1....14...82......7.43........512.4.6.8.4.718.....6..72...24.7..6...71.....88.6..1....14...82......7.43........512.4.6...4.718.....68.72...24.7..6.1.7......88.6..1....14...82......7.43........5.2.4.6.8.4.71......68.72.1.24.7.86...71......8.6..1....14...82......7.43........512.4.6.8.4.71......68.72...24.7.86...71......8.6..1....14...82......7.43........512.4.6.8.4.718.....6..72...24.7.86...71......8.6..1....14...82......7.43........512.4.6.8.4.71......68.72...24.7.86.1.7.......8.6..1....14...82......7.43........512.4.6.8.4.71......68.72.1.24.7.86...7.......8.6..1....14...82......7.43........5....567...571.....6.972.....6........7569..12..12.....5.2....71......9.4...9..5.3....567...571.....6.972.1...6........7569..12..12.....5.2....7.......9.4...9..5.31...567...571.....6.972.....6........7569..12..12.....5.2....7.......9.4...9..5.3....567...571.....6.972.....6........7569..12..12.....592....71......9.4......5.3....567...571.....6.972.1...6........7569..12..12.....592....7.......9.4......5.31...567...571.....6.972.....6........7569..12..12.....592....7.......9.4......5.3....567...571.9...6.972.....6........756...129.12.....5.2....71......9.4...9..5.3....567...571..2..6.972.....6........7569..1.9.12.....5.2....71......9.4...9..5.3....567...571.92..6.972.....6........756...1.9.12.....5.2....71......9.4...9..5.3....567...571..2..6.972....26........7569..1...12.....5.2....71......9.4...9..5.3....567...571.9...6.972.1...6........756...129.12.....5.2....7.......9.4...9..5.31...567...571.9...6.972.....6........756...129.12.....5.2....7.......9.4...9..5.3....567...571..2..6.972.1...6........7569..1.9.12.....5.2....7.......9.4...9..5.31...567...571..2..6.972.....6........7569..1.9.12.....5.2....7.......9.4...9..5.3....567...571.92..6.972.1...6........756...1.9.12.....5.2....7.......9.4...9..5.31...567...571.92..6.972.....6........756...1.9.12.....5.2....7.......9.4...9..5.3....567...571..2..6.972.1..26........7569..1...12.....5.2....7.......9.4...9..5.31...567...571..2..6.972....26........7569..1...12.....5.2....7.......9.4...9..5.3....567...571.9...6.972.....6........756...129.12.....592....71......9.4......5.3....567...571..2..6.972.....6........7569..1.9.12.....592....71......9.4......5.3....567...571..2..6.972....26........7569..1...12.....592....71......9.4......5.3....567...571.9...6.972.1...6........756...129.12.....592....7.......9.4......5.31...567...571.9...6.972.....6........756...129.12.....592....7.......9.4......5.3....567...571..2..6.972.1...6........7569..1.9.12.....592....7.......9.4......5.31...567...571..2..6.972.....6........7569..1.9.12.....592....7.......9.4......5.3....567...571..2..6.972.1..26........7569..1...12.....592....7.......9.4......5.31...567...571..2..6.972....26........7569..1...12.....592....7.......9.4......5.3....567...571.92..6.972....26........756...1.9.12.....592....71......9.4......5.3....567...571.92..6.972.1..26........756...1.9.12.....592....7.......9.4......5.31...567...571.92..6.972....26........756...1.9.12.....592....7.......9.4......5.31.3...7...56..9....89......2..6..39........21.1....6.7...96.2....12.3..6....179.31.3...7...56..9....89......2..6.139........21......6.7...96.2....12.3..6....179.31.3...7...56..9....89......2..6..39........21.1....6.7...96.21....2.3..6....179.3123...7...56..9....89.........6..39........21.1....6.7...96.2....12.3..6..2.179.3123...7...56..9....89.........6.139........21......6.7...96.2....12.3..6..2.179.3123...7...56..9....89.........6..39........21.1....6.7...96.21....2.3..6..2.179.3`

EDIT
the 77 puzzles in B7B originate from 6 solution grids.
Here are the maxi-expands for these - they are in minlexsolutiongrid format which shows the swopped pairs in the first 3 These minimize to the same 77 minimal puzzles.
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`12..56....571.9..66.927...127.69.....917.5.....6.12.9.......8.2...52......2...3.5 ED=11.6/11.6/2.6 12..56....571.9..66.927...127.96.....917.5.....6.12.9.......3.2...52......2...8.5 ED=11.6/11.6/2.6 12..56....571.9..66.927...129.76.....719.5.....6.12.9.......3.2...52......2...8.5 ED=11.6/11.6/2.6 ...4.6.....7....36.......5.24.6.7...7.8.14..2.6182......274.1...14.68...87.2.1... ED=11.6/11.6/9.2 12.....89.5.1..2.66.82..15....9..........4.....5..7....86.9..125.2...96.91..628.5 ED=11.7/11.7/10.5..3.567.9..71.9.63...73.15..3.51.69.....93......6.73.........1..7..6....84....5.. ED=11.8/11.8/3.4 `

the 8 maxi-expands in minlexsolutiongrid format for those with BpB>8 are
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`.2.4.678....18.2.6.8..27.142......4.3...6....9.5.........6.2.78...81.4.28.2.7.16.1.3.56....5718..3.68.7.3....3587....8.63.1....1..653.8.6....4.....6.7.........96212..56..9.571.9...6.972....2.....34.7.....8.....2......7.56....5.2.17.6..619.2...1.3.5.7.9.57....3669..3.51...13.567.36....1.5.75....93..6..2........39.....8.4...1.3.5.7.9.57....3669..7.15..165..39.53......17.9...6.5.....2.6...1..5......8.4.1.1.3.5.7.9.......3669..7.15.....386..3.6.........264...5.9....6773....91..61...5..1.3..67.9.57..9.3669....15..16....9337....5.19.5....7....8.....7316.5.......4....1.3.56..9.571.9...69.73.........7.4..3.............82.3.6.95...57...169..1967....`
coloin

Posts: 2425
Joined: 05 May 2005
Location: Devon

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

Hi Coloin
Great work.

coloin wrote:Hi Denis Thank you for your program

Do you mean SudoRules? If you mean SHC, it's François's program.

coloin wrote:Firstly ... I have expanded my minimal puzzles further than mini-expanding with singles, and its possible to get a maxi-expand to "pearl"

I'm not sure what you mean by "maxi-expand to "pearl"".
With mith, we understand min-expand as expansion by Singles and max-expand as further addition of candidates until adding more would make the puzzle loose one depth of T&E. [Indeed, we considered only the case of a puzzle in T&E(3), but I think this is the right definition of max-expand in the general case.]

coloin wrote:Your 16 puzzles with B9B and above originate from 8 solution grids, and here are the maxi-expands
[...]
These minimize to 50 minimal puzzles all presumably with same rating
Code: Select all
`...98765.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....27......5.8   28    only one minimal !...`

There's no reason for all the minimals of an expansion to have the same rating (be it SER or BpB).
Indeed the puzzle with only 1 minimal is the original puzzle with BpB = 10 - still the only known one with such a high BpB classif as of now.
The other 49 puzzles have BpB = 9, which drastically increases the number of known minimal puzzles with BpB = 9.

coloin wrote:Here are the puzzles that I found in T&E(2) greater than B6B. They are in minlexsolution grid format as this is easier to work with and visualise differences.
...
These too have many less minimal puzzles than the rest of my collection of maxi-expands

The first 78 puzzles are in B7B and the last 6 in B8B, which provides the first 6 examples of minimal puzzles in B8B.

: all the puzzles in the list of 50 and in the list of 84 have a non-degenerate tridagon pattern with few guardians.
All of them can be solved with short ORk-chains based on this pattern, except the last 6 ones in the list of 84 (the 6 B8B puzzles), that require longer chains.
.
denis_berthier
2010 Supporter

Posts: 4045
Joined: 19 June 2007
Location: Paris

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

Thanks Denis for providing me with Francois's program i should have said !

I expanded the puzzles so that the overal SE rating was unchanged up to the limit when ED rating [ER/EP/ED] where ER=EP. P in this case stands for Pearl.

coloin wrote: ....These minimize to 50 minimal puzzles all presumably with same rating

perhaps I also should have said presumably with at least this BpB rating ... as SE does have a flaw whereby adding a clue increases the rating / removing a clue reduces the rating. I understand this annoying situation does not occur with your program !!!
coloin

Posts: 2425
Joined: 05 May 2005
Location: Devon

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

.
OK, thanks for the clarifications.

coloin wrote:I expanded the puzzles so that the overal SE rating was unchanged up to the limit when ED rating [ER/EP/ED] where ER=EP. P in this case stands for Pearl.

I think expansion can usefully be extended much beyond (indeed to the point of reaching the limit of T&E(1)), in order to find more puzzles with large BpB classif.

coloin wrote: ... as SE does have a flaw whereby adding a clue increases the rating / removing a clue reduces the rating. I understand this annoying situation does not occur with your program !!!

I confirm. This is totally impossible with T&E-depth and the B, BpB or BpBB classifications and other SER problems such as dependence on isomorphisms are also impossible.
denis_berthier
2010 Supporter

Posts: 4045
Joined: 19 June 2007
Location: Paris

BpB 10 puzzles

The invert of the BpB has 18 solutions, and so there are 18 similar maxi-expands in BpB 10.
All 23 resulting minimal puzzles will probably have the same solution path and are BpB 10 too.
Code: Select all
`98765.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....277.9...5.8  ** original78965.......4..........3...87..2.9.6.92.6..576.5...82.25.....9..68....729.7...5.878965.......4..........3...87..2.9.6.95.6..276.2...85.25.....9..68....729.7...5.878965.......4..........3...87..2.9.6.95.6..726.2...85.25.....9..67....289.8...5.778965.......4..........3...87..2.9.6.95.6..726.2...85.25.....9..68....279.7...5.878965.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..67....289.8...5.778965.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....279.7...5.887965.......4..........3...78..2.9.6.92.6..576.5...82.25.....9..68....729.7...5.887965.......4..........3...78..2.9.6.95.6..276.2...85.25.....9..68....729.7...5.887965.......4..........3...78..2.9.6.95.6..726.2...85.25.....9..67....289.8...5.787965.......4..........3...78..2.9.6.95.6..726.2...85.25.....9..68....279.7...5.887965.......4..........3...78..6.9.2.95.2..766.2...85.25.....9..67....289.8...5.787965.......4..........3...78..6.9.2.95.2..766.2...85.25.....9..68....279.7...5.897865.......4..........3...78..2.9.6.95.6..726.2...85.25.....9..67....288.9...5.797865.......4..........3...78..6.9.2.95.2..766.2...85.25.....9..67....288.9...5.798765.......4..........3...87..2.9.6.92.6..576.5...82.25.....9..68....727.9...5.898765.......4..........3...87..2.9.6.95.6..276.2...85.25.....9..68....727.9...5.898765.......4..........3...87..2.9.6.95.6..726.2...85.25.....9..68....277.9...5.898765.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....27......5.8  ** original78965.......4..........3...87..2.9.6.9..6..57..5...82.25.....9..68....729.7...5.878965.......4..........3...87..2.9.6.92.6..57..5...8..25.....9..68....729.7...5.878965.......4..........3...87..2.9.6.95.6..27..2...85.25.....9..68....729.7...5.878965.......4..........3...87..2.9.6.95.6..72..2...85.25.....9..67....289.8...5.778965.......4..........3...87..2.9.6.95.6..72..2...85.25.....9..68....279.7...5.878965.......4..........3...87..6.9...95.2..76..2...85.25.....9..67....289.8...5.778965.......4..........3...87..6.9...95.2..76..2...85.25.....9..68....279.7...5.887965.......4..........3.......2.9.6.9..6..57..5...82.25.....9..68....729.7...5.887965.......4..........3.......2.9.6.92.6..57..5...8..25.....9..68....729.7...5.887965.......4..........3.......2.9.6.95.6..27..2...85.25.....9..68....729.7...5.887965.......4..........3.......2.9.6.95.6..72..2...85.25.....9..67....289.8...5.787965.......4..........3.......2.9.6.95.6..72..2...85.25.....9..68....279.7...5.887965.......4..........3.......6.9...95.2..76..2...85.25.....9..67....289.8...5.787965.......4..........3.......6.9...95.2..76..2...85.25.....9..68....279.7...5.897865.......4..........3.......2.9.6.95.6..72..2...85.25.....9..67....288.....5.797865.......4..........3....8..2.9.6.95.6..72..2...85.25.....9..67....28......5.797865.......4..........3.......6.9...95.2..76..2...85.25.....9..67....288.....5.797865.......4..........3....8..6.9...95.2..76..2...85.25.....9..67....28......5.798765.......4..........3...87..2.9.6.9..6..57..5...82.25.....9..68....72......5.898765.......4..........3...87..2.9.6.92.6..57..5...8..25.....9..68....72......5.898765.......4..........3...87..2.9.6.95.6..27..2...85.25.....9..68....72......5.898765.......4..........3...87..2.9.6.95.6..72..2...85.25.....9..68....27......5.8`
coloin

Posts: 2425
Joined: 05 May 2005
Location: Devon

Re: BpB 10 puzzles

coloin wrote:The invert of the BpB has 18 solutions, and so there are 18 similar maxi-expands in BpB 10.

Can you define "invert" and "similar" ?
denis_berthier
2010 Supporter

Posts: 4045
Joined: 19 June 2007
Location: Paris

Re: BpB 10 puzzles

denis_berthier wrote:Can you define "invert" and "similar" ?

Code: Select all
`98765.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....277.9...5.8.....1234523.7861941629.785..13.5.4.3..8.41...4.917..3..47863.11..5394...3.142.6.   invert grid has 18 sol`

All the puzzles will have have this invert - so all the PM grids will be the same so they will have the same solution path
Code: Select all
`* *                            *   *  * *  **  *    *                 *** *        14 clue UA98765.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....277.9...5.8  ** original78965.......4..........3...87..2.9.6.92.6..576.5...82.25.....9..68....729.7...5.8`

Code: Select all
`+-------------------+-------------------+-------------------+| 9     8     7     | 6     5     12    | 1234  134   134   | | 135   123   136   | 4     1789  12789 | 12367 1368  1359  | | 145   124   146   | 12789 1789  3     | 12467 1468  1459  | +-------------------+-------------------+-------------------+| 8     7     134   | 135   6     145   | 9     134   2     | | 134   9     5     | 138   2     148   | 134   7     6     | | 6     134   2     | 1379  13479 1479  | 8     5     134   | +-------------------+-------------------+-------------------+| 2     5     134   | 1378  13478 14678 | 1346  9     134   | | 134   6     8     | 1359  1349  1459  | 134   2     7     | | 7     134   9     | 123   134   1246  | 5     1346  8     | +-------------------+-------------------+-------------------++-------------------+-------------------+-------------------+| 7     8     9     | 6     5     12    | 1234  134   134   | | 135   123   136   | 4     1789  12789 | 1267  168   59    | | 145   124   146   | 12789 1789  3     | 1267  168   59    | +-------------------+-------------------+-------------------+| 8     7     134   | 135   2     145   | 9     134   6     | | 134   9     2     | 138   6     148   | 134   5     7     | | 6     134   5     | 1379  13479 1479  | 8     2     134   | +-------------------+-------------------+-------------------+| 2     5     134   | 1378  13478 14678 | 1346  9     134   | | 134   6     8     | 1359  1349  1459  | 134   7     2     | | 9     134   7     | 123   134   1246  | 5     1346  8     | +-------------------+-------------------+-------------------+`
coloin

Posts: 2425
Joined: 05 May 2005
Location: Devon

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

.
I wouldn't use the word "invert" to mean the complementary givens of a 1-solution grid.
What about "similar"? Do you mean isomorphic?
denis_berthier
2010 Supporter

Posts: 4045
Joined: 19 June 2007
Location: Paris

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

The invert was coined by dobrichev and yes it is the complement of the givens !
as the command to do this is
gridcheckernew --similar --invert . < file.txt > fileinvert.txt

but i should have said that the pattern of the 18 maxi-expands is similar / the same.

They are all individually different - but have the same solution. I imagine we have many ? twin puzzles which share a UA in the givens
coloin

Posts: 2425
Joined: 05 May 2005
Location: Devon

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