The New Sudoku Players' Forum

[denis_berthier]

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The systematic procedure for generating high B puzzles in T&E(1) from T&E(3) minimals also works when starting from T&E(2) minimals.

Here is a non-minimal B30 puzzle I obtained starting from part of eleven's T&E(2) tamagotchi collection:

Code: Select all

......7....71.9..686..7......8.6.1.7.......2..7...2.64..1.9.6..5.......3.4.3...5.

This puzzle has only 3 minimals, all in T&E(2), which explains why no T&E(1) puzzle with B ≥ 30 is found when minimizing it:

Code: Select all

......7....71.9...86..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9...86..7......8.6.1.7.......2..7...2..4..1.9.6..5.......3.4.3...5.
......7....71.9..686..7......8.6.1.........2..7...2..4..1.9.6..5.......3.4.3...5.

See the Puzzles section if you want to solve it.
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[denis_berthier]

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I think it's worth showing with the previous puzzle how simple the procedure is and how easy it is to track the origin of the high B puzzles:
The starting point is eleven's puzzle in B2B:

Code: Select all

......7....71.9...86..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5. mins

Its BRT-expand is:

Code: Select all

......7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5. MEU

The latter has 57 1-expands, 29 of which are in T&E(1) (the "p1U-d1" puzzles):

Code: Select all

.2....7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
...4..7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
....5.7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......78...71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7.9..71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7..4.71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7...571.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....7189..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.92.686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9.3686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..6869.7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686.27......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..73.....8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..7...5..8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..7....2.8.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..7.....38.6.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..7......856.1.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..7......8.641.........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..7......8.6.19........2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..7......8.6.1.7.......2..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..7......8.6.1........52..7...2.64..1.9.6..5.......3.4.3...5.
......7....71.9..686..7......8.6.1.........2..7...2.64.81.9.6..5.......3.4.3...5.
......7....71.9..686..7......8.6.1.........2..7...2.64..179.6..5.......3.4.3...5.
......7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..59......3.4.3...5.
......7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.2.....3.4.3...5.
......7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.....8.3.4.3...5.
......7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5......73.4.3...5.
......7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.32..5.
......7....71.9..686..7......8.6.1.........2..7...2.64..1.9.6..5.......3.4.3.8.5.

Their B ratings are:

Code: Select all

3
7
14
6
5
13
16
10
6
11
13
5
19
6
11
4
10
10
14
30
12
12
5
12
20
6
12
15
18

In my approach to expansion of large collections, all this is drowned in millions of puzzles; but I have functions to find the max-value of a rating; then I can easily identify where it happens by using the Finder (file-name contains p1U-d1-B + content contains 30).
Once I have the directory associated to the corresponding solution grid, all is trivial.
In the present case, there is only one minimal puzzle in the collection for this solution.

Walking back from the max value 30, the B30 puzzle is identified as:

Code: Select all

......7....71.9..686..7......8.6.1.7.......2..7...2.64..1.9.6..5.......3.4.3...5.

It's only difference with the MEU Puzzle above is the additional 7.
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[denis_berthier]

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This is again about my systematic procedure for generating high B puzzles in T&E(1) from minimal puzzles in T&E(3) or T&E(2).

Initially, I thought it was successful due to the continued presence of a tridagon or some degenerate form of it. But my recent results involving non-tridagon puzzles prove it is not the case. I've now run the procedure on 3 sets of minimal puzzles:
1) mith's latest collection mith-TE3 of T&E(3) puzzles (all of which have a non-degenerate tridagon);
2) the collection col-TE2 of mastermins-1-to-15 assembled by coloin (and found mainly by coloin, Hendrik Monard and Paquita), all in T&E(2) with BxB ≥ 7 (all of which have a non-degenerate tridagon);
3) a sub-collection el-TE2 of eleven's tamagotchi high SER puzzles (none of which has a non-degenerate tridagon).

I've measured the throughput as the ratio: output-nb-minimals-in-B12+ / input-nb-min-expands.
I think this is the right quotient to consider (because the effective input is the min-expands, not the minimals).
The results allow no appeal; the success of the procedure can't be due only to the tridagon pattern (though it may play some role within T&E(2)):

- 1.285 B12+ minimal puzzle for each min-expand in mith-TE3
- 7.30 B12+ minimal puzzle for each min-expand in col-TE2
- 2.68 B12+ minimal puzzle for each min-expand in el-TE2

Why T&E(2) puzzles give better results than T&E(3) ones may be because T&E(2) is closer to T&E(1) than T&E(3). It may also be due to the saturation of mith-TE3 by minimisation of the min-expands, which could imply proportionately fewer p1U puzzles (but the stats don't confirm this).
Why, within T&E(2), the puzzles with BxB≥7 give better results, tends to contradict the previous first pseudo-explanation.

Conclusion: clear facts; no real explanation of the results.
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[denis_berthier]

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All the definitions and results reported in this thread - and much more- are now available in the 3rd edition of [HCCS]:
http://forum.enjoysudoku.com/hierarchical-classifications-in-constraint-satisfaction-t42076.html
https://www.lulu.com/shop/denis-berthier/hierarchical-classifications-in-constraint-satisfaction-third-edition/paperback/product-4587d42.html?page=1&pageSize=4

One of the topics not discussed here is the (1+BRT) distance of a T&E(n) puzzle to the T&E(n) border. Indeed several notions of distance can be defined, including the most natural one related to the shortest (1+BRT)-expansion paths.

One apparently surprising result for the latter is, whereas the maximum length of expansion paths increases drastically from T&E(3) to T&E(1), it is not the case for the thickness of the T&E(n) domains.
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[denis_berthier]

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All the data relevant to the exploration of the T&E(3) kingdom via (1+BRT)-expansion of T&E(3) minimal puzzles, as described in [HCCS3], have been published:
All-time latest release: https://doi.org/10.5281/zenodo.17500794
Download all (2.5 GB), unzip and see the README.md file for details.

Similar data for the T&E(2) and T&E(1) kingdoms will be published soon.
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[denis_berthier]

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All the data relevant to the exploration of the T&E(1) kingdom via (1+BRT)-expansion of T&E(1) minimal puzzles, as described in [HCCS3], have been published:
https://doi.org/10.5281/zenodo.17505247
Download all (1 GB), unzip (=> 20 GB) and see the README.md file for details.

Similar data for the T&E(2) kingdom will be published later.
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[denis_berthier]

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All the data relevant to the exploration of the pre-tridagon, low BxB part of the T&E(2) kingdom via (1+BRT)-expansion of T&E(2) minimal puzzles, as described in [HCCS3], have been published:
https://doi.org/10.5281/zenodo.17510758
Download all (500 MB), unzip (=> 10 GB) and see the README.md file for details.

Similar data for the post-tridagon, high BxB part of the T&E(2) kingdom will be published later.
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[denis_berthier]

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Finally, all the data relevant to the exploration of the post-tridagon, high BxB part of the T&E(2) kingdom via (1+BRT)-expansion of T&E(2) minimal puzzles, as described in [HCCS3], have been published:https://zenodo.org/records/17529657
Download all, unzip and see the README.md file for details.

Note that additional data used in [HCCS3] had already been published:
https://github.com/denis-berthier/Controlled-bias_Sudoku_generator_and_collection
https://github.com/denis-berthier/Sudoku-classif
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[denis_berthier]

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[Moved from the "BxB classification" thread.
The collection referred to was defined here: http://forum.enjoysudoku.com/the-bxb-classification-of-t-e-2-puzzles-t41922-375.html and next posts.]

After analysing Paquita's new high BxB puzzles (as collated by coloin) by my (1+BRT)-expansion technique, the record of the longest expansion path in T&E(2) is beaten: 13 (instead of 12 previously):

Code: Select all

.23...78.45.78..237.8...5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 43c +BRT -> --p13EU
.23...78.45.78..237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 42c +p13
.23...78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 41c +BRT -> --p12EU
.23...78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 41c +p12
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 40c +BRT -> --p11EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...93.1.8... 40c +p11
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...9..1.8... 39c +BRT -> --p10EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3...9..1.8... 39c +p10
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3......1.8... 38c +BRT -> --p9EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..97483284...3......1.8... 38c +p9
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 37c +BRT -> --p8EU
.2....78.45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 37c +p8
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 36c +BRT -> --p7EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9748.284...3......1.8... 36c +p7
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..974..284...3......1.8... 35c +BRT -> --p6EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..974..284...3......1.8... 35c +p6
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9.4..284...3......1.8... 34c +BRT -> --p5EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.75..9.4..284...3......1.8... 34c +p5
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.7...9.4..284...3......1.8... 33c +BRT -> --p4EU
.2....7..45.7...237.....5.42.58.73..37...2.58.84..52.7...9.4..284...3......1.8... 33c +p4
.2....7..45.7...237.....5.42.5..73..37...2.58.84..52.7...9.4..284...3......1.8... 32c +BRT -> --p3EU
.2....7..45.7...237.....5.42....73..37...2.58.84..52.7...9.4..284...3......1.8... 31c +p3
.2....7..45.7...237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 30c +BRT -> --p2EU
.2....7..45.7...237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 30c +p2
.2....7..45.....237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 29c +BRT -> --p1EU
.2....7..45.....237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 29c +p1
.2.......45.....237.....5.4.....73..37...2.58.84..52.7...9.4..284...3......1.8... 28c +BRT -> --p0EU
.2.......45.....237.....5.4.....73..37...2.58.84..5..7...9.4..284...3......1.8... 27c +p0
computation-time = 2.68s

There are actually 3 puzzles in the collection with such a path. The upper terminations of the paths are related to each other by permutation of clues in some UR1.

[Edit]: as noted by an attentive reader of [HCCS3], the T&E(2) record is not broken; it was already 13, as mentioned in [HCCS3, section 7.2.3]. What's broken is the record for the part of T&E(2) with BxB ≥ 7.
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