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:

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......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:

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......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):

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.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:

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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-10 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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