i haven't tried either te2 or te3 puzzles
naively, the idea is to start with a minimal puzzle whose brt-expansion has a large number of redundant values, and then find minimal puzzles whose brt-expansion reduces the number of redundant values as slowly as possible
17c puzzles that are solved by singles are good candidates for this, an exhaustive search of these puzzles, if possible, should find even longer chains
i'll see if i can find some good starting points for te2 and te3 puzzles
(1+BRT) expansion paths within T&E(n) and beyond
Re: (1+BRT) expansion paths within T&E(n) and beyond
by P.O. » Sat Jul 26, 2025 3:17 pm
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Re: (1+BRT) expansion paths within T&E(n) and beyond
by P.O. » Mon Jul 28, 2025 4:04 pm
from Blue's 780 te2 on your github pages
Hidden Text: Show
- Code: Select all
p1 + (51 2) = p0 / p2 + (47 6) = p1 / p3 + (35 1) = p2 / p4 + (23 2) = p3
p5 + (61 2) = p4 / p6 + (48 3) = p5 / p7 + (74 8) = p6
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Re: (1+BRT) expansion paths within T&E(n) and beyond
by denis_berthier » Tue Jul 29, 2025 5:09 am
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good. Again, I didn't "expect so long chains in T&E(2) (because of the constraint with minimal puzzles).
See http://forum.enjoysudoku.com/post354007.html#p354007 for a topological interpretation of the challenge.
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good. Again, I didn't "expect so long chains in T&E(2) (because of the constraint with minimal puzzles).
See http://forum.enjoysudoku.com/post354007.html#p354007 for a topological interpretation of the challenge.
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Re: (1+BRT) expansion paths within T&E(n) and beyond
by P.O. » Tue Jul 29, 2025 4:56 pm
from this collection
with te3 puzzles the second constraint, 1brt-expansion = previous brt-expansion sometimes fails, which i have not observed for te1 and te2 puzzles
with te3 puzzles the second constraint, 1brt-expansion = previous brt-expansion sometimes fails, which i have not observed for te1 and te2 puzzles
Hidden Text: Show
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Re: (1+BRT) expansion paths within T&E(n) and beyond
by denis_berthier » Tue Jul 29, 2025 5:49 pm
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Difficulty of satisfying the additional constraint may be due to the rarity of minimal T&E(3) puzzles.
As for the shorter sequence, I'm not surprised either: the expansion paths are shorter also in T&E(3).
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Difficulty of satisfying the additional constraint may be due to the rarity of minimal T&E(3) puzzles.
As for the shorter sequence, I'm not surprised either: the expansion paths are shorter also in T&E(3).
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Re: (1+BRT) expansion paths within T&E(n) and beyond
by denis_berthier » Sat Aug 09, 2025 7:42 am
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As explained in previous posts, I have a systematic procedure for generating extreme B T&E(1) puzzles from minimal T&E(3) ones, or from their min-expands. As previously, I consider "extreme B" to mean "B ≥ 12" (justified by the unbiased B distribution).
Reminder: the procedure is very simple (but time consuming in the "compute minimals" part): take the 1-expands of the T&E(3) min-expands, filter those in T&E(1) and with B ≥ 12, compute the minimals of the latter and filter those in T&E(1) (which are guaranteed to have B ≥ 12). Notice that, for each puzzle in T&E(3), the whole process remains within the same solution grid (in particular, there's no {-p +q} search.
As mentioned in previous posts, the mean throughput is 1.28 B12+ puzzle for each T&E(3) min-expand. As far as I know, this is the first time some kind of extreme puzzle can be obtained from another kind in a systematic way. What's also noticeable is, no similar procedure works to obtain high BxB puzzles in T&E(2).
I've just published on my Google drive a zipped collection of 504,481 such puzzles with their B ratings (corresponding to only a part of mith's T&E(3) collection):
https://drive.google.com/file/d/1wSkSokvR8maE9yQJI3_X1NSb5ank35IU/view?usp=share_link
The distribution of B ratings in % (in the [12 24] interval is as follows:
For the most extreme values, this means
.
As explained in previous posts, I have a systematic procedure for generating extreme B T&E(1) puzzles from minimal T&E(3) ones, or from their min-expands. As previously, I consider "extreme B" to mean "B ≥ 12" (justified by the unbiased B distribution).
Reminder: the procedure is very simple (but time consuming in the "compute minimals" part): take the 1-expands of the T&E(3) min-expands, filter those in T&E(1) and with B ≥ 12, compute the minimals of the latter and filter those in T&E(1) (which are guaranteed to have B ≥ 12). Notice that, for each puzzle in T&E(3), the whole process remains within the same solution grid (in particular, there's no {-p +q} search.
As mentioned in previous posts, the mean throughput is 1.28 B12+ puzzle for each T&E(3) min-expand. As far as I know, this is the first time some kind of extreme puzzle can be obtained from another kind in a systematic way. What's also noticeable is, no similar procedure works to obtain high BxB puzzles in T&E(2).
I've just published on my Google drive a zipped collection of 504,481 such puzzles with their B ratings (corresponding to only a part of mith's T&E(3) collection):
https://drive.google.com/file/d/1wSkSokvR8maE9yQJI3_X1NSb5ank35IU/view?usp=share_link
The distribution of B ratings in % (in the [12 24] interval is as follows:
- Code: Select all
12 13 14 15 16 17 18 19 20 21 22 23 24
45.02 25.81 14.09 8.88 3.70 1.54 0.62 0.23 0.091 0.018 0.0040 0.00079 0.00040
For the most extreme values, this means
- Code: Select all
3126 B18 puzzles
1141 B19 puzzles
461 B20 puzzles
92 B21 puzzles
25 B22 puzzles
4 B23 puzzles
2 B24 puzzles
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Re: (1+BRT) expansion paths within T&E(n) and beyond
by denis_berthier » Wed Aug 20, 2025 7:30 am
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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:
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:
See the Puzzles section if you want to solve it.
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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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Re: (1+BRT) expansion paths within T&E(n) and beyond
by denis_berthier » Fri Aug 22, 2025 4:04 am
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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:
Its BRT-expand is:
The latter has 57 1-expands, 29 of which are in T&E(1) (the "p1U-d1" puzzles):
Their B ratings are:
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:
It's only difference with the MEU Puzzle above is the additional 7.
.
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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Re: (1+BRT) expansion paths within T&E(n) and beyond
by denis_berthier » Fri Aug 29, 2025 8:17 am
.
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.
.
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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