The New Sudoku Players' Forum

[denis_berthier]

.
I extracted a random sample of 1,000 puzzles from the collection of 158, 276 min-expands in T&E(3).
I didn't let SER run until the end. In the first 110, I found 37 with "low" SER (with uniqueness enabled).

Code: Select all

...4.67.9.......3....1.2.4.2....1..8.38.2.1..6.1.48...3.486.....62.1.......2...6. ED=10.6/2.6/2.6
....56....5.1.9...69.37..1........3.37....6.2......8.473.6.59...1579.3..9.6...... ED=10.4/2.0/2.0
12...6...4.7...2..689.23................7...8...83..42.7.2.84...6..47.23.4.36.8.7 ED=10.4/4.0/2.6
..345..8945......3.8.73.....9.....3537....8.45.....97......43.883.21....94..6.... ED=9.3/4.5/2.6
12.4.6.............8..31...2.....645...164..8.6....17..4.6.83..6..34.8..83..124.. ED=10.4/5.4/2.6
...45.........9.3.79.213....1.8.....6.....81.98..6..7336....19..71...3.88.9....67 ED=10.9/10.0/7.1
.2..5....4......3668..37....76.15.4.....7......13.46.75..7...647..5..1.3.....357. ED=10.4/2.6/2.6
.2.......45..89...9.83.2........38613.....925....2.3.....8..4...392.45..84...5... ED=10.4/2.0/2.0
1..4.678....18..3.8.........3.6.8.17...3..46..6...4....42.61...6.5.43....7....64. ED=10.4/2.0/2.0
....567.....1..26.6..3.2...27...4...3.4..867..68..34.27.6...82.84....3.....8...4. ED=10.1/9.4/2.6
1.3.56...4.6....3..89.31.............6..7.4.3..7.6..153..61...76..3.7.4.....453.6 ED=10.4/4.5/2.6
12....7..4.71.9....98.7241..8..14....7492......17.8...........87.2...65.8.9...3.. ED=10.4/10.4/3.4
12..56..9.57..9..66.9.7..............76.2195.91...526.......43.7......9.....12... ED=10.5/4.5/2.6
..3.5678...718..3...8...1......38..737.5..6.858.67.31.7.6..5...84......39.......1 ED=10.4/2.8/2.6
..34........78.......2.156..41...3..6.5...94.9....4.1.31.94.65.5.436..91......4.. ED=10.3/4.5/2.6
1...5.7.9.57...26.6.9.2..512.....91.............2.16.55..8.4...76.395.......725.. ED=10.9/2.0/2.0
12..5.7.9..7...26.6...2..512.....91..1.......97....6.5...8.4...76.395.......7259. ED=10.9/7.1/7.1
...4.678.4....9.366..3....4...8.3.97....97....7.64.8.339576....71..3....86....37. ED=10.4/2.0/2.0
1.3.......57..9...8.6.23................3.4.8.34.18.923...4192....39.8.19..8.2..3 ED=10.9/2.0/2.0
.2.......4.71.923...9..7.4...48.1.......72.1....6.5...3.....1.2..1...39.9.2.1..74 ED=11.2/2.0/2.0
1...56....5.1.9.6.69.73..5...169.3.553..71....69......37......8.1....4.2......53. ED=10.4/4.5/2.6
1.3.5678..57....3.68...........1.96.3.1....75......4..5..67....7.8.31......5.8..7 ED=11.0/2.0/2.0
1..4.6...4.6.89......21..642.4.............37.....12.5.629.48..84.1..9..9.1...... ED=9.2/2.6/2.6
1...56.8....18...66..2.7.152357.....79.......81.....72..28.51.7...........16...28 ED=10.3/2.0/2.0
.23..6......78.....89231....3.........8.4392...4..8..73.2...89..9.8..4.384.3...7. ED=11.0/2.6/2.6
12.4.6......1......86.274........5.6...6.4.72.6....194.712....864.7.8...8.2.....7 ED=10.3/2.0/2.0
....56....5.18..3.68.3.7.1..16..8...73.5.1...8..............9...7....46....7.3.58 ED=11.2/2.0/2.0
1.3.......5...9...78....54....96.8......4562....8.2.9.6.2...45..........9..6.42.8 ED=10.6/8.3/2.6
1.345....45...91...97.3........9346.374...91.....4...2...3.4.71....7....7..91..5. ED=10.6/2.0/2.0
..34.678.4.6......78..23....3..48...64.2.7..88..36.....6....912...6.28.7......65. ED=10.9/4.5/2.6
...4.678.......2.6.....2.45231..7...796..8.....5....7.....65.....482..6...87..52. ED=10.4/2.6/2.6
12....7.94..1..23........1.29..4....3.4.1..72.71.3.49.....219..74...8...91.5..... ED=11.0/10.2/2.6
1.3.5.....57.8..3668..7.5.1.......583.58..16...8...3.75.6..4.......3..1...19..... ED=10.9/10.4/2.6
...4.6.8.....89...79813.....17......5.9.1...783..9..51........5.75....1898.5...3. ED=10.4/3.0/2.6
1...56....5.18...686.7.3....85...36.63.8.5.....1...85.37.....9......76.3.1....4.7 ED=10.4/2.0/2.0
12........567..12.7.82.156.2.....49.68..............15...5.8....6..17.....762.... ED=10.5/3.4/2.6
1...567.....1.92..6.927.5..261...9......2164......5128.....7...5.6.92...7...1...2 ED=10.9/2.0/2.0

Without uniqueness (option -M), all of them are 11.6 or 11.7.

BTW, CSP-Rules has functions for randomly extracting puzzles: see http://forum.enjoysudoku.com/csp-rules-sudorules-kakurules-t38200-114.html
.

[coloin]

New TE3 puzzles

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+---+---+---+
|1.3|...|78.|
|.57|18.|.36|
|68.|3..|1.5|
+---+---+---+
|...|..5|8.3|
|76.|843|...|
|83.|9..|...|
+---+---+---+
|.1.|...|6.8|
|..6|..8|...|
|.78|..1|35.|
+---+---+---+

1.3...78..5718..3668.3..1.5.....58.376.843...83.9......1....6.8..6..8....78..135.   #98352 FNBP C36/M2.18.364#

1649 maximal expand puzzles in 1571 solution grids with 41772 minimal puzzles.
The expanded puzzles are sorted by -q2 which groups the twin puzzles
Almost all the minimal puzzles expand to a single large maximal puzzle - only a few dont.

Expanded puzzles
minimals

[denis_berthier]

Hi coloin

New TE3 puzzles
1649 maximal expand puzzles in 1571 solution grids with 41772 minimal puzzles.

Great work, again. I have a few questions:
- Did you compute the corresponding list of min-expands?
- I observe your ratio minimals/max-expands = 25.33; in a random sample of 1,000 taken from mith 48,071 list of max-expands, from which I generated all the non-isomorphic minimals, the ratio was 74.1. I understand this difference by the ways we proceeded: I from the max-expands, you from the minimals. Am I right to think you didn't try to find all the minimals for all the max-expands obtained?
- Did you keep the "hard" T&E(2) puzzles you found on the way?

Almost all the minimal puzzles expand to a single large maximal puzzle - only a few don't.

Maybe because in many cases, the max-expand is equal to the min-expand.
.

[coloin]

Am I right to think you didn't try to find all the minimals for all the max-expands obtained?
- Did you keep the "hard" T&E(2) puzzles you found on the way?....

No all the minimals are produced,and duplicates removed. If the max expand has less clues there will be less minimal puzzles.

Miths file contains the minimals,progressive expanded non minimals and maybe the [absolute] max-expand [ up to TE3]

I initially got the TE3 puzzles as a by-product of searching BxB6 for [-4], but this is prohibitively slower compared to just searching for BxBB 2.

I did get 2 new BxB13 which I will post but they were only single guardian tridagons.

Having said that no new or old BxB 7,8,9,10 were found by adding a clue and minimizing the TE3 puzzles..... a sort of reverse process ... I think the BxB>6 are very uncommon.

It will be interesting to see if any of the new TE3 give anything to comment on...as a general observation the high-q2 tend to be more complex.

Optimstically I did have a collect file if any BxBB 3 should turn up on the minimals found but none so far !!

[coloin]

Maybe because in many cases, the max-expand is equal to the min-expand.
.

No the expand function that I use [-E] with gsf's program I think does slightly more than just singles . The absolute max expand is performed by adding clues and testing.
Usually several rounds of adding are required ....If there is a better option I would use it

[denis_berthier]

Maybe because in many cases, the max-expand is equal to the min-expand.

No the expand function that I use [-E] with gsf's program I think does slightly more than just singles . The absolute max expand is performed by adding clues and testing.
Usually several rounds of adding are required ....If there is a better option I would use it

Starting from minimals, the best option IMO is to first compute the min-expands: you can be sure they will have the same classifications as the corresponding minimals. In terms of numbers of clues, the difference max-expands - min-expands is in the mean much smaller than min-expands - minimals. This should reduce the number of "rounds".

[champagne]

Maybe because in many cases, the max-expand is equal to the min-expand.
.

No the expand function that I use [-E] with gsf's program I think does slightly more than just singles . The absolute max expand is performed by adding clues and testing.
Usually several rounds of adding are required ....If there is a better option I would use it

The "max expand" limit can use any rule keeping the final goal.
Looking for a T&E(3) here, nothing object to have a "max expand" doing all eliminations/assignments coming from the T&E(1) (and T&E(2) if you want only T&E(3)).
You can also use many rules as naked/hidden locked sets , fishes at least for low orders, but then, you must be sure that the corresponding rules keep untouched your property.

[coloin]

Certainly the min expand is the best option for analysing puzzles…. As Denis says it groups equivalent puzzles conveniently . For generating puzzles however the max expand with TE3 gives rise to further puzzles and with more clues twin puzzles are more likely to be generated. A minimal puzzle is definitive but can be expanded variably. Most of the time all the TE3 minimal puzzles expand to one large max expand TE3 puzzle…. Sometimes a new not previously found minimal puzzle can be found on extracting the minimals from the max expand. This puzzle potentially is more complex than the others …

[denis_berthier]

Certainly the min expand is the best option for analysing puzzles…. As Denis says it groups equivalent puzzles conveniently . For generating puzzles however the max expand with TE3 gives rise to further puzzles …

Indeed, as described in [HCCS2, section 4.3], instead of adding one clue at a time for expansions, you can proceed systematically from minimals as follows:

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- minimals satisfying your filtering criteria
- BRT-expands (--> the min-expands) (with SHC); at this point, you're sure your filtering criteria are still satisfied
- (eliminate redundancies, e.g. with gsf software)
loop:
- 1-expands of the previous (with SudoRules)
- (eliminate redundancies, e.g. with gsf software)
- check your filtering criteria  (with SHC if they are T&E, B, BxB or BxBB)
-BRT-expands of the previous (no need to re-check your filtering criteria)
- (eliminate redundancies, e.g. with gsf software)
end loop

See also Fig. 4.2 for a stratification of all the puzzles wrt the 1+BRT expansion process.
.

[denis_berthier]

I can give you the exact count in the current database:

• 4634322 (minimals)
• 1112250 (expanded forms)
• 667883 (singles expansions of minimals)
• 207652 (approximate min-expands by my definition based on 2022-11 dataset)
• 63067 (approximate max-expands based on 2022-11 dataset)

I have the 4634322 minimals but I'm unable to find a reference to the link from where I downloaded them. Does anyone have the link?

.

[denis_berthier]

.
Hi mith
No news of you for a long time. I hope all's going well for you.
I've been working on a sample of 1000 solution grids from the 67,546 different ones for your 4,634,322 minimals.
I've found some non-minimals, suggesting some (rare) error in your scripts.
The two non-minimals I found are (in gsf-solution-minlex form)

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1.3.56....5718....68.3.7....68.....537.......5.16....8.......23......197...7.385.
1...56.8..5718....6..3.7....68.....537.......5.16....8.......23.3....197...7.385.

In the same sub-collection, each of them has two real minimals:

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1.3.56....5718....68.3.7....68.....537.........16....8.......2.......197...7.385.
1.3.56....5718....68.3.7....68.....537.......5.16....8.......2.......197...7.38..

1...56.8..5718....6..3.7....68.....537.........16....8.......2..3....197...7.385.
1...56.8..5718....6..3.7....68.....537.......5.16....8.......2..3....197...7.38..

After correction, there are 65,579 minimals in the collection for the 1000 unique solution grids.
And there are 10,155 unique min-expands (expansions of those minimals by Singles). (The number is highly variable with each grid, from 1 to several hundreds.)

I'm surprised to find that this collection is closed under expansion by Singles and minimisation.
From your previous declarations, one might have expected relative closure within T&E(3), but as far as I understood it, you didn't explicitly rule out the possibility of obtaining puzzles in T&E(2) or T&E(1) by minimisation of the min-expands [the case T&E(0) is excluded by setting M>0 in gsf's command line]. But no.
To be explicit, I use the command line you gave us in a previous post:
./sudoku-gsf.exe -f'%#.c' -m -qFN -e'M>0&&uniq()&&minimal==1' < in.txt > out.txt

Neither expansion by Singles nor minimisation can destroy the tridagon (they can only change the number of guardians). But this is not enough to prove that all the minimals are in T&E(3). My sample isn't very large. I'm curious to know if you have found cases with new minimals in T&E(2 or 1).

.