The New Sudoku Players' Forum

[champagne]

So that is more reassuring as to the completeness perhaps. Another repeat process will be theoretically less productive as it doubles back on itself.

This is a repetitive question.
In the 17 clues search, some did a +- 3 depth search, and, at the end, all 17 were there.
The proof has been a long long scan.

"Mathimagics" started also with a vicinity search to detect solution grids with a 18. When he reached a low yield, I started with him a full scan with a lot of fresh entries.

Having to test the fresh DLLs that I created, I was curious to see what was the status here. A data base with around 65000 different solution grids out of 5472730537 was an interesting start point.

if we are thinking of a "close to the completeness" status, this means that around 1/85000 solution grids have such puzzles.
I started investigations and the first fact is that many more solution grids have a potential to produce such puzzles.
I'll try to see what explains why they did not come.

[mith]

I don't have much confidence that we are close to completeness.

The neighborhood searching that I've done has primarily been at -2+1 on the minimals, and even that isn't particular close to "closed" (over 500k minimals haven't had this run yet). I wasn't tracking yield but it didn't seem like it was slowing down much if at all. Given that I last posted minimals well over a year ago, and that others have been searching (including at T&E(2)) since then, it's not surprising that some new ones would have been found while I haven't been active.

I need to find time to finish updating and pulling in those new puzzles that have been posted, but I'll see if I can get a preliminary update once I've verified all minimals are accounted for and that the dataset on my end is closed under the expanded puzzle scripts (adder/transformer/minimizer).

[champagne]

I am not too far to have a dirty code to find puzzles with a pure tridagon in the 11 diagonal cells, but my test missed the loki. I don't have yet the right filters;
In this test,in a file of 19531 grids with the right start PM, I got these unusual grids

.7..4.9....3.....8.1..........68..42.4.1.28.9..2.9416.....26.9....9.82.4...41.68.;=10.4/10.4/10.2 31
5...4.9....3.....821..........68..42.4.1.28.9....9416.....26.9....9.82.4...41.68.;=10.5/10.4/10.2 31
5...4.9....3.....8.1..........68..42.4.1.28.9..2.9416.....26.9....9.82.4.2.41.68.;=10.5/10.5/9.3 32
5.....9....3.....821.........168..42.4.1.28.9....9416.....26.9....9.82.4...41.68.;=10.2/10.2/9.2 31
.7..4.9....3.....821..........68..42.4.1.28.9....9416.....26.9....9.82.4...41.68.;=10.5/10.4/9.1 31
5.....9....3.....8.1.........168..42.4.1.28.9..2.9416.....26.9....9.82.4.2.41.68.;=10.2/10.2/9.0 32
5..8..92...3.......1.........168..426..1.28.9..2.9416.....26.9....9.82.4...41.68.;=9.7/9.7/9.1 32
5..8..92...3.......1.........168..426..1.28.98...9416.....26.9....9.82.4...41.68.;=9.7/9.7/9.1 32
5..8..92...3.......1.........168..42.4.1.28.9..2.9416.....26.9....9.82.4...41.68.;=9.7/9.7/7.2 32
5..8..92...3.......1.........168..42.4.1.28.98...9416.....26.9....9.82.4...41.68.;=9.7/9.7/7.2 32

Unless I made a mistake in the coding, they all should be minimal (hitting all UAs)
They all have 24 given in the boxes 5689 of the tridagon square
No clue in box 7
A very high number of clues 31/32.

Surely, for most of them, solving box9 with the tridagon rule will be very efficient

[denis_berthier]

.
These puzzles all have a (non-degenerate) tridagon with a single guardian, but you can't solve block b9 by using only the tridagon. What this rule leaves in b9 is a triplet on the tridagon digits in two of the tridagon cells + another cell (useless in b9).
They are easy to solve.
However, two of the puzzles are easier to solve if one uses some of eleven's impossible patterns (EL14c159 EL13c290 EL14c13 from my Select1 subset (the most frequent ones, with patterns close to the tridagon).
.

[denis_berthier]

I don't have much confidence that we are close to completeness.
The neighborhood searching that I've done has primarily been at -2+1 on the minimals, and even that isn't particular close to "closed" (over 500k minimals haven't had this run yet). I wasn't tracking yield but it didn't seem like it was slowing down much if at all...

As I wrote in [HCCS2], I think there should be two parts of the search process; but it seems they have been mixed up until now in all the available generation softwares.

1) one part should remain within a fixed solution grid. Even {-p +q} search should be confined to the fixed grid - so that the +q part only adds clues from the solution. If everything is kept in solution-minlex form, this part of the search should have no problems for checking duplicates ("non-isomorphic" = "different"). Within a fixed grid, completeness should be easy to check wrt various operations (minimisation, BRT-expansion, confined {-p +q} search, possibly BRT+1 expansion if you want to analyse the grid in more detail, ...) .

2) another part should be the usual {+p +q} search of minimals, followed by re-distribution of the minimals thus obtained either to existing solution grids or to new ones. For this part of the search, I doubt completeness can ever be reached. Only an extremely small part of the solution grids has been explored and there's no reason why new grids wouldn't keep popping up. It's kind of a question of {+p +q} connectedness of the set of minimals - a connectedness that can't be interpreted in a strict metric or topological sense, as I've sown in [HCCS2], but it's easy to imagine what I mean.

I now think each line in all the published puzzle collections (minimals, min-expands in my sense, max-expands...) should have its own index + indices that refer directly to those of the collections "above" it:
- for each minimal: reference to min-expand, max-expand, solution
- for each min-expand in my sense: reference to max-expand, solution
- for min-expands in your sense (which I once called absolute min-expands): no need of a separate collection: just a symbol in the previous collection; but if you prefer to keep a separate collection, each puzzle should have the same index as the identical puzzle in the min-expand collection;
- for max-expands: reference to solution.
.

[champagne]

I continue to work on a third idea, a direct search on a solution grid having a potential for a tridagon pattern.
As usual, good and bad news.
Starting on the "bad news" side, many more solution grids than I assumed have the potential.
This is not in favour of a completeness hope, but pushes to have another selection criteria and a "One solution search" of a reasonable cost.

I made the test on my dirty first shot with the solution grid containing the loki puzzle.
Contrary to what I wrote earlier, the process does not produces only minimal puzzles, so this test has been added using the classical brute force test.
A first run produced grids with up to 27 clues. All grids have, If the filter is correct, a non degenerated tridagon.
It took 10h30 to get 30648 grids.

I then reduced the maximal size to 26 and got 11843 grids in 6h30.

Good for the results, but bad for the run time if we have so many solution grids to test.

The first test delivered 1888 grids with a skfr rating 10.x and 11 grids with a rating 11.x.
I still have a small redundancy in the results, but this will be solved in due time.

This test starts with a list of unavoidable sets far from my target and as I said, the "Minimal property" has to be checked in a different way.

But anyway, as the run time will remain relatively high, it's impossible to think of a test of all solution grids having the potential.

Here if the list of the highest skfr ratings in the output.

Hidden Text: Show

Code: Select all

57....9..........8.1...9......68..4....1.2.....2.9416...4.26.9......82.....41.68.;10.7/1.2/1.2
57....9..........8.1...9......68..4....1.2.....2.9416...4.26.9......82.4....1.68.;10.7/1.2/1.2
57....9..........8.1...9......68..42...1.......2.9416...4.26.9......82.....41.68.;10.7/1.2/1.2
57..4.92.........8.1.........168..42...1.......2.9.16.....2..9..6.9.8..4...41.68.;10.9/1.2/1.2
57..4.92.........8.1.........168..42...1..8....2.9.16.....2..9..6.9.8..4...41.6..;10.9/1.2/1.2
57.8..9............18........168..42...1..8....2.9416.....2..9..6.9....4...41.68.;10.9/1.2/1.2
57.8..9............18..9.....16...42...1..8....2.9416.....2..9..6...8..4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........1.8..4.6....2.....2.9416.....26.9....9..2.4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........1.8..4.6....2..9..2.9416.....26......9..2.4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........1.8..426....2.....2.9416.....26.9....9....4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........1.8..426....2..9..2.9416.....26......9....4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........1.8..426..1.......2.9416.....26.9....9....4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........1.8..426..1....9..2.9416.....26......9....4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........168..4......2.....2.9416.....2..9..6.9..2.4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........168..4......2..9..2.9416.....2.....6.9..2.4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........168..42.....2.....2.9416.....2..9..6.9....4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........168..42.....2..9..2.9416.....2.....6.9....4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........168..42...1.......2.9416.....2..9..6.9....4...41.68.;10.9/1.2/1.2
57.8..9..........8.1.........168..42...1....9..2.9416.....2.....6.9....4...41.68.;10.9/1.2/1.2
57.8..9..........8.1...9.....168..42...1.......2.9416.....2..9..6......4...41.68.;10.9/1.2/1.2
57...............8.1...9.....1.8..4.6....2..9..2.9416.....26.9......82.4...41.68.;11.0/1.2/1.2
57...............8.1...9.....1.8..4.6....28.9..2.9416.....26.9......82.4...41.6..;11.0/1.2/1.2
57....9..........8.1.........1.8..4.6....28.9..2.9416.....26......9.82.4...41.6..;11.0/1.2/1.2
57.8.............8.1...9.....1.8..4.6....2..9..2.9416.....26.9.......2.4...41.68.;11.0/1.2/1.2
57...........6...8.1...9.....168..42...1....9..2.9416.....2..9..6...8..4...41.68.;11.1/1.2/1.2
57...........6...8.1...9.....168..42...1..8.9..2..416.....2..9..6.9.8..4...41.6..;11.1/1.2/1.2
57...........6...8.1...9.....168..42...1..8.9..2.9416.....2..9..6...8..4...41.6..;11.1/1.2/1.2
57....9..........8.1.........1.8..4.6....2..9..2.9416.....26......9.82.4...41.68.;11.1/1.2/1.2
57.8..9............18........168..42...1..8....2.9416.....26.9....9....4...41.68.;11.1/1.2/1.2
57.8..9............18..9.....16...42...1..8....2.9416.....26.9......8..4...41.68.;11.1/1.2/1.2
57....9..........8.1.........168..4......28.9..2.9416.....2.....6.9.82.4...41.6..;11.8/1.2/1.2

[champagne]

needs some days to implement it, but I could have the key to go down in the process from ten hours to some seconds.

[coloin]

needs some days to implement it, but I could have the key to go down in the process from ten hours to some seconds.

look forward to hearing this !
Im not sure its easy at all to go from a solution grid to a puzzle !!!
As a contribution Ive known that these puzzles all have the clue frequency values xxxxxx110

This means that the 3 clues 27UA is solvable in 2 clues which is common...
Except in these puzzles there are boxes with diagonal clues - which form the potential tridagon.

Here are 5 unrelated puzzles with the pattern, all BxB >7 SE > 11.

Code: Select all

1..4.678.4..18..368...731.4.4..678.3...81.4.....3.4....9....6..6.2......7146.8...#1
..3.567.9..71.9.36..937.51.2.6.......4....6..9756.3.......379.....9......9.56.3.1#2
12.......4571.9.....8....1...5.1439....79..5....5.3...5..94.17.7..3.19.59...75.43#3
1.3..6.8..57....3668......1....18357...2.........4....53..7.8..7.6...1.5.185...73#4
.23.5....4.7....36.8........4..65.73....1.6.4.6....15...6.413.7...5.346...467..15#5

Here is an an example of a 3clue UA27 whch needs 2 clues to complete/solve in isolation.

Code: Select all

+---+---+---+ 
|..3|2..|.1.| 
|.2.|.1.|.3.| 
|1..|..3|..2| 
+---+---+---+ 
|2..|...|1.3| 
|.3.|1.2|...| 
|..1|.3.|2..| 
+---+---+---+ 
|..2|3.1|...| 
|.1.|...|32.| 
|3..|.2.|..1| 
+---+---+---+#1
               
+---+---+---+ 
|...|...|...| 
|...|...|...| 
|...|...|...| 
+---+---+---+ 
|...|...|...| 
|...|...|...| 
|...|...|...| 
+---+---+---+ 
|...|...|...| 
|...|...|.2.| 
|...|...|..1| 
+---+---+---+

Here are the 5 puzzles morphed to have the 123 clues in diagonal pattern in B1B2B4

Code: Select all

56..784..4.86.95...9754.8...7698..5.8.4.5....95.......68....745....6..2.......6.1 #1
......................................................................2.........1 #1
..32...1..2..1..3.1....3..22.....1.3.3.1.2.....1.3.2....23.1....1....32.3...2...1 #1
4532...1.627.1..3.189..3..22.....1.3.3.1.2.....1.3.2....23.1....1....32.3...2...1 #1   641159 sols


98..467..6.57.94...4758.9...564.8.9.7.49......9.......46....579...6...2.......6.1 #2
..31....2.2..3..1.1....2.3.2.....1.3.3..21.....13..2....2.13....1....32.3..2....1
4531....2627.3..1.189..2.3.2.....1.3.3..21.....13..2....2.13....1....32.3..2....1      647070 sols


94..785..6.85.97...7564.9...84.96..55.6......79..5....8.9...457......82.....8...1 #3
..12....3.2..3..1.3....1..21.....23..3..2.1....21.3....1.3.2.....3.1..2.2.....3.1
4512....3627.3..1.389..1..21.....23..3..2.1....21.3....1.3.2.....3.1..2.2.....3.1      627242 sols


94...86..7.56.9....684......59.8..7.8.49.7..567.54.......79584........2.........1 #4
..13....2.2..1.3..3....21..1..2.3....3....21...2..1.3.21......3...13..2...3.2...1
4513....2627.1.3..389..21..1..2.3....3....21...2..1.3.21......3...13..2...3.2...1     1015210 sols

46..59...9.74.8.6..8576..4..796.5..46.48.....85......6.96...47....5...92........1 #5
..13...2..2..1...33....21..1...3.2...3..21.....2...31.2..1.3....13.....2...2...31
4513...2.627.1...3389..21..1...3.2...3..21.....2...31.2..1.3....13.....2...2...31     1077252 sols

So they have all different UA27 [no surprise of course]
But maybe it could be a filter for you to use....although most grid perhaps will have many instances of these UA27s with the diagonal clues

[champagne]

needs some days to implement it, but I could have the key to go down in the process from ten hours to some seconds.

look forward to hearing this !
Im not sure its easy at all to go from a solution grid to a puzzle !!!
As a contribution Ive known that these puzzles all have the clue frequency values xxxxxx110

Hi coloin,
I can tell more.

Im not sure its easy at all to go from a solution grid to a puzzle !!!

Surely not. Gary Mc Guire team had a code to scan 16 clues puzzles in a solution grid in about 3 seconds per solution grid.
The check that all 17 where known took several years with an average 20 cores active using blue's approach,

So working in the area 25-27 clues seems not realistic.
But if we take as limit that we are looking for puzzles producing a pure tridagon PM at the start, then several things happen.
25 cells can not be given:
the 12+1 cells of the tridagon pattern,
The 12 cells of the 3 digits in boxes 2347

This was my start with the relatively disappointing run time of 10 hours

But I missed a key point. To get a pure tridagon, each of the 12 cells in the4 boxes square must see the 6 other digits
This constraint appears as an unavoidable set of two or three cells.
12*6 = 72 unavoidable sets of size 2 or 3, but cleaning redundancy and subsets, this ends around 45 UAs of size 2 and 3.

As the cells exclusion also reduces the size of classical unavoidable sets, we start with something completely different from the usual case.

In the loki solution grids, I got the smallest following UAs

Hidden Text: Show

Code: Select all

...................................1.....1....................................... 0  n=2
..................................1...............1.............................. 1  n=2
..............................1............................1..................... 2  n=2
...............................1....................................1............ 3  n=2
.............................1.....................1............................. 4  n=2
...................................1.................................1........... 5  n=2
........................1.........1.............................................. 6  n=2
...............................1..........1...................................... 7  n=2
.......................................1....................................1.... 8  n=2
.........................................1................1...................... 9  n=2
............................................1....1............................... 10  n=2
..................................1..1........................................... 11  n=2
....................................1...............1............................ 12  n=2
..........................................1....................................1. 13  n=2
............................................1................1................... 14  n=2
.......................................1...........1............................. 15  n=2
..................................................1........................1..... 16  n=2
..............................1.....................1............................ 17  n=2
.................................................1................1.............. 18  n=2
........1..........................................1............................. 19  n=2
...................................1...........1................................. 20  n=2
..........................1.........................1............................ 21  n=2
............1.............................................1...................... 22  n=2
........................................................1..................1..... 23  n=2
.............................................................1....1.............. 24  n=2
..........................................................1..........1........... 25  n=2
...........................................................1..................1.. 26  n=2
......1......................................................1................... 27  n=2
......................................................................1.....1.... 28  n=2
..............1.............................................................1.... 29  n=2
....................................................................1..........1. 30  n=2
.......................................................................1...1..... 31  n=2
..........................1...................................................1.. 32  n=2
.................1.............................................................1. 33  n=2
........................................................1..............1......... 34  n=2
1..........1..................................................................... 35  n=2
.1.........1..................................................................... 36  n=2
11............................................................................... 37  n=2

The current code delivered 500k puzzles in 27 seconds.
In theory, all minimal puzzles of size 25-27 giving the expected start PM.

I have seen some redundancy and bugs (or missing code) in the minimal check, but for sure, the final code will find an exhaustive list of size 25-26 in some seconds.
Still high for a full scan, but good to look for fresh seeds and to scan the known 65000 solution grids of mith's file.

I tried to cut in the output testing back doors with the zhou brute force basic rules (no guess).
Using this set of rules, loki has a back door 2, not 3. Using skfr, I got a SER rating 2.0, something that Zhou brute force solves without guess.
But excluding all back doors 1, the output could be cut by 90%

Referring to a previous post, I would say that the process can be applied saving much time for any new solution grid.

[champagne]

I have still a lot of work to finish the coding and secure the code, but I have more to share now.

I made deeper investigations on the loki solution grid.
I have 2 puzzles in mith’s file for this solution grid
And we have 6 different ways to build the tridagon pattern in it, with the triplets digits 357 (loki),135,159,249 (2x),468.
The triplets 249 did not deliver puzzles, likely something to fix in the code, but by far, the main results came out of the “loki” target with the digits 357.
The full scan looking for puzzles with <=27 clues lasted 34 seconds (for the six possibilities) and delivered more than 500 K puzzles.
I clearly have no idea of what I could do with so many puzzles, likely known for most of them by other members of the forum.
Applying my backdoor test (using the zhou set of rules), I reduced the count to 58013 puzzles having 2/3 backdoors with the classical stte rule. This is the file checked using skfr ratings.
It seems that all puzzles rating (skfr) 11.x are in the “loki” tridagon case.
Here the list of the 64 such puzzles.

Hidden Text: Show

Code: Select all

57...............8.1...9.....1.8..4.6....2..9..2..416.....26.9....9.82.4...41.68.;11.0/1.2/1.2
57...............8.1...9.....1.8..4.6....2..9..2.9416.....26.9......82.4...41.68.;11.0/1.2/1.2
57...............8.1...9.....1.8..4.6....28.9..2..416.....26.9....9.82.4...41.6..;11.0/1.2/1.2
57...............8.1...9.....1.8..4.6....28.9..2.9416.....26.9......82.4...41.6..;11.0/1.2/1.2
57....9..........8.1.........1.8..4.6....28.9..2.9416.....26......9.82.4...41.6..;11.0/1.2/1.2
57....9..........8.1.........1.8..4.64...28.9..2.9.16.....26......9.82.4...41.6..;11.0/1.2/1.2
57....9..........8.1...9.....1.8..4.6....2.....2.9416.....26.9......82.4...41.68.;11.0/1.2/1.2
57....9..........8.1...9.....1.8..4.6....2..9..2..416.....26......9.82.4...41.68.;11.0/1.2/1.2
57....9..........8.1...9.....1.8..4.6....28....2.9416.....26.9......82.4...41.6..;11.0/1.2/1.2
57....9..........8.1...9.....1.8..4.64...28.9..2...16.....26......9.82.4...41.6..;11.0/1.2/1.2
57..4.9..........8.1.........1.8..4.6....28.9..2.9.16.....26......9.82.4...41.6..;11.0/1.2/1.2
57..4.9..........8.1...9.....1.8..4.6....2.....2.9.16.....26.9......82.4...41.68.;11.0/1.2/1.2
57..4.9..........8.1...9.....1.8..4.6....2..9..2...16.....26......9.82.4...41.68.;11.0/1.2/1.2
57..4.9..........8.1...9.....1.8..4.6....28....2.9.16.....26.9......82.4...41.6..;11.0/1.2/1.2
57..4.9..........8.1...9.....1.8..4.6....28.9..2...16.....26......9.82.4...41.6..;11.0/1.2/1.2
57.8.............8.1...9.....1....4.6....28.9..2.9416.....26.9......82.4...41.6..;11.0/1.2/1.2
57.8.............8.1...9.....1.8..4.6....2..9..2..416.....26.9....9..2.4...41.68.;11.0/1.2/1.2
57.8.............8.1...9.....1.8..4.6....2..9..2.9416.....26.9.......2.4...41.68.;11.0/1.2/1.2
57.8..9..........8.1.........1....4.64...28.9..2.9.16.....26......9.82.4...41.6..;11.0/1.2/1.2
57.8..9..........8.1.........1....4264...28.9..2.9.16.....26......9.8..4...41.6..;11.0/1.2/1.2
57.8..9..........8.1.........1....4264.1..8.9..2.9.16.....26......9.8..4...41.6..;11.0/1.2/1.2
57.84............8.1...9.....1....4.6....28.9..2.9.16.....26.9......82.4...41.6..;11.0/1.2/1.2
57.84............8.1...9.....1.8..4.6....2..9..2...16.....26.9....9..2.4...41.68.;11.0/1.2/1.2
57.84............8.1...9.....1.8..4.6....2..9..2.9.16.....26.9.......2.4...41.68.;11.0/1.2/1.2
57....9..........8.1.........1.8..4.6....2.....2.9416.....26.9....9.82.4...41.68.;11.1/1.2/1.2
57....9..........8.1.........1.8..4.6....2..9..2.9416.....26......9.82.4...41.68.;11.1/1.2/1.2
57....9..........8.1.........1.8..4.6....28....2.9416.....26.9....9.82.4...41.6..;11.1/1.2/1.2
57....9..........8.1.........168..4......2.....2.9416.....2..9..6.9.82.4...41.68.;11.1/1.2/1.2
57....9..........8.1.........168..4......2..9..2.9416.....2.....6.9.82.4...41.68.;11.1/1.2/1.2
57....9..........8.1.........168..4......28....2.9416.....2..9..6.9.82.4...41.6..;11.1/1.2/1.2
57....9..........8.1.........168..4..4...28.9..2.9.16.....2.....6.9.82.4...41.6..;11.1/1.2/1.2
57....9..........8.1.........168..4..4...28.9..2.9.16.....26......9.82.4...41.6..;11.1/1.2/1.2
57....9..........8.1...9.....168..4......2.....2.9416.....2..9..6...82.4...41.68.;11.1/1.2/1.2
57....9..........8.1...9.....168..4......2..9..2..416.....2.....6.9.82.4...41.68.;11.1/1.2/1.2
57....9..........8.1...9.....168..4......28....2.9416.....2..9..6...82.4...41.6..;11.1/1.2/1.2
57....9..........8.1...9.....168..4..4...28.9..2...16.....2.....6.9.82.4...41.6..;11.1/1.2/1.2
57....9..........8.1...9.....168..4..4...28.9..2...16.....26......9.82.4...41.6..;11.1/1.2/1.2
57..4............8.1...9.....1.8..4.6....2..9..2...16.....26.9....9.82.4...41.68.;11.1/1.2/1.2
57..4............8.1...9.....1.8..4.6....2..9..2.9.16.....26.9......82.4...41.68.;11.1/1.2/1.2
57..4............8.1...9.....1.8..4.6....28.9..2...16.....26.9....9.82.4...41.6..;11.1/1.2/1.2
57..4............8.1...9.....1.8..4.6....28.9..2.9.16.....26.9......82.4...41.6..;11.1/1.2/1.2
57..4............8.1...9.....168..4......2..9..2...16.....2..9..6.9.82.4...41.68.;11.1/1.2/1.2
57..4............8.1...9.....168..4......2..9..2.9.16.....2..9..6...82.4...41.68.;11.1/1.2/1.2
57..4............8.1...9.....168..4......28.9..2...16.....2..9..6.9.82.4...41.6..;11.1/1.2/1.2
57..4............8.1...9.....168..4......28.9..2.9.16.....2..9..6...82.4...41.6..;11.1/1.2/1.2
57..4.9..........8.1.........1.8..4.6....2.....2.9.16.....26.9....9.82.4...41.68.;11.1/1.2/1.2
57..4.9..........8.1.........1.8..4.6....2..9..2.9.16.....26......9.82.4...41.68.;11.1/1.2/1.2
57..4.9..........8.1.........1.8..4.6....28....2.9.16.....26.9....9.82.4...41.6..;11.1/1.2/1.2
57..4.9..........8.1.........168..4......2.....2.9.16.....2..9..6.9.82.4...41.68.;11.1/1.2/1.2
57..4.9..........8.1.........168..4......2..9..2.9.16.....2.....6.9.82.4...41.68.;11.1/1.2/1.2
57..4.9..........8.1.........168..4......28....2.9.16.....2..9..6.9.82.4...41.6..;11.1/1.2/1.2
57..4.9..........8.1...9.....168..4......2.....2.9.16.....2..9..6...82.4...41.68.;11.1/1.2/1.2
57..4.9..........8.1...9.....168..4......2..9..2...16.....2.....6.9.82.4...41.68.;11.1/1.2/1.2
57..4.9..........8.1...9.....168..4......28....2.9.16.....2..9..6...82.4...41.6..;11.1/1.2/1.2
57.8..9..........8.1.........1....4.6....28.9..2.9416.....26......9.82.4...41.6..;11.1/1.2/1.2
57.8..9..........8.1.........1....426....28.9..2.9416.....26......9.8..4...41.6..;11.1/1.2/1.2
57.8..9..........8.1.........1....426..1..8.9..2.9416.....26......9.8..4...41.6..;11.1/1.2/1.2
57.8..9..........8.1.........16...4..4...28.9..2.9.16.....26......9.82.4...41.6..;11.1/1.2/1.2
57.8..9..........8.1.........16...42.4...28.9..2.9.16.....26......9.8..4...41.6..;11.1/1.2/1.2
57.8..9..........8.1.........16...42.4.1..8.9..2.9.16.....26......9.8..4...41.6..;11.1/1.2/1.2
57..4.9..........8.1...9.....168..4......28.9..2...16.....2.....6.9.82.4...41.6..;11.4/1.2/1.2
57....9..........8.1...9.....168..4......28.9..2..416.....2.....6.9.82.4...41.6..;11.7/1.2/1.2
57....9..........8.1.........168..4......28.9..2.9416.....2.....6.9.82.4...41.6..;11.8/1.2/1.2


I also started investigations in solution grids not in mith’s file.I tested the first 100 solution grids of the catalog and got 148 possibilities to build a tridagon.
The scan lasted 7mn to produce 420K puzzles with the non-degenerated tridagon pattern. 6621 of them passed the test of “more than one backdoor” and have been rated with skfr.
The highest rating has been 10.4, far from the target.
My surprise has been to see some low ratings with no backdoor (zhou set of rules) like theses one

Code: Select all

....53.....1.......728......5.....981..9.84......4513...4..9.53...4.18...9..3....;3.2/1.2/1.2
....53.....1.......728.....4......9.1..9.84.5.8...513........53..54.18.9.9..3....;3.2/1.2/1.2


I’ll finish the coding and the debugging of this code, but with no clear idea of what is expected, I don’t intend to tell more except if I see new very high ratings in solution grids not in mith’s file.