The New Sudoku Players' Forum

by **eleven** » Tue May 03, 2022 4:45 pm

Using Mladen's extremely fast tool for minlexing patterns made it much faster for me to generate impossible 3-digit paterns. Below is a list with new ones in up to 6 boxes. It turned out, that my 5-box list was all than complete.
Having these 380 i stopped, because these are already too much for me for manually checking. I would need a tool for evaluating, how hard it is for a solver to crack the pattern (eliminate 123 in one of the cells), in order to pick the interesting ones, but i cannot write one (SukakuExplainer does not help me, and i can't program in java).
Can only post them here in lines.

10 cells

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12 cells

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13 cells

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14 cells

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15 cells

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16 cells

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Website · by **denis_berthier** » Tue May 03, 2022 6:18 pm

eleven wrote:Short answer:
A bivalue oddagon is a loop with an odd number of cells having exactly 2 candidates.
In whatever way you place one digit of the "trivalue oddagon" correctly (in the 4 boxes), a bivalue oddagon is formed with the other 2 digits.
E.g.
Code: Select all
. . 1 | 23 . . . 23 . | . 23 . * . . | . . 1 ---------+-------- 1 . . | 23 . . . 23 . | . 1 . . . 23 | . . 23

The proof has to handle all ways of placing a single digit, which makes it longer than known ones.

OK, this way I see what you mean. However, invoking oddagons here is not necessary. The contradiction can also be proven by a mere bivalue chain.

Website · by **denis_berthier** » Tue May 03, 2022 6:44 pm

eleven wrote:Using Mladen's extremely fast tool for minlexing patterns made it much faster for me to generate impossible 3-digit paterns. Below is a list with new ones in up to 6 boxes. It turned out, that my 5-box list was all than complete.
Having these 380 i stopped, because these are already too much for me for manually checking. I would need a tool for evaluating, how hard it is for a solver to crack the pattern (eliminate 123 in one of the cells), in order to pick the interesting ones, but i cannot write one (SukakuExplainer does not help me, and i can't program in java).

I should be able to do something with SudoRules, but let me first make sure what you want.
You already know each pattern is impossible.
You want to find "how hard it is ... to crack the pattern (eliminate 123 in one of the cells)". Can we re-formulate this as "how hard is it to prove the contradiction'? (It seems to be different, but taking isomorphisms into account, it's probably the same thing).
The main problem I met with tridagons in proving the contradiction by dumb T&E is the huge number of candidates at the start (when each "." is replaced by 123456789). As a result, it's very slow. A much better way would be to use guided T&E (e.g. restricting the tried candidates to be in the pattern). I think I could easily write a modification of my T&E procedure. In this approach, you'd get the T&E level of the contradiction, which is IMO the best way to evaluate its potential for having hard puzzles.

I also think that Subsets (Triplets) should be allowed at the start, in order to eliminate lots of irrelevant candidates.

by **eleven** » Tue May 03, 2022 9:57 pm

Yes, that's what i meant. E.g. we can forget all the patterns, which can be resolved (proved impossible by contradiction) by 1-digit chains (the same chain for all 3 digits). All of the 5-box patterns i posted (apart from the TH pattern) are of that kind, and i assume many of the new ones are, too.
I don't think, that there is another pattern, which is as hard for chaining methods as Thor's Hammer, but it would be interesting to see, how hard they could be.

Website · by **denis_berthier** » Wed May 04, 2022 3:39 am

.
I could easily modify a few of the existing functions (to make them able to read your input). Just to make sure: all your patterns lie in the first two bands? (I completed with one full band). For allowing to check what"s solved, the starting pattern is printed (in the form usable by SudoRules).

Here is what I get for the first puzzles in the 10-cells list (when only Subsets, Finned Fish and whips are loaded):

Code: Select all: #1 +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123456789 123 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! 123456789 123 123 ! ! 123456789 123456789 123 ! 123456789 123 123 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ Resolution state after Singles and whips[1]: +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123456789 123 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! 123456789 123 123 ! ! 123456789 123456789 123 ! 123456789 123 123 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ 669 candidates. naked-triplets-in-a-row: r6{c3 c5 c6}{n3 n2 n1} ==> r6c9≠3, r6c9≠2, r6c9≠1, r6c8≠3, r6c8≠2, r6c8≠1, r6c7≠3, r6c7≠2, r6c7≠1, r6c4≠3, r6c4≠2, r6c4≠1, r6c2≠3, r6c2≠2, r6c2≠1, r6c1≠3, r6c1≠2, r6c1≠1 naked-triplets-in-a-row: r5{c6 c8 c9}{n3 n2 n1} ==> r5c7≠3, r5c7≠2, r5c7≠1, r5c5≠3, r5c5≠2, r5c5≠1, r5c4≠3, r5c4≠2, r5c4≠1, r5c3≠3, r5c3≠2, r5c3≠1, r5c2≠3, r5c2≠2, r5c2≠1, r5c1≠3, r5c1≠2, r5c1≠1 naked-triplets-in-a-block: b5{r5c6 r6c5 r6c6}{n3 n2 n1} ==> r4c6≠3, r4c6≠2, r4c6≠1, r4c5≠3, r4c5≠2, r4c5≠1, r4c4≠3, r4c4≠2, r4c4≠1 naked-triplets-in-a-block: b6{r4c9 r5c8 r5c9}{n3 n2 n1} ==> r4c8≠3, r4c8≠2, r4c8≠1, r4c7≠3, r4c7≠2, r4c7≠1 naked-triplets-in-a-column: c9{r3 r4 r5}{n3 n2 n1} ==> r9c9≠3, r9c9≠2, r9c9≠1, r8c9≠3, r8c9≠2, r8c9≠1, r7c9≠3, r7c9≠2, r7c9≠1, r2c9≠3, r2c9≠2, r2c9≠1, r1c9≠3, r1c9≠2, r1c9≠1 naked-triplets-in-a-column: c6{r3 r5 r6}{n3 n2 n1} ==> r9c6≠3, r9c6≠2, r9c6≠1, r8c6≠3, r8c6≠2, r8c6≠1, r7c6≠3, r7c6≠2, r7c6≠1, r2c6≠3, r2c6≠2, r2c6≠1, r1c6≠3, r1c6≠2, r1c6≠1 naked-triplets-in-a-row: r3{c3 c6 c9}{n3 n2 n1} ==> r3c8≠3, r3c8≠2, r3c8≠1, r3c7≠3, r3c7≠2, r3c7≠1, r3c5≠3, r3c5≠2, r3c5≠1, r3c4≠3, r3c4≠2, r3c4≠1, r3c2≠3, r3c2≠2, r3c2≠1, r3c1≠3, r3c1≠2, r3c1≠1 whip[3]: r6n1{c6 c3} - r4n1{c3 c9} - r3n1{c9 .} ==> r5c6≠1 whip[1]: r5n1{c9 .} ==> r4c9≠1 whip[1]: r4n1{c3 .} ==> r6c3≠1 whip[3]: r6n2{c6 c3} - r4n2{c3 c9} - r3n2{c9 .} ==> r5c6≠2 naked-single ==> r5c6=3 hidden-single-in-a-block ==> r4c9=3 hidden-single-in-a-row ==> r3c3=3 GRID 1 HAS NO SOLUTION : NO CANDIDATE FOR FOR BN-CELL b4n3 MOST COMPLEX RULE TRIED = W[3]

Code: Select all: #2 +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123456789 123 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! 123456789 123 123 ! ! 123456789 123456789 123 ! 123 123 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ Resolution state after Singles and whips[1]: +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123456789 123 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! 123456789 123 123 ! ! 123456789 123456789 123 ! 123 123 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ 669 candidates. naked-triplets-in-a-row: r6{c3 c4 c5}{n3 n2 n1} ==> r6c9≠3, r6c9≠2, r6c9≠1, r6c8≠3, r6c8≠2, r6c8≠1, r6c7≠3, r6c7≠2, r6c7≠1, r6c6≠3, r6c6≠2, r6c6≠1, r6c2≠3, r6c2≠2, r6c2≠1, r6c1≠3, r6c1≠2, r6c1≠1 naked-triplets-in-a-row: r5{c6 c8 c9}{n3 n2 n1} ==> r5c7≠3, r5c7≠2, r5c7≠1, r5c5≠3, r5c5≠2, r5c5≠1, r5c4≠3, r5c4≠2, r5c4≠1, r5c3≠3, r5c3≠2, r5c3≠1, r5c2≠3, r5c2≠2, r5c2≠1, r5c1≠3, r5c1≠2, r5c1≠1 naked-triplets-in-a-block: b5{r5c6 r6c4 r6c5}{n3 n2 n1} ==> r4c6≠3, r4c6≠2, r4c6≠1, r4c5≠3, r4c5≠2, r4c5≠1, r4c4≠3, r4c4≠2, r4c4≠1 naked-triplets-in-a-block: b6{r4c9 r5c8 r5c9}{n3 n2 n1} ==> r4c8≠3, r4c8≠2, r4c8≠1, r4c7≠3, r4c7≠2, r4c7≠1 naked-triplets-in-a-column: c9{r3 r4 r5}{n3 n2 n1} ==> r9c9≠3, r9c9≠2, r9c9≠1, r8c9≠3, r8c9≠2, r8c9≠1, r7c9≠3, r7c9≠2, r7c9≠1, r2c9≠3, r2c9≠2, r2c9≠1, r1c9≠3, r1c9≠2, r1c9≠1 naked-triplets-in-a-row: r3{c3 c6 c9}{n3 n2 n1} ==> r3c8≠3, r3c8≠2, r3c8≠1, r3c7≠3, r3c7≠2, r3c7≠1, r3c5≠3, r3c5≠2, r3c5≠1, r3c4≠3, r3c4≠2, r3c4≠1, r3c2≠3, r3c2≠2, r3c2≠1, r3c1≠3, r3c1≠2, r3c1≠1 whip[3]: r6n1{c5 c3} - r4n1{c3 c9} - r3n1{c9 .} ==> r5c6≠1 whip[1]: r5n1{c9 .} ==> r4c9≠1 whip[1]: r4n1{c3 .} ==> r6c3≠1 whip[3]: r6n2{c5 c3} - r4n2{c3 c9} - r3n2{c9 .} ==> r5c6≠2 naked-single ==> r5c6=3 hidden-single-in-a-block ==> r4c9=3 hidden-single-in-a-row ==> r3c3=3 GRID 2 HAS NO SOLUTION : NO CANDIDATE FOR FOR BN-CELL b4n3 MOST COMPLEX RULE TRIED = W[3]

and at the end of dealing with all the puzzles in the file:

Code: Select all: No-sol list = (1 2 3 4 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28)

For this list in particular, the hardest rule necessary to prove a contradiction in each puzzle is a whip[3].
For the other puzzles, harder techniques than the above listed ones must be used.

In case a puzzle is not proven contradictory with the chosen set of rules, here is how it appears:

Code: Select all: #5 Resolution state after Singles and whips[1]: +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123456789 123 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123456789 123 ! ! 123456789 123456789 123 ! 123456789 123 123456789 ! 123456789 123 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ 669 candidates. naked-triplets-in-a-row: r6{c3 c5 c8}{n3 n2 n1} ==> r6c9≠3, r6c9≠2, r6c9≠1, r6c7≠3, r6c7≠2, r6c7≠1, r6c6≠3, r6c6≠2, r6c6≠1, r6c4≠3, r6c4≠2, r6c4≠1, r6c2≠3, r6c2≠2, r6c2≠1, r6c1≠3, r6c1≠2, r6c1≠1 naked-triplets-in-a-row: r5{c3 c6 c9}{n3 n2 n1} ==> r5c8≠3, r5c8≠2, r5c8≠1, r5c7≠3, r5c7≠2, r5c7≠1, r5c5≠3, r5c5≠2, r5c5≠1, r5c4≠3, r5c4≠2, r5c4≠1, r5c2≠3, r5c2≠2, r5c2≠1, r5c1≠3, r5c1≠2, r5c1≠1 naked-triplets-in-a-block: b6{r4c9 r5c9 r6c8}{n3 n2 n1} ==> r4c8≠3, r4c8≠2, r4c8≠1, r4c7≠3, r4c7≠2, r4c7≠1 naked-triplets-in-a-column: c9{r3 r4 r5}{n3 n2 n1} ==> r9c9≠3, r9c9≠2, r9c9≠1, r8c9≠3, r8c9≠2, r8c9≠1, r7c9≠3, r7c9≠2, r7c9≠1, r2c9≠3, r2c9≠2, r2c9≠1, r1c9≠3, r1c9≠2, r1c9≠1 naked-triplets-in-a-row: r3{c3 c6 c9}{n3 n2 n1} ==> r3c8≠3, r3c8≠2, r3c8≠1, r3c7≠3, r3c7≠2, r3c7≠1, r3c5≠3, r3c5≠2, r3c5≠1, r3c4≠3, r3c4≠2, r3c4≠1, r3c2≠3, r3c2≠2, r3c2≠1, r3c1≠3, r3c1≠2, r3c1≠1 naked-triplets-in-a-column: c3{r3 r5 r6}{n3 n2 n1} ==> r9c3≠3, r9c3≠2, r9c3≠1, r8c3≠3, r8c3≠2, r8c3≠1, r7c3≠3, r7c3≠2, r7c3≠1, r4c3≠3, r4c3≠2, r4c3≠1, r2c3≠3, r2c3≠2, r2c3≠1, r1c3≠3, r1c3≠2, r1c3≠1 PUZZLE 5 IS NOT SOLVED. 81 VALUES MISSING. Final resolution state: +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 456789 ! 123456789 123456789 123456789 ! 123456789 123456789 456789 ! ! 123456789 123456789 456789 ! 123456789 123456789 123456789 ! 123456789 123456789 456789 ! ! 456789 456789 123 ! 456789 456789 123 ! 456789 456789 123 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 456789 ! 123456789 123456789 123456789 ! 456789 456789 123 ! ! 456789 456789 123 ! 456789 456789 123 ! 456789 456789 123 ! ! 456789 456789 123 ! 456789 123 456789 ! 456789 123 456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 456789 ! 123456789 123456789 123456789 ! 123456789 123456789 456789 ! ! 123456789 123456789 456789 ! 123456789 123456789 123456789 ! 123456789 123456789 456789 ! ! 123456789 123456789 456789 ! 123456789 123456789 123456789 ! 123456789 123456789 456789 ! +-------------------------------+-------------------------------+-------------------------------+

Before I try the other files and harder techniques, is this the kind of result you were looking for?

by **eleven** » Wed May 04, 2022 7:40 am

Yes, exactly.

by **ryokousha** » Wed May 04, 2022 8:16 am

Until we have a good way to generate and classify all the patterns in an arbitrary number of boxes up to a certain number of cells, here are a few more patterns I found manually. Forgive me if they already came up as morphs, I didn't check too carefully.
10 cells in 6 boxes (this might be in the latest list by eleven, but as a nice variation on the Patto Patto pattern it's notable)

Code: Select all: . . . | . . . | . . . . * . | . * . | . * . . . . | . . . | . . . ------+-------+------ . * . | * . . | . * . . . . | . * . | . . . . * . | . . * | . * . ------+-------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .

Then there are a couple more in 6 boxes:
This variation of the "socks" pattern

Hidden Text: Show

also these three

Hidden Text: Show

Also I do have two more examples for higher "chromatic numbers".
This is not 4-colorable

Code: Select all: . . . | . . . | . . . . . . | . . . | . . . . . * | . * . | * . . ------+-------+------ . . . | . * . | . . . . . * | * . * | * . . . . . | . * . | . . . ------+-------+------ . . * | * . * | * . . . . * | * . * | * . . . . . | . . . | . . .

(r3c5 is limited to r78 in c37, the resulting x-wing excluding it from b8. Can also be seen as a finned (multi-)fish, excluding all digits from r3c5)
Using complements, it follows that patterns with all "chromatic numbers" from 2 to 8 exist in 9x9 Sudoku. Here's an explicit example for a non-5-colorable one:

Code: Select all: . * . | * . * | . * . . . . | . . . | . . . . * . | * . * | . * . ------+-------+------ . * . | . . . | . * . * . * | . . * | * . * . * . | . . . | . * . ------+-------+------ . . . | . . . | . . . . * . | * . * | . * . . . . | . . . | . . .

Website · by **denis_berthier** » Wed May 04, 2022 8:19 am

eleven wrote:Yes, exactly.

Good
Still using the same set of rules (Subsets + Finned Fish +Whips of any length), here are the results for all your lists:
(being in no-sol-list means contradiction is proven with only these rules)

10 cells:

Code: Select all: No-sol list = (1 2 3 4 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28)

Most complex rule used: whip[3]

12 cells:

Code: Select all: No-sol list = (4 7 8 9 10 12 13 14 15 16 17 19 20 21 22 23 24)

Most complex rule used: whip[4]

13 cells:

Code: Select all: No-sol list = (1 3 4 5 10 11 12 13 14 15 16 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 125 126 127 128 129 130 131 132 133 134 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 182 188 191 192 193 194 195 196 197 198 199 200 213 215 216 217 218 219 221 228 229 230)

Most complex rule used: whip[4] (but most patterns require only whips[3]

14 cells:

Code: Select all: No-sol list = ()

15 cells:

Code: Select all: No-sol list = (1 2 3 4 5 6 7 8 11 12 13 14 19 20 23 24 25 26)

Most complex rule used: whip[4] (all the patterns)

16 cells:

Code: Select all: No-sol list = ()

The next step would be to check which patterns can be proven contradictory in T&E(SFin) or in T&E(2). But for reasonable computation times, I still have to restrict the candidates tried.
Are you interested in having the specially modified functions in SudoRules (in Goodies) so that you can try your own combinations of rules?

by **ryokousha** » Wed May 04, 2022 8:41 am

Denis' approach looks fruitful to find the most "interesting" patterns among all the generated ones. Another line of thinking would be to classify the patterns by the edge- and node-minimal 4-chromatic subgraph(s) they contain (could potentially be multiple of these). The structure of these subgraphs should then correspond somehow to the complexity of the resolving strategy.

I haven't implemented this with the minimality condition yet. Just classifying eleven's list by isomorphism of the full connection graphs gives this - somewhat unsatisfying - result:

10c: 29 patterns -> 19 graphs
12c: 29 patterns -> 23 graphs
13c: 213 patterns -> 135 graphs
14c: 46 patterns -> 41 graphs
15c: 42 patterns -> 32 graphs
16c: 3 patterns -> 3 graphs

For example these 7 patterns have the same connection graph:

Code: Select all: 000000000000001011001001001000001000000010011001010100 000000000000001011001001001000001000000010011001100100 000000000000001011001001001001000000010000011010001100 000000000000001011001001001001000000010000011100001100 000000000000001011001001100000001000000010011001010001 000000000000001011001001100000001000000010011001100001 000000000000001011001001100000001000001000011001010001

Note that not all cell patterns can be classified this way. For example the connection graph of

Code: Select all: * * * | . . . | . . . . . . | * * * | . . . . . . | . . . | . . . ------+-------+------ . . . | . . . | . . . . . . | . . . | . . * . . . | . . . | . . * ------+-------+------ . . . | . . . | . * . . . . | . . . | . * . . . . | . . . | . * .

is 3-chromatic, but the pattern is not 3-colorable in a Sudoku grid. Such patterns (I doubt there are very many of them) would fall out during the classification process.

Website · by **denis_berthier** » Wed May 04, 2022 9:27 am

.
I've finally checked which patterns can be proven contradictory in T&E(2). Only 1 cannot:

Code: Select all: 15-cells #37: +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! 123456789 123456789 123 ! ! 123456789 123456789 123 ! 123456789 123456789 123456789 ! 123456789 123 123456789 ! ! 123456789 123 123456789 ! 123456789 123 123456789 ! 123 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123 123456789 ! 123456789 123456789 123 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123 123456789 123456789 ! ! 123456789 123 123456789 ! 123 123456789 123456789 ! 123456789 123 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+

Which makes me wonder: the trivalue oddagon is not in your list of 12-cells?

by **eleven** » Wed May 04, 2022 9:35 am

What you mean with the "No-sol list" ? Those are the easy patterns, which only require whip[3] ?
I never have used Sudo Rules, so i don't know, what effort it would be to do it myself (as i suppose yours, my free time is restricted).

[Added:]
E.g. from my point of view nr 6 of the 10 cell patterns is easy to see:
X in r4c9 kills Xr3c9 and leaves an x.wing in r56c36, which kills the other 2 X's in r3. Is this a whip(4) for Sudo Rules ?

Code: Select all: . . . | . . . | . . . . . . | . . . | . . . . . X | . . X | . . X ------------------------------- . . . | . . . | . . X . . X | . . X | . X . . . X | . . X | . X .

Website · by **denis_berthier** » Wed May 04, 2022 9:49 am

eleven wrote:What you mean with the "No-sol list" ? Those are the easy patterns, which only require whip[3] ?
I never have used Sudo Rules, so i don't know, what effort it would be to do it myself (as i suppose yours, my free time is restricted).

Being in no-sol-list means the pattern is proven contradictory with the selected set of rules.

SudoRules is very easy to use. You just have to select your rules in the configuration file.

Website · by **denis_berthier** » Wed May 04, 2022 10:24 am

eleven wrote:[Added:]
E.g. from my point of view nr 6 of the 10 cell patterns is easy to see:
X in r4c9 kills Xr3c9 and leaves an x.wing in r56c36, which kills the other 2 X's in r3. Is this a whip(4) for Sudo Rules ?
Code: Select all
. . . | . . . | . . . . . . | . . . | . . . . . X | . . X | . . X ------------------------------- . . . | . . . | . . X . . X | . . X | . X . . . X | . . X | . X .

No, whips don't include x-wings as sub-patterns.
It may be an S2-whip - not coded in SudoRules.
If it was a whip[4], SudoRules would find it.

Here is what you get in detail; it cannot be proven contradictory using only Subests+FinnedFish+whips:
For this pattern and these rules, SudoRules finds only Subsets and Finned-Fish.

Code: Select all: 000000000000000000001001001000000001001001010001001010 +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123456789 123 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123 123456789 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ Resolution state after Singles and whips[1]: +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123456789 123 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123 123456789 ! ! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+ 669 candidates. naked-triplets-in-a-row: r6{c3 c6 c8}{n3 n2 n1} ==> r6c9≠3, r6c9≠2, r6c9≠1, r6c7≠3, r6c7≠2, r6c7≠1, r6c5≠3, r6c5≠2, r6c5≠1, r6c4≠3, r6c4≠2, r6c4≠1, r6c2≠3, r6c2≠2, r6c2≠1, r6c1≠3, r6c1≠2, r6c1≠1 naked-triplets-in-a-row: r5{c3 c6 c8}{n3 n2 n1} ==> r5c9≠3, r5c9≠2, r5c9≠1, r5c7≠3, r5c7≠2, r5c7≠1, r5c5≠3, r5c5≠2, r5c5≠1, r5c4≠3, r5c4≠2, r5c4≠1, r5c2≠3, r5c2≠2, r5c2≠1, r5c1≠3, r5c1≠2, r5c1≠1 naked-triplets-in-a-block: b6{r4c9 r5c8 r6c8}{n3 n2 n1} ==> r4c8≠3, r4c8≠2, r4c8≠1, r4c7≠3, r4c7≠2, r4c7≠1 naked-triplets-in-a-column: c6{r3 r5 r6}{n3 n2 n1} ==> r9c6≠3, r9c6≠2, r9c6≠1, r8c6≠3, r8c6≠2, r8c6≠1, r7c6≠3, r7c6≠2, r7c6≠1, r4c6≠3, r4c6≠2, r4c6≠1, r2c6≠3, r2c6≠2, r2c6≠1, r1c6≠3, r1c6≠2, r1c6≠1 naked-triplets-in-a-row: r3{c3 c6 c9}{n3 n2 n1} ==> r3c8≠3, r3c8≠2, r3c8≠1, r3c7≠3, r3c7≠2, r3c7≠1, r3c5≠3, r3c5≠2, r3c5≠1, r3c4≠3, r3c4≠2, r3c4≠1, r3c2≠3, r3c2≠2, r3c2≠1, r3c1≠3, r3c1≠2, r3c1≠1 naked-triplets-in-a-column: c3{r3 r5 r6}{n3 n2 n1} ==> r9c3≠3, r9c3≠2, r9c3≠1, r8c3≠3, r8c3≠2, r8c3≠1, r7c3≠3, r7c3≠2, r7c3≠1, r4c3≠3, r4c3≠2, r4c3≠1, r2c3≠3, r2c3≠2, r2c3≠1, r1c3≠3, r1c3≠2, r1c3≠1 finned-swordfish-in-rows: n3{r6 r5 r3}{c6 c3 c8} ==> r2c8≠3, r1c8≠3 finned-swordfish-in-rows: n2{r6 r5 r3}{c6 c3 c8} ==> r2c8≠2, r1c8≠2 finned-swordfish-in-rows: n1{r6 r5 r3}{c6 c3 c8} ==> r2c8≠1, r1c8≠1 PUZZLE 6 IS NOT SOLVED. 81 VALUES MISSING. Final resolution state: +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 456789 ! 123456789 123456789 456789 ! 123456789 456789 123456789 ! ! 123456789 123456789 456789 ! 123456789 123456789 456789 ! 123456789 456789 123456789 ! ! 456789 456789 123 ! 456789 456789 123 ! 456789 456789 123 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 456789 ! 123456789 123456789 456789 ! 456789 456789 123 ! ! 456789 456789 123 ! 456789 456789 123 ! 456789 123 456789 ! ! 456789 456789 123 ! 456789 456789 123 ! 456789 123 456789 ! +-------------------------------+-------------------------------+-------------------------------+ ! 123456789 123456789 456789 ! 123456789 123456789 456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 456789 ! 123456789 123456789 456789 ! 123456789 123456789 123456789 ! ! 123456789 123456789 456789 ! 123456789 123456789 456789 ! 123456789 123456789 123456789 ! +-------------------------------+-------------------------------+-------------------------------+

It cannot be proven contradictory in T&E(S2, 2) - probably because it requires Subsets[3] at the start.

It can be proven contradictory in T&E(2).

It can also easily be proven contradictory in T&E(S3+W3, 1) as shown below:

Code: Select all: (solve-eleven-sudoku-string "000000000000000000001001001000000001001001010001001010") naked-triplets-in-a-row: r6{c3 c6 c8}{n3 n2 n1} ==> r6c9≠3, r6c9≠2, r6c9≠1, r6c7≠3, r6c7≠2, r6c7≠1, r6c5≠3, r6c5≠2, r6c5≠1, r6c4≠3, r6c4≠2, r6c4≠1, r6c2≠3, r6c2≠2, r6c2≠1, r6c1≠3, r6c1≠2, r6c1≠1 naked-triplets-in-a-row: r5{c3 c6 c8}{n3 n2 n1} ==> r5c9≠3, r5c9≠2, r5c9≠1, r5c7≠3, r5c7≠2, r5c7≠1, r5c5≠3, r5c5≠2, r5c5≠1, r5c4≠3, r5c4≠2, r5c4≠1, r5c2≠3, r5c2≠2, r5c2≠1, r5c1≠3, r5c1≠2, r5c1≠1 naked-triplets-in-a-block: b6{r4c9 r5c8 r6c8}{n3 n2 n1} ==> r4c8≠3, r4c8≠2, r4c8≠1, r4c7≠3, r4c7≠2, r4c7≠1 naked-triplets-in-a-column: c6{r3 r5 r6}{n3 n2 n1} ==> r9c6≠3, r9c6≠2, r9c6≠1, r8c6≠3, r8c6≠2, r8c6≠1, r7c6≠3, r7c6≠2, r7c6≠1, r4c6≠3, r4c6≠2, r4c6≠1, r2c6≠3, r2c6≠2, r2c6≠1, r1c6≠3, r1c6≠2, r1c6≠1 naked-triplets-in-a-row: r3{c3 c6 c9}{n3 n2 n1} ==> r3c8≠3, r3c8≠2, r3c8≠1, r3c7≠3, r3c7≠2, r3c7≠1, r3c5≠3, r3c5≠2, r3c5≠1, r3c4≠3, r3c4≠2, r3c4≠1, r3c2≠3, r3c2≠2, r3c2≠1, r3c1≠3, r3c1≠2, r3c1≠1 naked-triplets-in-a-column: c3{r3 r5 r6}{n3 n2 n1} ==> r9c3≠3, r9c3≠2, r9c3≠1, r8c3≠3, r8c3≠2, r8c3≠1, r7c3≠3, r7c3≠2, r7c3≠1, r4c3≠3, r4c3≠2, r4c3≠1, r2c3≠3, r2c3≠2, r2c3≠1, r1c3≠3, r1c3≠2, r1c3≠1 *** STARTING T&E IN CONTEXT 0 with 0 csp-variables solved and 573 candidates remaining *** STARTING PHASE 1 IN CONTEXT 0 with 0 csp-variables solved and 573 candidates remaining GENERATING CONTEXT 1 AT DEPTH 1, SON OF CONTEXT 0, FROM HYPOTHESIS n3r6c8. x-wing-in-columns: n3{c3 c6}{r3 r5} ==> r3c9≠3 naked-pairs-in-a-column: c9{r3 r4}{n1 n2} ==> r1c9≠1, r1c9≠2, r2c9≠1, r2c9≠2, r7c9≠1, r7c9≠2, r8c9≠1, r8c9≠2, r9c9≠1, r9c9≠2 whip[2]: c9n2{r4 r3} - c6n2{r3 .} ==> r4c5≠2, r4c4≠2 whip[1]: b5n2{r5c6 .} ==> r3c6≠2 whip[2]: r4n2{c1 c9} - r3n2{c9 .} ==> r6c3≠2, r5c3≠2 naked-single ==> r6c3=1 naked-single ==> r6c6=2 naked-single ==> r5c3=3 naked-single ==> r5c6=1 naked-single ==> r5c8=2 naked-single ==> r4c9=1 NO POSSIBLE VALUE for csp-variable 231 IN CONTEXT 1. RETRACTING CANDIDATE n3r6c8 FROM CONTEXT 0. BACK IN CONTEXT 0 with 0 csp-variables solved and 572 candidates remaining. whip[3]: b6n3{r4c9 r5c8} - c3n3{r5 r6} - c6n3{r6 .} ==> r3c9≠3 x-wing-in-rows: n3{r3 r6}{c3 c6} ==> r5c6≠3, r5c3≠3 hidden-single-in-a-row ==> r5c8=3 naked-pairs-in-a-column: c9{r3 r4}{n1 n2} ==> r9c9≠2, r9c9≠1, r8c9≠2, r8c9≠1, r7c9≠2, r7c9≠1, r2c9≠2, r2c9≠1, r1c9≠2, r1c9≠1 whip[2]: c9n2{r3 r4} - b5n2{r4c4 .} ==> r3c6≠2 whip[1]: c6n2{r6 .} ==> r4c4≠2, r4c5≠2 whip[2]: r3n2{c3 c9} - r4n2{c9 .} ==> r6c3≠2, r5c3≠2 naked-single ==> r5c3=1 naked-single ==> r5c6=2 naked-single ==> r6c3=3 naked-single ==> r3c3=2 naked-single ==> r3c9=1 naked-single ==> r3c6=3 naked-single ==> r4c9=2 GRID 0 HAS NO SOLUTION : NO CANDIDATE FOR FOR BN-CELL b4n2

Note that all the above results about contradictory patterns don't say much about the puzzles built close to them. Other clues can completely reduce their complexity.

But I consider them as filters for possible hard patterns. If your goal is to find hard puzzles, you should try with pattern #37 in the 15-cells list.

by **eleven** » Wed May 04, 2022 10:27 am

Ah, thanks. So it's what basically i wanted, to filter out the easier ones.

The clips binary is not running on linux (Exec format error), so i will have to install one for linux (it's not in the standard ubuntu libraries). I'll have a look another time.

Website · by **denis_berthier** » Wed May 04, 2022 10:40 am

eleven wrote:Ah, thanks. So it's what basically i wanted, to filter out the easier ones.

The clips binary is not running on linux (Exec format error), so i will have to install one for linux (it's not in the standard ubuntu libraries). I'll have a look another time.

easy: compile it by typing "make" in the CLIPS/clips-core directory

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