The New Sudoku Players' Forum

[Serg]

Hi, Blue!

Now I think there exist 800-1000 maximal invalid anticorner patterns.

It's worse than that.
If I'm right, it's 1428, including the 95 from your opening post.

Edited again: oops, right the first time ... 1428

I've finished the search for maximal invalid patterns and got 1397 patterns only

Serg

[blue]

Hi Serg,

I've finished the search for maximal invalid patterns and got 1397 patterns only

Impressive
I get puzzles for 3 of your shapes, and the other 1394 are in my list.

Code: Select all

shapes:
.................1..1..111.......111......111.....1111..1111111.1.111111.1.111111
...........1.......1......1......111.....11111.1...111...111111..11111111..111111
........1..1.....1.1.....11......111......111.....1111...111111..1111111111111111

puzzles:
.................8..7..934.......156......279.....7483..4593721.5.718694.1.264835
...........5.......4......9......864.....13923.8...517...139748..78429568..576123
........6..8.....4.7.....13......468......921.....1375...693157..9185642516742839

I do have another 34 shapes, to make the total of 1428. None of them map to a subshape of one of the 3 from above.

These five (all related), seem too big for you to have missed.
Are they misplaced somehow ?
Maybe I have a bug in the code that's saying that also, none of the 34, maps to a subshape of one of your other 1394 shapes ?

Code: Select all

+-------+-------+-------+    +-------+-------+-------+    +-------+-------+-------+
| . . . | . . . | . 1 1 |    | . . . | . 1 . | . . 1 |    | . . . | . . 1 | . . 1 |
| . . . | . . . | . 1 1 |    | . . . | . 1 . | . . 1 |    | . . . | . . 1 | . . 1 |
| . . . | 1 1 1 | 1 1 1 |    | . . . | 1 1 1 | 1 1 1 |    | . . . | 1 1 1 | 1 1 1 |
+-------+-------+-------+    +-------+-------+-------+    +-------+-------+-------+
| . . . | . . 1 | 1 1 1 |    | . . . | . . 1 | 1 1 1 |    | . . . | . . 1 | 1 1 1 |
| . . . | . . 1 | 1 1 1 |    | . . . | . . 1 | 1 1 1 |    | . . . | . . 1 | 1 1 1 |
| . . . | . . 1 | 1 1 1 |    | . . . | . . 1 | 1 1 1 |    | . . . | . . 1 | 1 1 1 |
+-------+-------+-------+    +-------+-------+-------+    +-------+-------+-------+
| . . . | 1 1 1 | 1 1 1 |    | . . . | 1 1 1 | 1 1 1 |    | . . . | 1 1 1 | 1 1 1 |
| 1 1 1 | 1 1 1 | 1 1 1 |    | 1 1 1 | 1 1 1 | 1 1 1 |    | 1 1 1 | 1 1 1 | 1 1 1 |
| 1 1 1 | 1 1 1 | 1 1 1 |    | 1 1 1 | 1 1 1 | 1 1 1 |    | 1 1 1 | 1 1 1 | 1 1 1 |
+-------+-------+-------+    +-------+-------+-------+    +-------+-------+-------+

+-------+-------+-------+    +-------+-------+-------+
| . . . | 1 1 . | . . . |    | . . . | . 1 1 | . . . |
| . . . | 1 1 . | . . . |    | . . . | . 1 1 | . . . |
| . . . | 1 1 1 | 1 1 1 |    | . . . | 1 1 1 | 1 1 1 |
+-------+-------+-------+    +-------+-------+-------+
| . . . | . . 1 | 1 1 1 |    | . . . | . . 1 | 1 1 1 |
| . . . | . . 1 | 1 1 1 |    | . . . | . . 1 | 1 1 1 |
| . . . | . . 1 | 1 1 1 |    | . . . | . . 1 | 1 1 1 |
+-------+-------+-------+    +-------+-------+-------+
| . . . | 1 1 1 | 1 1 1 |    | . . . | 1 1 1 | 1 1 1 |
| 1 1 1 | 1 1 1 | 1 1 1 |    | 1 1 1 | 1 1 1 | 1 1 1 |
| 1 1 1 | 1 1 1 | 1 1 1 |    | 1 1 1 | 1 1 1 | 1 1 1 |
+-------+-------+-------+    +-------+-------+-------+

.......11.......11...111111.....1111.....1111.....1111...111111111111111111111111
....1...1....1...1...111111.....1111.....1111.....1111...111111111111111111111111
.....1..1.....1..1...111111.....1111.....1111.....1111...111111111111111111111111
...11.......11.......111111.....1111.....1111.....1111...111111111111111111111111
....11.......11......111111.....1111.....1111.....1111...111111111111111111111111


Cheers,
Blue.

[Serg]

Hi, Blue!
Thank you very much for your crosschecks! I am lucky to collaborate with you.

My patterns checking program has a bug - it finds no valid puzzles for those 3 wrong maximal invalid patterns. So, I must fix the bug and process all patterns again. It probably will take me several weeks.

Anyway I am happy to get help from you.

Serg

[Serg]

Hi, Blue!
I've found and fixed a bug in my program. Now it finds valid puzzles for those 3 patterns having valid puzzles (and those were wrongly declared earlier as maximal invalid patterns). I rechecked all remaining 1394 maximal invalid patterns - the program confirms that those 1394 patterns are maximal invalid patterns. The program also confirms that your last 5 patterns are maximal invalid.

Now I am thinking about methods to check - is given maximal invalid anticorner patterns set complete? I've found more than 12000 resctricted minimal valid anticorner patterns (including 322 valid patterns with 6 clues only in anticorner area). I am sure that my list is not complete. So, sets of valid and invalid anticorner patterns are complete iff any anticorner pattern is either subset of some invalid patterns or superset of some valid pattern. I think direct check is impossible because of huge number of possible anticorner patterns.

Serg

[blue]

Hi Serg,

It's great that you found your bug, but ...

I've found more than 12000 resctricted minimal valid anticorner patterns (including 322 valid patterns with 6 clues only in anticorner area).

Have you checked subsets of these patterns, since the bug fix ?
I think there are only 11706 such patterns ... with size distribution:
Edit: These are definitely the wrong numbers ...

Code: Select all

  6 |   322
  7 |  3744
  8 |  4499
  9 |  1781
 10 |   953
 11 |   317
 12 |    90
----+------
any | 11706

More to follow ...

Preview: I produced the list of 11706, from a shorter list of 10090 shapes, that

1. Includes non-minimal cases, with 9 clues in one or more of {r7,r8,r9,c7,c8,c9}
2. Doesn't include shapes with exactly 8 clues in any of {r7,r8,r9,c7,c8,c9}
3. Has this size distribtion ...

Code: Select all

  6 |   322
  7 |  3658
  8 |  3880
  9 |  1267
 10 |   542
 11 |   185
 12 |    56
 13 |   136
 14 |    40
 15 |     4
----+------
all | 10090

[Serg]

Hi, Blue!
At the moment I have 12058 (restricted) minimal valid anticorner patterns. Some of them have 8 clues in a row/column/box. Here is distribution of patterns by clue multiplicity in anticorner area (B123457):

Code: Select all

Number of clues in B1-B5, B7 boxes
 6    322
 7   3627
 8   4539
 9   2024
10   1108
11    305
12    133

I attached 12-clue patterns list to this post to compare my 133 patterns with your 90 patterns.

Serg

[blue]

Hi Serg,

Your list of size 12 shapes was fine -- verified as "(restriced) minimal valid" on my end.
Also, It does include all 90 shapes from my list.

The problem is on my end ... sorry for the confusion.
For me, producing the true list of "(restricted) minmal valid" shapes, will be a lot more complicated than I thought it would be.
I'm not sure it's even practical to attempt it

The problem is due to what I hinted at: I don't have direct "does/doesn't have puzzles" data about shapes with 8 clues in one of {r7,r8,r9,c7,c8,c9}.
For the most part, it's redundant, because such shapes have puzzles, if and only if thier expanded versions have puzzles.

For an example of the start of what went wrong on my end, here's a 12-clue shape from your list, that wasn't in my list, with the 8-clue rows/cols expanded to 9 clues:

Code: Select all

+-------+-------+-------+
| . . . | . . . | . 2 2 |
| . . . | . . . | . 1 1 |
| . . . | . . . | . 1 1 |
+-------+-------+-------+
| . . . | . . . | 1 1 1 |
| . . 1 | . . 1 | 1 1 1 |
| . . 1 | . . 1 | 1 1 1 |
+-------+-------+-------+
| . . 1 | 1 1 1 | 1 1 1 |
| . 1 . | 1 1 1 | 1 1 1 |
| 1 2 1 | 1 1 1 | 1 1 1 |
+-------+-------+-------+

My data shows it as having puzzles (of course).
But my (erroneous) "minimal valid" extraction code, ignored it, because *this* shape has puzzles:

Code: Select all

+-------+-------+-------+
| . . . | . . . | . 2 2 |
| . . . | . . . | . 1 1 |
| . . . | . . . | . 1 1 |
+-------+-------+-------+
| . . . | . . . | 1 1 1 |
| . . 1 | . . 1 | 1 1 1 |
| . . 1 | . . 1 | 1 1 1 |
+-------+-------+-------+
| . . 1 | 1 1 1 | 1 1 1 |
| . 1 . | 1 1 1 | 1 1 1 |
| . 2 . | 1 1 1 | 1 1 1 |
+-------+-------+-------+

[coloin]

I'm not sure it's even practical to attempt it

It must be difficult !!

Trying to interpret the tables ....

322 is the number of valid patterns with 6 clues ... { up from 315 posted !]
3627 is the number of potentially valid 7 clue patterns but doesnt include the patterns generated from the 322 plus 1 clue ... is this correct ?

There wont be many 12 clue patterns which arnt valid ...
for other readers.. this [? maximal} pattern takes out many ...

Code: Select all

+---+---+---+
|...|.6.|...|
|...|.1.|...|
|..1|372|458|
+---+---+---+
|..4|821|635|
|123|456|789|
|..8|793|124|
+---+---+---+
|..9|687|513|
|..7|245|896|
|..6|139|247|
+---+---+---+  invalid pattern

Of course the saving grace is that it gets easier to provide a puzzle once the number of clues increases above 7 ....
So maybe providing valid puzzles is a quicker way to check all the possible valid patterns ... which is the table ? and hence the invalid patterns can be found ?

Splitting it up may be useful ?

With 5 clues we have 36 patterns with 5 clues in B12347 and a full B5 .....
With 6 clues we have either 5 clues in B12347 and 1 in B5, 6 clues in B12347 and 0 in B5.
With 7 clues we have either 5 clues in B12347 and 2 in B5, 6 clues in B12347 and 1 in B5, 7 clues in B12347 and 0 in B5
and so on with 8 clues ... 5 clues in B12347 and 3 in B5, 6 clues in B12347 and 2 in B5, 7 clues in B12347 and 1 in B5 8 clues in B12347 and 0 in B5

I have been able to generate 442 [ dont think there are more] different valid patterns with 6 clues in B12347 and a full B5

Adding respective clues to B5 [4 ways] might give valid / invalid patterns to progress with ...

[blue]

Trying to interpret the tables ....

322 is the number of valid patterns with 6 clues ... { up from 315 posted !]
3627 is the number of potentially valid 7 clue patterns but doesnt include the patterns generated from the 322 plus 1 clue ... is this correct ?

That's the idea, yes.
I think the 7-clue number is at least 3744, though.

There wont be many 12 clue patterns which arnt valid ...
for other readers.. this [? maximal} pattern takes out many ...

Code: Select all

+---+---+---+
|...|.6.|...|
|...|.1.|...|
|..1|372|458|
+---+---+---+
|..4|821|635|
|123|456|789|
|..8|793|124|
+---+---+---+
|..9|687|513|
|..7|245|896|
|..6|139|247|
+---+---+---+  invalid pattern

Of course the saving grace is that it gets easier to provide a puzzle once the number of clues increases above 7 ....
So maybe providing valid puzzles is a quicker way to check all the possible valid patterns ... which is the table ? and hence the invalid patterns can be found ?

Right. If you had a table that listed every (ED) "anti-corner" shape, and whether it has puzzles, then to produce the lists of maximal invalid and (restricted) minimal valid shapes, then you could do this:

For maximal invalid shapes:

1. For each shape, initialize an "is a proper subset of an invalid shape" flag to 'false'
2. Loop the shapes from the largest size to the smallest
3. If the shape has puzzles, or it is already flagged as being a proper subset of an invalid shape, then ignore it.
4. Otherwise, add it to the list of "maximal invalid" shapes, and see that all of its proper subsets get the flag from (1) set to true.
   (Likely, some will already be flagged).

For (restricted) minimal valid shapes:

1. For each shape, initialize an "is a proper superset of an valid shape" flag to 'false'
2. Loop the shapes from the smallest size to the largest
3. If the shape doesn't have puzzle, or it is already flagged as being a proper superset of an valid shape, then ignore it.
4. Otherwise, add it to the list of "(restricted) minimal invalid" shapes, and see that all of its proper supersets get the flag from (1) set to true.
   (Likely, some will already be flagged).

The main problem with doing all of that, is that as Serg said, the number of ED shapes, is huge ... on the order of 400,000,000,000.
If you discard the shapes with 8 clues in one of {r7,r8,r9,c7.c8,c9} it's still over 37,000,000,000.

For Serg: what I did to get started, was generate the ~37e+9 shapes, and filter out cases that were proper subsets of shapes that we had previously verified as being invalid, and filter out shapes that were proper supersets of ~2000 "seed puzzle" shapes that I generated. That brought the count down to around ~47 million. At that level, an 8-byte "shape tag" and a "flags" byte, could fit in RAM.

After a lot of work, I had results summarized like this:

Code: Select all

  Sz |    Total | HasPuzzles | NoPuzzles | Questionable |
-----+----------+------------+-----------+--------------+
   5 |       32 |          0 |        32 |            0 |
   6 |      831 |        322 |       509 |            0 |
   7 |     5084 |       3758 |      1326 |            0 |
   8 |    28349 |      26564 |      1785 |            0 |
   9 |   107902 |     105896 |      2006 |            0 |
  10 |   328498 |     326827 |      1671 |            0 |
  11 |   809307 |     808115 |      1192 |            0 |
  12 |  1650518 |    1649826 |       692 |            0 |
  13 |  2831846 |    2831460 |       386 |            0 |
  14 |  4151321 |    4151103 |       218 |            0 |
  15 |  5281938 |    5281791 |       147 |            0 |
  16 |  5925743 |    5925631 |       112 |            0 |
  17 |  5953330 |    5953265 |        65 |            0 |
  18 |  5431674 |    5431645 |        29 |            0 |
  19 |  4554218 |    4554202 |        16 |            0 |
  20 |  3540766 |    3540757 |         9 |            0 |
  21 |  2568250 |    2568244 |         6 |            0 |
  22 |  1744090 |    1744079 |        11 |            0 |
  23 |  1110320 |    1110311 |         9 |            0 |
  24 |   662319 |     662311 |         8 |            0 |
  25 |   368913 |     368910 |         3 |            0 |
  26 |   190695 |     190673 |        22 |            0 |
  27 |    90302 |      90287 |        15 |            0 |
  28 |    38369 |      38369 |         0 |            0 |
  29 |    14056 |      14056 |         0 |            0 |
  30 |     4139 |       4133 |         6 |            0 |
  31 |      839 |        839 |         0 |            0 |
  32 |       81 |         78 |         3 |            0 |
  36 |        1 |          0 |         1 |            0 |
-----+----------+------------+-----------+--------------+
     | 47393731 |   47383452 |     10279 |            0 |

For an arbitrary anti-corner shape, I can do this now, to check whether it has puzzles:

1. Expand 8-clue r7,r8,r9,c7,c8,c9's to 9 clues.
2. Look for the shape in the list.
3. If it's there, check the flags for whether it has or doesn't have puzzles.
4. If it isn't there, then check it for being proper subset of one of the original "known to be invalid" shapes.
   If that's the case, then and it doesn't have puzzles ... otherwise it's a proper superset of one of the initial puzzle shapes, and it has puzzles.

For what it's worth, right now, I'm doing something similar to what I did to get started: generate the ~400e+9 ED shapes, and filtering out cases that are known to be valid or invalid ... using my lists of 1428 maximal invalids, and 10090 "no-8-clue-r/c" valids. In ~another (8 cores @) 8 hours, I'll have a list of ~3,000,000 shapes (I think) to work with. After flagging the ones that are known (or at least "believed") to be invalid, the rest should have puzzles. I'll run through my list of 10090 puzzles and the 11706 reductions with 8-clue rows/cols, and get thier shapes and thier supersets flagged. At that point, and I'll set my "puzzle finder" code onto anything that still isn't flagged. When the dust clears, I should be able to produce a proper "minimal valid" list, using the method that I outlined for Colin.

[Serg]

Hi!
I'll try another idea to get full anticorner maximal/minimal inalid/valid patterns lists.

Let's consider "birth" procedure, when 2 known (restricted) minimal valid anticorner patterns give birth to a maximal invalid anticorner pattern.
1. Merge 2 minimal patterns clue sets to get starting pattern.
2. Intersect the same 2 minimal patterns clue sets to get "removal" clue set.
3. For all clues in "removal" clue set remove in turn 1 next clue from starting pattern to get candidate pattern. Typically candidate pattern will be valid, but sometimes it will be invalid (or will have unknown status).

There exists equivalent procedure of giving birth to a (restricted) valid anticorner pattern by 2 maximal invalid anticorner patterns.

I belive (but without proof yet) that any maximal invalid anticorner pattern must be produced by some pair (pairs) of (restricted) minimal valid patterns. So, having some list of known (restricted) minimal valid patterns we shall be able to produce some maximal invalid anticorner patterns and vice versa. If birth procedures produce known invalid/valid patterns only, I belive invalid/valid pattern lists are full.

Serg

[blue]

I finished the job I outlined abouve.
For the (restricted) minimal valid patterns distribution (by B123457 clue count), I get:

Code: Select all

  6 |   322
  7 |  3767
  8 |  4851
  9 |  2211
 10 |  1149
 11 |   360
 12 |   133
----+------
all | 12793

The 12-clue shapes match Serg's list, exactly.

[coloin]

very impressive work
to check your AC-plus-7 clue valid puzzles... here are a few Ive just made.... they are not common puzzle patterns !!

Code: Select all

..............8.....6..1.........6752...6.9383.....241...584123...197456.4.236789##      ##   .................X.....X..XXXX......XXX.X....XXX.X..X.XXX...XXXXXX...XXXXXXX..XXX
..............2.....6..3.........964.2...45385.....271...498123...271456..4356789##      ##   .................X.....X..XXXX......XXX.X....XXXX....XXXX...XXXXXX...XXXXXX..XXXX
..............6.....3..5.........835.9....6716...1.294...649123...187456..4352789##      ##   .................X.....X..XXXX......XXX.X....XXXX...X.XXX...XXXXXX...XXXXXX..XXXX
..............6.....3..5........4835.1....2949.....671...649123...187456..4352789##      ##   .................X.....X..XXXX.....XXXX.X....XXXX.....XXX...XXXXXX...XXXXXX..XXXX
..............6.....3..5.......1.835.1....2949.....671...649123...187456..4352789##      ##   .................X.....X..XXXX....X.XXX.X....XXXX.....XXX...XXXXXX...XXXXXX..XXXX
..............9.....2..1.....8...947.9.4..6353.....218...678123...392456...154789##      ##   .................X.....X..XXXX...XXXXXX...XXXXXX...XXXXXX..X...XXX.X....XXXX...X.
..............2.....8..9.....5.4.398.3....2747.....615...784123...193456...256789##      ##   .................X.....X..XXXX...XXXXXX...XXXXXX...XXXXXX..X.X.XXX.X....XXXX.....
.....9........4.....1.........7..123......456.3....789...9786158..3259749..641238##      ##   ........X........X.....X...XXX......XXX....X.XXX.X....XXX...XXXXXXX..XXXXXXX..XXX
.....3........7.....8............6959.....8477...5.312...976123...281456.2.435789##      ##   ........X........X.....X...XXX......XXX.X....XXX.X..X.XXX...XXXXXX...XXXXXXX..XXX
.....4........7.....6............931.4...98758.....642...945123...178456..1632789##      ##   ........X........X.....X...XXX......XXX.X....XXXX....XXXX...XXXXXX...XXXXXX..XXXX
.....4........7.....6............931.4..9.8758.....642...945123...178456..1632789##      ##   ........X........X.....X...XXX......XXX.X....XXXX...X.XXX...XXXXXX...XXXXXX..XXXX
.....5........8.....9........6...937.8...32157.....648...864123...397456...512789##      ##   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X...XXX.X....XXXX....X
.....3........9.....8........7.2.618.6....3424.....975...754123...398456...216789##      ##   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X.X.XXX.X....XXXX.....
.....5.......1......9.......7...3541.8....2971.....368...874123...932456...651789##      ##   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X...XXXXX.....
.....5.......1......9.......7.2..541.8....3971.....268...874123...932456...651789##      ##   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X.X..XXXX.....

If it is productive i can post the plus 8 puzzles ....

[coloin]

Here are some ? rare valid plus 8s .... [ unfortunately they do include the above patterns plus 1 clue] ... so not many new then ...

Hidden Text: Show

Code: Select all

..............7.....8..3......65.123......456......789..1362948.4.8156376..794512      #   .................X.....X..XXXX......XXX......XXX...XX.XXX..XXXXXXX.X.XXXXXXX..XXX
..............4.....5..9.........123......456..1.52789...437695.7.9852144..621378      #   .................X.....X..XXXX......XXX......XXX..X.XXXXX...XXXXXX.X.XXXXXXX..XXX
..............5.....9..7.........123......456..613.789...564237.3.7819655..329841      #   .................X.....X..XXXX......XXX......XXX..XXX.XXX...XXXXXX.X.XXXXXXX..XXX
..............8.....4..6.........123......456.5.21.789...3796153..1528941..864237      #   .................X.....X..XXXX......XXX......XXX.X.XX.XXX...XXXXXXX..XXXXXXX..XXX
..............5.....6..7.........123.....8456...2..789..7432698.4.8765122..159347      #   .................X.....X..XXXX......XXX.....XXXX....X.XXX..XXXXXXX.X.XXXXXXX..XXX
..............5.....2..8........9123......456..3.4.789...793245.5.8619379..524861      #   .................X.....X..XXXX......XXX.....XXXX..X.X.XXX...XXXXXX.X.XXXXXXX..XXX
..............9.....2..6.......4.123......456...3..789..4261875.8.5379411..984362      #   .................X.....X..XXXX......XXX....X.XXX...X..XXX..XXXXXXX.X.XXXXXXX..XXX
..............8.....9..4.........123...2..456..6..1789...987235.2.5438618..126974      #   .................X.....X..XXXX......XXX....X.XXX..X..XXXX...XXXXXX.X.XXXXXXX..XXX
..............2.....8..9......4..123......456..51..789...945618.1.6832474..271395      #   .................X.....X..XXXX......XXX....X.XXX..X.X.XXX...XXXXXX.X.XXXXXXX..XXX
..............1.....9..6......8..123......456..4.3.789...148275.8.5936141..762938      #   .................X.....X..XXXX......XXX....X.XXX..XX..XXX...XXXXXX.X.XXXXXXX..XXX
..............4.....1..7.........123....9.456.2...5789...9386159..5728345..641972      #   .................X.....X..XXXX......XXX....X.XXX.X...XXXX...XXXXXXX..XXXXXXX..XXX
..............9.....1..5.........123...8..456.4..2.789...7462187..5823948..913567      #   .................X.....X..XXXX......XXX....X.XXX.X.X..XXX...XXXXXXX..XXXXXXX..XXX
..............5.....9..1.........123...3.7456..6...789...249835.8.7569415..813672      #   .................X.....X..XXXX......XXX....XXXXX..X...XXX...XXXXXX.X.XXXXXXX..XXX
..............5.....3..9.........123...12.456..6...789...754218.7.2986342..631597      #   .................X.....X..XXXX......XXX...XX.XXX..X...XXX...XXXXXX.X.XXXXXXX..XXX
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..............6.....2..8.....845.672.6....9157.....348...675123...981456...324789      #   .................X.....X..XXXX...XXXXXX...XXXXXX...XXXXXX..XXX.XXX.X....XXXX.....
...........7...........5..4......798......312.2..89456...3941676..5728434..618925      #   .................X..X..X......XXX......XXX....XXXXX.X.XXXXXX...XXXXXXX..XXXXXXX..
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...........6...........9..8......123.....2456.1..4.789...8215677..6948328..357914      #   .................X..X..X......XXX.....XXXX....X.XXX.X.XXXXXX...XXXXXXX..XXXXXXX..
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...........8...........6..4......3176..3..8427....2965...895123...237456.5.614789      #   .................X..X..X......XXX.....XXXX.X..X.XXX.X.XXXXXX...XXXXXX...XXXXXXX..
...........8...........5..6...1..798......231.3.7..465...5781245..3416894..692573      #   .................X..X..X......XXX....X.XXX....X.XXX.X.XXXXXX...XXXXXXX..XXXXXXX..
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...........3...........1..5....482975.....6487.....531...984123...723456.2.615789      #   .................X..X..X......XXX.X....XXX.X..XXXXX...XXXXXX...XXXXXX...XXXXXXX..
...........5...........2..4...78.6129.....5372.....948...596123...178456.6.324789      #   .................X..X..X......XXX.X....XXX.X.XX.XXX...XXXXXX...XXXXXX...XXXXXXX..
...........1...........3..8.....49353....58129.....647...479123...128456.4.536789      #   .................X..X..X......XXX.X...XXXX.....XXXX.X.XXXXXX...XXXXXX...XXXXXXX..
...........2...........6..7...9..123.....8456.4....789...5372187..2849658..169374      #   .................X..X..X......XXX.X...XXXX....X.XXX...XXXXXX...XXXXXXX..XXXXXXX..
...........7...........5..4.....23718..1..2454.....968...679123...823456.6.514789      #   .................X..X..X......XXX.X...XXXX....X.XXX.X.XXXXXX...XXXXXX...XXXXXXX..
...........5...........3..7....4.2989.....6757....6341...458123...279456.4.361789      #   .................X..X..X......XXX.X...XXXX.X..X.XXX...XXXXXX...XXXXXX...XXXXXXX..
...........5...........2..7...7..123...3..456.4....789...8375617..1253941..496872      #   .................X..X..X......XXX.X..X.XXX....X.XXX...XXXXXX...XXXXXXX..XXXXXXX..
...........9...........5..8...9..3748.....9626..7..815...479123...831456.4.526789      #   .................X..X..X......XXX.X..X.XXX....X.XXX.X.XXXXXX...XXXXXX...XXXXXXX..
...........6...........3..4....6.123...2..456.1....789...7293153..6189477..354862      #   .................X..X..X......XXX.X..X.XXX...X..XXX...XXXXXX...XXXXXXX..XXXXXXX..
...........5...........3..7....4.2989.....6757..5..341...458123...279456.4.361789      #   .................X..X..X......XXX.X..X.XXX...X..XXX.X.XXXXXX...XXXXXX...XXXXXXX..
.....7........1.....3.........65.123......456......789..6539278.8.1746357..286914      #   ........X........X.....X...XXX......XXX......XXX...XX.XXX..XXXXXXX.X.XXXXXXX..XXX
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.....5........1.....4............123....8.456...6..789..8473612.1.2593783..168594      #   ........X........X.....X...XXX......XXX....X.XXX...X..XXX..XXXXXXX.X.XXXXXXX..XXX
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.....3........4.....8............123...7..456..25..789...148275.1.3798644..625391      #   ........X........X.....X...XXX......XXX....X.XXX..X.X.XXX...XXXXXX.X.XXXXXXX..XXX
.....5........2.....8.........9..123......456..3.6.789...621574.5.7392682..458931      #   ........X........X.....X...XXX......XXX....X.XXX..XX..XXX...XXXXXX.X.XXXXXXX..XXX
.....3........9.....6.........4..123......456.2...5789...5348727..6913453..287961      #   ........X........X.....X...XXX......XXX....X.XXX.X...XXXX...XXXXXXX..XXXXXXX..XXX
.....9........4.....1.........7..123......456.3.4..789...9786158..3259749..641238      #   ........X........X.....X...XXX......XXX....X.XXX.X..X.XXX...XXXXXXX..XXXXXXX..XXX
.....8........6.....1..........7.123......456.4.2..789...5293188..6149759..837264      #   ........X........X.....X...XXX......XXX....X.XXX.X.X..XXX...XXXXXXX..XXXXXXX..XXX
.....5........3.....4............123....98456..1...789...746935.5.3812677..529841      #   ........X........X.....X...XXX......XXX....XXXXX..X...XXX...XXXXXX.X.XXXXXXX..XXX
.....3........9.....6.........4.6123......456.2....789...5348727..6913453..287961      #   ........X........X.....X...XXX......XXX....XXXXX.X....XXX...XXXXXXX..XXXXXXX..XXX
.....5........2.....8.........87.123......456..4...789...591632.2.7489155..236874      #   ........X........X.....X...XXX......XXX...XX.XXX..X...XXX...XXXXXX.X.XXXXXXX..XXX
.....2........9.....7............123...37.456.5....789...9418671..5863929..237514      #   ........X........X.....X...XXX......XXX...XX.XXX.X....XXX...XXXXXXX..XXXXXXX..XXX
.....8........9.....3............2419.....6757...52398...684123...397456.4.125789      #   ........X........X.....X...XXX......XXX.X....XXX.X..XXXXX...XXXXXX...XXXXXXX..XXX
.....3........9.....6............8727.....3453..28.961...476123...928456.2.315789      #   ........X........X.....X...XXX......XXX.X....XXX.X.XX.XXX...XXXXXX...XXXXXXX..XXX
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.....8........3.....9............971.3....5646..79.238...547123...389456..4621789      #   ........X........X.....X...XXX......XXX.X....XXXX..XX.XXX...XXXXXX...XXXXXX..XXXX
.....2........7.....3............9687....52344....9571...698123...173456.1.254789      #   ........X........X.....X...XXX......XXX.X...XXXX.X...XXXX...XXXXXX...XXXXXXX..XXX
.....8........9.....3............2419....36757..4..398...684123...397456.4.125789      #   ........X........X.....X...XXX......XXX.X...XXXX.X..X.XXX...XXXXXX...XXXXXXX..XXX
.....4........7.....6............931.4...98758....3642...945123...178456..1632789      #   ........X........X.....X...XXX......XXX.X...XXXXX....XXXX...XXXXXX...XXXXXX..XXXX
.....6........2.....9............968.2.8..3746....7512...645123...798456..4123789      #   ........X........X.....X...XXX......XXX.X...XXXXX...X.XXX...XXXXXX...XXXXXX..XXXX
.....3........9.....6............8727..6..3453..2..961...476123...928456.2.315789      #   ........X........X.....X...XXX......XXX.X..X.XXX.X..X.XXX...XXXXXX...XXXXXXX..XXX
.....3........9.....2............5173..1..2987...8.634...678123...291456.6.534789      #   ........X........X.....X...XXX......XXX.X..X.XXX.X.X..XXX...XXXXXX...XXXXXXX..XXX
.....8........3.....9............971.3.8..5646..7..238...547123...389456..4621789      #   ........X........X.....X...XXX......XXX.X..X.XXXX...X.XXX...XXXXXX...XXXXXX..XXXX
.....7........1.....3............864.7..4.2311..6..597...964123...178456..4325789      #   ........X........X.....X...XXX......XXX.X..X.XXXX..X..XXX...XXXXXX...XXXXXX..XXXX
.....1........6.....3..........4.123.....8456..2...789...624871.8.1735921..589634      #   ........X........X.....X...XXX.....XXXX....X.XXX..X...XXX...XXXXXX.X.XXXXXXX..XXX
.....4........7.....5...........5123...2..456.6....789...3268977..4582313..971564      #   ........X........X.....X...XXX.....XXXX....X.XXX.X....XXX...XXXXXXX..XXXXXXX..XXX
.....4........7.....5...........68977.....2313....1564...765123...289456.6.143789      #   ........X........X.....X...XXX.....XXXX.X....XXX.X...XXXX...XXXXXX...XXXXXXX..XXX
.....8........9.....3...........62419.....6757..4..398...684123...397456.4.125789      #   ........X........X.....X...XXX.....XXXX.X....XXX.X..X.XXX...XXXXXX...XXXXXXX..XXX
.....4........7.....6...........6931.4...98758.....642...945123...178456..1632789      #   ........X........X.....X...XXX.....XXXX.X....XXXX....XXXX...XXXXXX...XXXXXX..XXXX
.....7........1.....3...........2864.7..4.2311.....597...964123...178456..4325789      #   ........X........X.....X...XXX.....XXXX.X....XXXX...X.XXX...XXXXXX...XXXXXX..XXXX
.....3........4.....8.........4..123...7..456..2...789...148275.1.3798644..625391      #   ........X........X.....X...XXX....X.XXX....X.XXX..X...XXX...XXXXXX.X.XXXXXXX..XXX
.....9........4.....1.........7..123...8..456.3....789...9786158..3259749..641238      #   ........X........X.....X...XXX....X.XXX....X.XXX.X....XXX...XXXXXXX..XXXXXXX..XXX
.....2........3.....9..........6.123...2..456..4...789...536812.3.7219452..498637      #   ........X........X.....X...XXX....X.XXX...X..XXX..X...XXX...XXXXXX.X.XXXXXXX..XXX
.....9........4.....1.........7..123....9.456.3....789...9786158..3259749..641238      #   ........X........X.....X...XXX....X.XXX...X..XXX.X....XXX...XXXXXXX..XXXXXXX..XXX
.....4........7.....5..........2.8977.....2313....1564...765123...289456.6.143789      #   ........X........X.....X...XXX....X.XXX.X....XXX.X...XXXX...XXXXXX...XXXXXXX..XXX
.....3........9.....6.........5..8727.....3453..2..961...476123...928456.2.315789      #   ........X........X.....X...XXX....X.XXX.X....XXX.X..X.XXX...XXXXXX...XXXXXXX..XXX
.....6........4.....7..........3.6789.....3146..8..295...758123...293456.5.461789      #   ........X........X.....X...XXX....X.XXX.X....XXX.X.X..XXX...XXXXXX...XXXXXXX..XXX
.....2........7.....1..........4.265.2...68348.....971...768123...293456..6514789      #   ........X........X.....X...XXX....X.XXX.X....XXXX....XXXX...XXXXXX...XXXXXX..XXXX
.....8........3.....9.........4..971.3....5646..7..238...547123...389456..4621789      #   ........X........X.....X...XXX....X.XXX.X....XXXX...X.XXX...XXXXXX...XXXXXX..XXXX
.....2........7.....1..........4.265.2.9..8348.....971...768123...293456..6514789      #   ........X........X.....X...XXX....X.XXX.X....XXXX..X..XXX...XXXXXX...XXXXXX..XXXX
.....4........7.....5..........268977.....2313.....564...765123...289456.6.143789      #   ........X........X.....X...XXX....XXXXX.X....XXX.X....XXX...XXXXXX...XXXXXXX..XXX
.....3........1.....7..........24691.1....3483.....572...549123...178456..5632789      #   ........X........X.....X...XXX....XXXXX.X....XXXX.....XXX...XXXXXX...XXXXXX..XXXX
.....6........4.....7.........13.6789.....3146.....295...758123...293456.5.461789      #   ........X........X.....X...XXX...XX.XXX.X....XXX.X....XXX...XXXXXX...XXXXXXX..XXX
.....1........6.....5.........95.831.4....6751.....294...897123...132456..3465789      #   ........X........X.....X...XXX...XX.XXX.X....XXXX.....XXX...XXXXXX...XXXXXX..XXXX
.....7........9.....2........6...842.3....5677...85931...964123...178456...523789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X...XXX.X....XXXX...XX
.....3........4.....5........2...518.3....6728..15.394...976123...218456...345789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X...XXX.X....XXXX..XX.
.....5........8.....9........6...937.8...32157....9648...864123...397456...512789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X...XXX.X...XXXXX....X
.....7........9.....2........6...842.3...25677...8.931...964123...178456...523789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X...XXX.X...XXXXX...X.
.....2........3.....4........7...841.1.9..5373..7..962...849123...217456...356789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X...XXX.X..X.XXXX...X.
.....7........4.....1........9...562.3..7.8146..4..397...849123...713456...652789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X...XXX.X..X.XXXX..X..
.....5........8.....9........6..1937.8...32157.....648...864123...397456...512789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X..XXXX.X....XXXX....X
.....5........2.....8........4..1935.5....6747...6.812...748123...139456...256789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X..XXXX.X....XXXX...X.
.....3........9.....8........7.2.618.6....3424....1975...754123...398456...216789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X.X.XXX.X....XXXX....X
.....5........2.....8........4.7.935.5....6747...6.812...748123...139456...256789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X.X.XXX.X....XXXX...X.
.....5........2.....8........4.7.935.5.9..6747.....812...748123...139456...256789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X.X.XXX.X....XXXX..X..
.....5........2.....8........48.1935.5....6747.....812...748123...139456...256789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..X.XXXXX.X....XXXX.....
.....5........2.....8........487.935.5....6747.....812...748123...139456...256789      #   ........X........X.....X...XXX...XXXXXX...XXXXXX...XXXXXX..XXX.XXX.X....XXXX.....
........2.......4...1.......9...7218.2....3943....1765...123589...456173...789426      #   ........X.......X......X.......X.XXX..X.X.XXX..XX..XXXXXX...XXXXXX...XXXXXX...XXX
........7.......6...5.......8....429.9.6..7857....5613...123978...456231...789546      #   ........X.......X......X.......X.XXX..X.X.XXX.X.X..XXXXXX...XXXXXX...XXXXXX...XXX
........8.......7...2.......6...1834.7...42168.....957...123495...456783...789621      #   ........X.......X......X.......X.XXX..XX..XXX..XX..XXXXXX...XXXXXX...XXXXXX...XXX
........3.......5...2.......6...8297.5..7.3644.....815...123548...456179...789632      #   ........X.......X......X.......X.XXX..XX..XXX.X.X..XXXXXX...XXXXXX...XXXXXX...XXX
.....3.......5......2.......6....548.9....3713...14962...548123...179456...632789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X....XXXX...XX
.....3.......5......2.......6....548.9....3713..8.4962...548123...179456...632789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X....XXXX..X.X
.....5.......1......9.......7...3541.8....2971....7368...874123...932456...651789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X...XXXXX....X
.....9.......5......3.......1....678.2...73455...3.291...795123...182456...346789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X...XXXXX...X.
.....9.......5......3.......1....678.2...73455..6..291...795123...182456...346789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X...XXXXX..X..
.....5.......1......9.......7..83541.8....2971.....368...874123...932456...651789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X..XXXXXX.....
.....5.......1......9.......7.2..541.8....3971....7268...874123...932456...651789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X.X..XXXX....X
.....5.......1......9.......7.2..541.8....3971..5..268...874123...932456...651789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X.X..XXXX..X..
.....9.......5......3.......1....678.2.6.73955.....241...795123...182456...346789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXX.X.X.XXXXX.....
.....5.......1......9.......7...3541.8...62971.....368...874123...932456...651789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXXX....XXXXX....X
.....5.......1......9.......7...3541.8..4.2971.....368...874123...932456...651789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXXX....XXXXX...X.
.....5.......1......9.......7...3541.8.1..2971.....368...874123...932456...651789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXXX....XXXXX..X..
.....5.......1......9.......7.2..541.8.1..3971.....268...874123...932456...651789      #   ........X.......X......X...XXX...XXXXXX...XXXXXX...XXXXXX.X....XXXX..X..XXXX..X..

[Serg]

Hi, Blue!
Very impressive and fast work!
Are you sure your lists of maximal invalid anticorner patterns and restricted minimal valid anticorner patterns are full?

Serg

[blue]

Hi Colin,

2 of the size 7's and 13 of the size 8's were supsersets of the same (valid) size 6.

Code: Select all

.....1.......1......11...........111......11111....111...111111...111111...111111

The remaining 7's (13) were in my list of minimals.
For the remaining 8's: 17 were minimals, and 123 were supersets of minmal 7's.