The New Sudoku Players' Forum

[ryokousha]

Oh, interesting!

Not to do injustice to marek, he did not claim to have a proof the pattern is TE2 - it was just a suspicion. I myself have to recuse from the discussion due to lack of competence

I do not have working puzzles for the patterns yet. For the first one that should be possible, but I don't know if there's much hope for "sausage roll". I will let you know if there's any progress on that.

[denis_berthier]

.
Just in case you'd want check the T&E-depth necessary to prove that a k-digit pattern is contradictory, CSP-Rules allows to do this very easily. See section 6.24.2 of the Basic User Manual.
(I added this feature when eleven found a big bunch of 3-digit patterns and wanted a quick way to find those in T&E(3).)

[marek stefanik]

The first pattern can be proven contradictory in T&E(3, BRT) but not in T&E(2, BRT).

Interesting, I believed that my proof was in T&E(2, singles).
I must have misunderstood the definition. Can you explain where I go wrong?

Hidden Text: Show

Naked triples at the start are in T&E(2) (for any elimination, any candidate in the first cell leaves a single in the second cell and a contradiction in the third one).
Suppose 1r8c3.

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------------------------------
  .  .  . | .  .  . | .  .  .
  .  .  . | .  .  . | .  .  .
  .  .  X | .  .  X | .  .  X
------------------------------
  .  .  X | .  .  . | X  .  .
  .  .  . | .  .  . | .  X  .
  .  .  . | .  .  . | .  .  X
------------------------------
  .  .  . | X  .  . | .  .  X
  .  .  1 | .  X  . | .  X  .
  .  .  . | .  .  X | X  .  .
------------------------------

A contradiction can be reached in T&E(1):
biv-chain[2]: r3n1{c9 c6} – b8n1{r9c6 r7c4} ==> r7c9≠1
hidden-single-in-a-box ==> r9c7=1
whip[2]: c3n2{r3 r4} – c7n2{r4 .} ==> r3c9≠2
whip[2]: c3n3{r3 r4} – c7n3{r4 .} ==> r3c9≠3
naked-single ==> r3c9=1
biv-chain[8]: r3c6{n2 n3} – r9c6{n3 n2} – r8c5{n2 n3} – r8c8{n3 n2} – r7c9{n2 n3} – r6c9{n3 n2} – r4c7{n2 n3} – r4c3{n3 n2} ==> r3c3≠2
biv-chain[8]: r3c6{n3 n2} – r9c6{n2 n3} – r8c5{n3 n2} – r8c8{n2 n3} – r7c9{n3 n2} – r6c9{n2 n3} – r4c7{n3 n2} – r4c3{n2 n3} ==> r3c3≠3
no digit left in r3c3
Analogical proofs exist for 23r3c8.

AFAIK this is a proof in T&E(T&E(1)), which is how T&E(2) is defined. Where do I go wrong?

To add a new pattern, this one appears in the most recent puzzle in the tridagon thread:

Code: Select all

   +---------+---------+---------+
   | .  .  . | .  .  . | .  .  . |
   | .  .  . | .  .  . | .  .  . |
   | .  .  . | .  .  . | .  .  . |
   +---------+---------+---------+
   | .  X  . | .  X  . | X  .  . |
   | .  .  . | .  .  . | .  .  . |
   | .  .  . | .  .  . | .  .  . |
   +---------+---------+---------+
   | .  .  . | .  X  . | .  .  . |
   | .  X  . | .  X  . | X  .  . |
   | .  X  . | .  .  X | .  .  X |
   +---------+---------+---------+

Each of r4789 must have the same parity (each cell in r8 sees the corresponding cells in the other rows).
For a given parity, there are three possible permutations, therefore at least one must repeat.
That creates a contradiction, as each two rows have at least one pair of corresponding cells linked in a column.
(More traditionally, there is an oddagon on the digit in r8c7.)

Marek

[ryokousha]

.
Just in case you'd want check the T&E-depth necessary to prove that a k-digit pattern is contradictory, CSP-Rules allows to do this very easily. See section 6.24.2 of the Basic User Manual.
(I added this feature when eleven found a big bunch of 3-digit patterns and wanted a quick way to find those in T&E(3).)

I will have a look at CSP-rules!

For the time being, can we also grade conventional impossible puzzles?
For example this

Code: Select all

..4..5.3..1623....5.....2...23.....56.....4.2...12..6...............3.1......4...

is a 21 given "minimal impossible" based on (a morph of) the sausage roll pattern. So it may or may not be hard to prove contradictory. I'm not 100% sure.

(Also I could generate those in the thousands if necessary. But then I'd have to rate them myself, after getting a grasp of CSP-rules)

[denis_berthier]

The first pattern can be proven contradictory in T&E(3, BRT) but not in T&E(2, BRT).

Interesting, I believed that my proof was in T&E(2, singles).
I must have misunderstood the definition. Can you explain where I go wrong?

Ah, sorry; I used function "solve-k-digit-pattern-string" (which basically launches a simplified form of T&E), but I forgot it is only intended as a filter of patterns. Said otherwise, it can prove that a pattern is contradictory in some T&E(n), but it can't conclude anything in the other case.
By applying the full T&E(2) procedure, this pattern is provably contradictory in T&E(2).

About your proof, it is correct. However, I would make it simpler (using shorter chains):

Code: Select all

Resolution state after Triplets:
   +-------------------------------+-------------------------------+-------------------------------+
   ! 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 123       ! 123456789 123456789 123456789 ! 123       456789    456789    !
   ! 123456789 123456789 456789    ! 123456789 123456789 123456789 ! 456789    123       456789    !
   ! 123456789 123456789 456789    ! 123456789 123456789 123456789 ! 456789    456789    123       !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 123456789 123456789 456789    ! 123       456789    456789    ! 456789    456789    123       !
   ! 456789    456789    123       ! 456789    123       456789    ! 456789    123       456789    !
   ! 123456789 123456789 456789    ! 456789    456789    123       ! 123       456789    456789    !
   +-------------------------------+-------------------------------+-------------------------------+

Level 1 of T&E: suppose r8c3=1

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(solve-sukaku-grid
   +-------------------------------+-------------------------------+-------------------------------+
   ! 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 123       ! 123456789 123456789 123456789 ! 123       456789    456789    !
   ! 123456789 123456789 456789    ! 123456789 123456789 123456789 ! 456789    123       456789    !
   ! 123456789 123456789 456789    ! 123456789 123456789 123456789 ! 456789    456789    123       !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 123456789 123456789 456789    ! 123       456789    456789    ! 456789    456789    123       !
   ! 456789    456789    1         ! 456789    123       456789    ! 456789    123       456789    !
   ! 123456789 123456789 456789    ! 456789    456789    123       ! 123       456789    456789    !
   +-------------------------------+-------------------------------+-------------------------------+
)
biv-chain[2]: r3n1{c6 c9} - b9n1{r7c9 r9c7} ==> r9c6≠1
singles ==> r7c4=1, r9c7=1
biv-chain[2]: r3n1{c6 c9} - b6n1{r6c9 r5c8} ==> r5c6≠1
biv-chain[2]: r4c7{n3 n2} - r4c3{n2 n3} ==> r4c4≠3, r4c5≠3, r4c6≠3, r4c1≠3, r4c2≠3
biv-chain[2]: r4c3{n2 n3} - r4c7{n3 n2} ==> r4c1≠2, r4c2≠2, r4c4≠2, r4c5≠2, r4c6≠2
z-chain[2]: c3n2{r3 r4} - c7n2{r4 .} ==> r3c9≠2
biv-chain[2]: r8n2{c5 c8} - c9n2{r7 r6} ==> r6c5≠2
z-chain[2]: c3n3{r3 r4} - c7n3{r4 .} ==> r3c9≠3
singles ==> r3c9=1, r5c8=1
biv-chain[2]: r8n3{c5 c8} - c9n3{r7 r6} ==> r6c5≠3
biv-chain[2]: r3c6{n3 n2} - r9c6{n2 n3} ==> r1c6≠3, r2c6≠3, r5c6≠3, r6c6≠3
biv-chain[2]: r9c6{n2 n3} - r3c6{n3 n2} ==> r5c6≠2, r6c6≠2, r1c6≠2, r2c6≠2
biv-chain[4]: b8n3{r9c6 r8c5} - b9n3{r8c8 r7c9} - b6n3{r6c9 r4c7} - c3n3{r4 r3} ==> r3c6≠3
singles ==> r3c6=2, r3c3=3, r4c3=2, r4c7=3, r6c9=2, r7c9=3, r8c8=2
GRID 0 HAS NO SOLUTION : NO CANDIDATE FOR FOR BN-CELL b8n2


Then, by symmetry, the same is bound to work for hypotheses r8c3=2 and fr8c3=3.

[denis_berthier]

can we also grade conventional impossible puzzles?
For example this

Code: Select all

..4..5.3..1623....5.....2...23.....56.....4.2...12..6...............3.1......4...

By activating either T&E(1) or T&E(2) or ... in the configuration file, standard function solve will either find a solution or prove a contradiction (or conclude nothing).

Example:
1) Choose T&E(2), then type (solve "..4..5.3..1623....5.....2...23.....56.....4.2...12..6...............3.1......4...").
You'll get:GRID 0 HAS NO SOLUTION : NO CANDIDATE FOR RN-CELL r7n8

2) Choose T&E(1), then type (solve "..4..5.3..1623....5.....2...23.....56.....4.2...12..6...............3.1......4...").
You'll get:PUZZLE 0 IS NOT SOLVED. 48 VALUES MISSING

It means this puzzle requires T&E(2) to be proven contradictory.

Needless to say, this broad classification of contradictory puzzles can be refined in exactly the same way as well-formed puzzles.

(Also I could generate those in the thousands if necessary. But then I'd have to rate them myself, after getting a grasp of CSP-rules)

CSP-Rules has functions for dealing with files of puzzles. It can output the list of solved or contradictory puzzles.

[ryokousha]

We just realized the sausage roll pattern on the last page contained a typo (the pair in b7 was one step too far to the right). This is the correct one:

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------------------------------
  .  X  . | X  .  . | X  .  .
  X  .  . | .  X  . | .  X  .
  .  .  . | .  .  . | .  .  .
------------------------------
  X  .  . | .  .  . | X  .  .
  .  X  . | .  .  . | .  X  .
  .  .  . | .  .  . | .  .  .
------------------------------
  X  .  . | X  .  . | .  X  .
  .  X  . | .  X  . | X  .  .
  .  .  . | .  .  . | .  .  .
------------------------------

Denis, you probably corrected for that typo before checking?

[denis_berthier]

We just realized the sausage roll pattern on the last page contained a typo (the pair in b7 was one step too far to the right). This is the correct one:

Code: Select all

------------------------------
  .  X  . | X  .  . | X  .  .
  X  .  . | .  X  . | .  X  .
  .  .  . | .  .  . | .  .  .
------------------------------
  X  .  . | .  .  . | X  .  .
  .  X  . | .  .  . | .  X  .
  .  .  . | .  .  . | .  .  .
------------------------------
  X  .  . | X  .  . | .  X  .
  .  X  . | .  X  . | X  .  .
  .  .  . | .  .  . | .  .  .
------------------------------

Denis, you probably corrected for that typo before checking?

No, I hadn't corrected. This one is provably contradictory in T&E(2).

[marek stefanik]

About your proof, it is correct. However, I would make it simpler (using shorter chains):

Thank you for having a look at it. I knew that the pairs would allow for shorter chains, but decided for an option that required much less typing (as I wasn't trying to prove that the pattern was in B4B, just that it was in T&E(2)).

Marek

[eleven]

To add a new pattern ...

It's nr 5 in my list of 10 cell patterns here.

Code: Select all

 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  # |  .  .  # |  .  .  o
-------------------------------
 .  .  . |  .  .  . |  .  .  X
 .  .  o |  .  .  # |  .  .  X
 .  .  # |  .  #  . |  .  o  .


The digit in r6c8 must be in r3c9 and r5c3 too, leaving an oddagon for the other 2 digits in the #-ed cells.

[Added:] The pattern above is possible, isn't it ?

Code: Select all

------------------------------
  .  1  . | 2  .  . | 3  .  .
  2  .  . | .  3  . | .  1  .
  .  .  . | .  .  . | .  .  .
------------------------------
  3  .  . | .  .  . | 2  .  .
  .  2  . | .  .  . | .  3  .
  .  .  . | .  .  . | .  .  .
------------------------------
  1  .  . | 3  .  . | .  2  .
  .  3  . | .  2  . | 1  .  .
  .  .  . | .  .  . | .  .  .
------------------------------

[marek stefanik]

To add a new pattern ...

It's nr 5 in my list of 10 cell patterns here.

You're right, I should have checked those.

The pattern above is possible, isn't it ?

Technically it is, but you'll always force two digits in b5 into r6c6.

Marek

[eleven]

The pattern above is possible, isn't it ?

Technically it is, but you'll always force two digits in b5 into r6c6.

Ah, got it, it would be clearer, if r6c6 was added to the pattern.

[ryokousha]

Here are some new 5-chromatic patterns. The process to arrive at these is somewhat involved, I may describe it another time.
They have 4 cells in each house and are obviously not minimal:

Code: Select all

..1..1.11..1.11..111.1..1....1..111..1.11.1..11..1...1.1..111..1..1...111.11...1.
..1..1.11..1.11..111.1..1....1.1.11..1.11.1..11...1..1.1..111..1..1...111.11...1.
..1..1.11..1.11..111.1..1....1.1.1.1.1.11.1..11...1.1..1..111..1..1...111.11...1.
....11.11.11..1..11.11..1....1.1..11.1..111..11.1..1...1.1...111...111..1.11...1.
....11.11.11..1..11.11..1....1.1..11.1..111..11.1..1....11...111...111..11.1...1.


This is a 20 cell minimal arising from those. We have not yet found any proof that this can't be 4-colored.

Code: Select all

------------------------------
  .  .  . | .  .  . | .  .  .
  .  .  . | .  .  . | .  .  .
  X  X  . | X  .  . | X  .  .
------------------------------
  .  .  . | .  .  . | X  .  .
  .  X  . | X  .  . | X  .  .
  X  X  . | .  X  . | .  .  X
------------------------------
  .  X  . | .  X  X | X  .  .
  X  .  . | X  .  . | .  .  .
  X  .  . | X  .  . | .  .  .
------------------------------

..................11.1..1........1...1.1..1..11..1...1.1..111..1..1.....1..1.....


Edit: A couple more of those minimals:

Code: Select all

....................1..1.11.......11....1...1..11.11.....1...1...1.1..11..1.111..
....................1..1.11.....1......11...1..1..111......1.1...1.1.11...111...1
....................1..1.11.....1.....1..1..1.1..1..11.....1..1..11..11...111..1.
....................1..1.11.....1.....1..1..1.1..1..11..1........111..1.11...1..1
....................1..1.11.....1.....1..1..1.1..1..11..1....1...1....1.11...1..1
....................1..1.11.....1.....111...111...1.1...1...1....1..1..1.1.....11
....................1..1.11.....1..1.....1..1..111..1...1...1....1..1.1..1.....11
....................1..1.11....1...1..11...11..11.11....1.11....1.1...1.11.....11
....................1..1.11....11....1.1...11.11..1..1..1.1..1...1.1.11..1...1..1
.................1..1.11.1......1.....1.11..1..11...11..1.......1..1...111..11...
.................1..1.11.1......1.....1.11..1..11...11..1.......1..11...11..1...1
..............1..1.11.1..1.........1..1..1.11.11..11.......1.11.1.11..1..111..1..
..............1..1.11.1..1...1.......1...1.1111..1..1...1..1....11..1...1...1..11
..............1.11..1.11..1....11.1...11...11.111..1...1.....11.11.1.1..1...111..
..............1.11..111.1.........11.11.....11.1..11....1....1..1...1.1111...11..
...........1..1..1..1.1..11..1.......1..1..1111...1.....1.1....1...11.1.11.....11
...........1..1..1..1.1..11..1....1..1..1..1111..1.1....1.1....1....1..111.1.1...
...........1..1..1.1..1.11............1.11..1.11.1...1.11......1....1.111...11.1.
...........1..1.11..1.11..1.....1..1...1..11...111..1..1..11....11.1....1..1...11
........1........1..1..111......1.1......1.11..111.1....1..1....1.....1.1.1.1...1
........1.......11..1.111.......1.....111.....11.1..1...1......1...11.1.11...1.1.
........1.....1....11.1..1........1...1..11.1.11..1..1..1..1....1.11...111..1..1.
........1.....1..1..1.1.11...1.....1.1....11.11...1.1...1..1.....1.11..111.1.....
........1....11.1...11..1.1..1..1..1..1.1..1.11.1..1....11......1..11..111...1...


[denis_berthier]

This is a 20 cell minimal arising from those. We have not yet found any proof that this can't be 4-colored.

Code: Select all

------------------------------
  .  .  . | .  .  . | .  .  .
  .  .  . | .  .  . | .  .  .
  X  X  . | X  .  . | X  .  .
------------------------------
  .  .  . | .  .  . | X  .  .
  .  X  . | X  .  . | X  .  .
  X  X  . | .  X  . | .  .  X
------------------------------
  .  X  . | .  X  X | X  .  .
  X  .  . | X  .  . | .  .  .
  X  .  . | X  .  . | .  .  .
------------------------------
..................11.1..1........1...1.1..1..11..1...1.1..111..1..1.....1..1.....

This pattern can be proven contradictory in T&E(2), more precisely in T&E(BC2, 1):

Code: Select all

(solve-k-digit-pattern-string 3 "..................11.1..1........1...1.1..1..11..1...1.1..111..1..1.....1..1.....")

Code: Select all

   +-------------------------------+-------------------------------+-------------------------------+
   ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 !
   ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 !
   ! 123       123       123456789 ! 123       123456789 123456789 ! 123       123456789 123456789 !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123       123456789 123456789 !
   ! 123456789 123       123456789 ! 123       123456789 123456789 ! 123       123456789 123456789 !
   ! 123       123       123456789 ! 123456789 123       123456789 ! 123456789 123456789 123       !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 123456789 123       123456789 ! 123456789 123       123       ! 123       123456789 123456789 !
   ! 123       123456789 123456789 ! 123       123456789 123456789 ! 123456789 123456789 123456789 !
   ! 123       123456789 123456789 ! 123       123456789 123456789 ! 123456789 123456789 123456789 !
   +-------------------------------+-------------------------------+-------------------------------+
609 candidates, 8514 csp-links and 8514 links. Density = 4.6%

GENERATING CONTEXT 1 AT DEPTH 1, SON OF CONTEXT 0, FROM HYPOTHESIS n3r9c4. <<< This is level 1 of T&E, in which BC2 is used.
biv-chain[2]: r8c4{n1 n2} - r5c4{n2 n1} ==> r7c4≠1, r3c4≠1, r2c4≠1, r1c4≠1, r6c4≠1, r4c4≠1 (this is also a Naked Pair).
singles ==> r3c4=2, r8c4=1
NO POSSIBLE VALUE for csp-variable 154 IN CONTEXT 1. RETRACTING CANDIDATE n3r9c4 FROM CONTEXT 0.

BACK IN CONTEXT 0 with 0 csp-variables solved and 608 candidates remaining. Only regular whips (in T&E(1)) are required to finish the proof.
whip[3]: r9c4{n1 n2} - r7c5{n2 n3} - r7c6{n3 .} ==> r9c6≠1
whip[3]: r9c4{n1 n2} - r7c5{n2 n3} - r7c6{n3 .} ==> r9c5≠1
whip[3]: r9c4{n1 n2} - r7c5{n2 n3} - r7c6{n3 .} ==> r8c6≠1
whip[3]: r9c4{n1 n2} - r7c5{n2 n3} - r7c6{n3 .} ==> r8c5≠1
whip[3]: r9c4{n1 n2} - r3c4{n2 n3} - r5c4{n3 .} ==> r8c4≠1
z-chain[3]: r8c4{n2 n3} - r5c4{n3 n1} - r9c4{n1 .} ==> r1c4≠2, r7c4≠2, r6c4≠2, r4c4≠2, r3c4≠2, r2c4≠2
biv-chain[3]: r9c4{n2 n1} - r3c4{n1 n3} - r8c4{n3 n2} ==> r5c4≠2, r7c5≠2, r7c6≠2, r8c5≠2, r8c6≠2, r9c5≠2, r9c6≠2
biv-chain[2]: r5c4{n3 n1} - r3c4{n1 n3} ==> r4c4≠3, r6c4≠3, r7c4≠3, r8c4≠3, r1c4≠3, r2c4≠3
singles ==> r8c4=2, r9c4=1, r3c4=3
PUZZLE 0 HAS NO SOLUTION : NO CANDIDATE FOR RC-CELL r5c4

[denis_berthier]

.
I assembled all your patterns in a single file:

Code: Select all

..1..1.11..1.11..111.1..1....1..111..1.11.1..11..1...1.1..111..1..1...111.11...1.
..1..1.11..1.11..111.1..1....1.1.11..1.11.1..11...1..1.1..111..1..1...111.11...1.
..1..1.11..1.11..111.1..1....1.1.1.1.1.11.1..11...1.1..1..111..1..1...111.11...1.
....11.11.11..1..11.11..1....1.1..11.1..111..11.1..1...1.1...111...111..1.11...1.
....11.11.11..1..11.11..1....1.1..11.1..111..11.1..1....11...111...111..11.1...1.
..................11.1..1........1...1.1..1..11..1...1.1..111..1..1.....1..1.....
....................1..1.11.......11....1...1..11.11.....1...1...1.1..11..1.111..
....................1..1.11.....1......11...1..1..111......1.1...1.1.11...111...1
....................1..1.11.....1.....1..1..1.1..1..11.....1..1..11..11...111..1.
....................1..1.11.....1.....1..1..1.1..1..11..1........111..1.11...1..1
....................1..1.11.....1.....1..1..1.1..1..11..1....1...1....1.11...1..1
....................1..1.11.....1.....111...111...1.1...1...1....1..1..1.1.....11
....................1..1.11.....1..1.....1..1..111..1...1...1....1..1.1..1.....11
....................1..1.11....1...1..11...11..11.11....1.11....1.1...1.11.....11
....................1..1.11....11....1.1...11.11..1..1..1.1..1...1.1.11..1...1..1
.................1..1.11.1......1.....1.11..1..11...11..1.......1..1...111..11...
.................1..1.11.1......1.....1.11..1..11...11..1.......1..11...11..1...1
..............1..1.11.1..1.........1..1..1.11.11..11.......1.11.1.11..1..111..1..
..............1..1.11.1..1...1.......1...1.1111..1..1...1..1....11..1...1...1..11
..............1.11..1.11..1....11.1...11...11.111..1...1.....11.11.1.1..1...111..
..............1.11..111.1.........11.11.....11.1..11....1....1..1...1.1111...11..
...........1..1..1..1.1..11..1.......1..1..1111...1.....1.1....1...11.1.11.....11
...........1..1..1..1.1..11..1....1..1..1..1111..1.1....1.1....1....1..111.1.1...
...........1..1..1.1..1.11............1.11..1.11.1...1.11......1....1.111...11.1.
...........1..1.11..1.11..1.....1..1...1..11...111..1..1..11....11.1....1..1...11
........1........1..1..111......1.1......1.11..111.1....1..1....1.....1.1.1.1...1
........1.......11..1.111.......1.....111.....11.1..1...1......1...11.1.11...1.1.
........1.....1....11.1..1........1...1..11.1.11..1..1..1..1....1.11...111..1..1.
........1.....1..1..1.1.11...1.....1.1....11.11...1.1...1..1.....1.11..111.1.....
........1....11.1...11..1.1..1..1..1..1.1..1.11.1..1....11......1..11..111...1...

and applied function (solve-n-grids-after-first-p-from-k-digit-pattern-string-file 3 "ryokousha-5chr.txt" 0 30)

All these patterns are proven contradictory in similar ways, in T&E(BC2) + W3, or in T&E(S2) + W3.