Chromatic Patterns

Advanced methods and approaches for solving Sudoku puzzles

Re: Chromatic Patterns

Postby 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?
Last edited by denis_berthier on Wed May 04, 2022 9:46 am, edited 1 time in total.
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Re: Chromatic Patterns

Postby 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  .
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Re: Chromatic Patterns

Postby 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.
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Re: Chromatic Patterns

Postby 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.
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Re: Chromatic Patterns

Postby 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.
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Re: Chromatic Patterns

Postby 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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Re: Chromatic Patterns

Postby eleven » Wed May 04, 2022 11:02 am

Ah, it's there and compiles.

Yes, this is a nice pattern.
Code: Select all
 .  .  . |  .  .  . |  .  .  b
 .  .  . |  .  X  X |  .  a  .
 .  .  b |  a  .  . |  .  X  .
------------------------------
 .  . ac |  .  .  . |  .  . ac
 .  X  . |  X  .  . |  X  .  .
 .  X  . |  X  .  . |  X  .  .

ar3c4 must be in r2c8 too, and br3c3 in r1c9.
a in r4c3 or r4c9 lead to bc in r56c49 or r56c24, so no a is left two a's are forced in the other box.
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Re: Chromatic Patterns

Postby denis_berthier » Wed May 04, 2022 1:34 pm

.
Now that things are clearer, I tried more things with #37
Considering it's not provably contradictory in T&E(2) - like the trivalue oddagon pattern - I wondered if it could be harder.
But no; they are at exactly at the same place in the T&E(Wk, 2) sub-hierarchy of T&E(3):
- none of them can be proven contradictory in T&E(W1, 2);
- both of them can be proven contradictory in T&E(W2, 2).
Indeed, whips[1] play NO role in these patterns.
(This is assuming my simplified T&E procedures, where only candidates in the 123-cells are tested for contradictions.)

So, it's interesting to see if one can find puzzles related to it and not in T&E(2).
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Re: Chromatic Patterns

Postby eleven » Thu May 05, 2022 12:01 am

Hi Denis,
i have tried SudoRules now, but cannot find quickly, how to input sukakus (in 729 format) from a file and write the results to a file.
Is it possible and can you give me additional hints for classifying these sukakus (using harder than the default rules), please ?
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Re: Chromatic Patterns

Postby denis_berthier » Thu May 05, 2022 2:48 am

eleven wrote:i have tried SudoRules now, but cannot find quickly, how to input sukakus (in 729 format) from a file and write the results to a file.


There is a function for solving a sukaku in 729-string format, solve-sukaku-string:
Code: Select all
(solve-sukaku-string "..3.5678.1.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.789123. 567891.3...7..12345.7..123....891234.678912.4...8.123..6.891........12345.789123456789 1234567..12345678.123456.8912345678912345678.123.56.89123456..9123456789.23456789...4. 678912.4567891.3.567891.34567891..45.789.234567891..4.678912.456789.23..6.891234.67891 23456789123.567891.3...7.912345.789123.567891234.678912.4..78.123456.891234.6...123456 789123.56..91234567.91234..7..123456.891234.6...12345678.1234567891...5678912.45678912 345678912345678.12.45678..23.567891.3456789123456789123.567891.....7.912.45.789123..6. 891234.678912.4..78..23.567891.3...7.912345.789123.56..91234567.9123456789123456.89123 4.6...12345678.1234567891234567.912345.7..")


There's a much better function, using the much more readable list format: solve-sukaku-list.


By default, all the results (resolution path, solution...) are printed to the standard output (Terminal / Command Window). You can change this by using the CLIPS function "dribble-on":
Code: Select all
(dribble-on "my-file")


I still have to write in the [BUM] many things about functions for sudokus in files; it seems I've been the only user of these functions until now:
- there are many more than the currently documented "solve-n-grids-after-first-p-from-text-file";
- in particular, there's a function "solve-n-grids-after-first-p-from-text-file-excluding" (which allows not to re-try those already solved or proven contradictory);
- there are also more specific functions for writing ratings to a file - but they are not useful when T&E is involved.
However, there's currently no function for dealing with collections of sukakus written in a file (in either format). I could easily add this.(°)

What I have done with your patterns until now is write a special function to read your 54-string format and properly initialise the corresponding sukaku + adaptations to T&E for restricting it to candidates in the cells of the pattern. I can publish all this (as a SudRules example) if you're interested.


I don't know exactly what you want in terms of classification, but two of the main tools for collections of puzzles are global variables:
- ?*solved-list* gives you the list of puzzles that have been solved by the current set of rules (by their number in the list)
- ?*no-sol-list* gives you the list of puzzles that can have no solution (e.g. patterns proven to be contradictory with the curent set of rules/techniques)
In order to get them, just type their name and "return" when SudoRules has finished its computations.
This is all I've used for all my results reported in this thread: I select a set of rules and/or T&E and I check which patterns are proven contradictory (are present in ?*no-sol-list*). For those that do not appear in this list, I launch new calculations with more powerful rules/techniques, using function "solve-n-grids-after-first-p-from-text-file-excluding".

eleven wrote:Is it possible and can you give me additional hints for classifying these sukakus (using harder than the default rules), please ?

The only way to select which rules (or forms of T&E) you want to apply is via the SudoRules configuration file - by adding or deleting leading semi-colons on the relevant lines (see chapter 5 of the [BUM], available in the Docs folder, for all the details). This also allows you to finely control what is printed.

In order to really understand how all this works, you need to carefully read at least chapter 5 (configuration file) and sections 1 to 3 of chapter 6 (SudoRules) of the [BUM].

*[Edit]: I've just added a few functions for this purpose. See http://forum.enjoysudoku.com/csp-rules-sudorules-kakurules-t38200-56.html
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Re: Chromatic Patterns

Postby eleven » Thu May 05, 2022 9:30 am

Thanks Denis, it works fine now for me with reading from and writing to a file.
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Re: Chromatic Patterns

Postby mith » Thu May 05, 2022 4:38 pm

I was able to construct a 9.9 (only depth 2) using the 15-cell pattern without too much effort. Here's a singles-expanded minimal of it:

Code: Select all
..7.9.45..9....6.74.567..89...45.76.7.49.68.5....87.94...8...7.3..7.....27......8  skfr_ER=10.1


The particular form I used is such that it's also one cell away from a trivalue oddagon, but even providing the digit in the guardian cell doesn't collapse the 15-cell pattern. The 15-cell has two guardians (the original 9.9 only has one), but one can be eliminated pretty easily. Making the elimination reduces the puzzle to 8.3.

I may do a bit of iterating on this to see if I can find a depth 3, but probably it would be more fruitful to just search the expanded database for this pattern vs. the 12-cell trivalue oddagon. (I'm not currently generating any puzzles, and the expanded database sits at 375103 puzzles. Still need to find time to get the solution-minlex scripts set up, and I'm letting SE rate the remaining puzzles - about 100k left - in the meantime.)
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Re: Chromatic Patterns

Postby denis_berthier » Fri May 06, 2022 3:10 am

.
Great example, mith: the two known T&E(3) patterns in the same puzzle!
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Re: Chromatic Patterns

Postby denis_berthier » Fri May 06, 2022 8:41 am

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eleven,
I'm curious about CLIPS running on other versions of Unix: in your system, are you able to copy/paste the config file into CLIPS or do you have to batch it?
.
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Re: Chromatic Patterns

Postby eleven » Mon May 09, 2022 10:18 am

I only used the command line version. My notebook does not have enough memory to check harder techniques, so i stopped trying it.
But this one also looks quite hard.
Code: Select all
 .  .  . |  .  .  X |  .  .  X
 .  .  . |  .  X  . |  .  X  .
 .  .  X |  .  .  X |  .  X  .
-------------------------------
 .  .  . |  .  X  . |  X  .  X
 .  .  X |  .  .  . |  .  X  .
 .  X  X |  .  X  . |  .  .  .   
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