## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### Re: Exotic patterns a resume

champagne wrote:The reason is quite simple; I put a limit in the number of permutations in the search to speed up the process. The second one exceeded the limit.

Aha, but that's a lot different than a "new pattern" as you stated earlier in ...
champagne wrote:the second and the third are on the list of "something to find" and I did not introduce a new pattern so far

After increasing the number of permutations, it's unclear whether or not your solver now detects a multi-fish in David P Bird's 3rd example too. Does it?
ronk
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### Re: Exotic patterns a resume

ronk wrote:
champagne wrote:the second and the third are on the list of "something to find" and I did not introduce a new pattern so far

After increasing the number of permutations, it's unclear whether or not your solver now detects a multi-fish in David P Bird's 3rd example too. Does it?

i can just repeat what I just wrote

The third one is a pattern I have already seen, not studied by my code limiting the search to rows columns having all the digits of the base;
champagne
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### Re: Exotic patterns a resume

champagne wrote:
ronk wrote:After increasing the number of permutations, it's unclear whether or not your solver now detects a multi-fish in David P Bird's 3rd example too. Does it?
i can just repeat what I just wrote ... The third one is a pattern I have already seen, not studied by my code limiting the search to rows columns having all the digits of the base;

Translation: Does not, because of clue r2c2=5.
ronk
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### Re: Exotic patterns a resume

Phil our eliminations for puzzle 2 are identical and you are using truth sets in the same rows as me.

For puzzle 3 my digit set is (6789) compared with your (1245) The rows I was using are 23457 with columns 2349. This doesn't produce a balance and is out by one. However this produces potential eliminations of (3)r8c8 and (3)r9c7 one of which must be invalid as these cells hold a (36)Naked Pair, so an adjusted balance is found and all the other eliminations can be made.

Your solution is both simpler and more immediately productive than mine, but after the follow-on eliminations we both end up with the same reduced grid with eliminations in 32 cells. I think you could model my roundabout route by adding an extra truth for (3) in box 9 if you wanted.

daj's post caused me to check the alternative digit set he gives for puzzle 2 where exactly the same situation arises with a (47)Naked Pair.

When you look at my logic for puzzle 1, there is a derived truth that one of the cells holding PEs in boxes 4679 must hold a member of the digit set. This could be added in the same way. I know Xsudo was modified to handle derived inferences but I'm not sure of the limitations.

DPB
David P Bird
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### Re: Exotic patterns a resume

David P Bird wrote:When you look at my logic for puzzle 1, there is a derived truth that one of the cells holding PEs in boxes 4679 must hold a member of the digit set. This could be added in the same way. I know Xsudo was modified to handle derived inferences but I'm not sure of the limitations.

DPB

David,

I don't know about an almost multi_fish logic, but the first puzzle has many specificities making it relatively easy to crack progressively using exocet properties.

Digit '8' is quickly kicked out of the base after 2 "abi loop" eliminations
Digit '9' is locked in r8c5 if valid
Digit 2 is locked in r5c46 in row 5 etc...
champagne
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### Re: Exotic patterns a resume

pjb wrote:
Code: Select all
1...5......7.....6.897.......89....3.7.......5...3.4...3.6....8.....21......4..2.
Found Multi-Fish pattern with base set of 1,2,4 and 5
19 Truths = {124R2, 1245R3, 1245R4, 1245R5, 1245R7}
19 Links = {24c1, 12c5, 145c6, 25c7, 145c8,  2n4, 3n9, 4n2, 5n3, 5n4, 5n9, 7n3}
15 Eliminations:  24<>3, 24<>8, 42<>6, 53<>3, 53<>6, 54<>8, 59<>9, 16<>4, 17<>2, 18<>4, 66<>1, 68<>1, 81<>4, 96<>1, 96<>5

Does this also work?

Code: Select all
<1245> C2349\r1689 + r24c2,r57c3,r25c4,r35c9
daj95376
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### Re: Exotic patterns a resume

daj95376 wrote:
Code: Select all
<1245> C2349\r1689 + r24c2,r57c3,r25c4,r35c9

it seems to be 15 Truths against 16 Links
champagne
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### Re: Exotic patterns a resume

daj95376 wrote:
Code: Select all
<1245> C2349\r1689 + r24c2,r57c3,r25c4,r35c9

There's a couple of problems with this notation: 1) r2c2 is a given, and 2) the row cover units are not valid for all digits of the base. Xsudo's notation at least accurate.

Code: Select all
15 Truths = {124C2349 5C349}
15 Links = {1r69 2r16 4r18 5r89 2n4 3n9 4n2 5n349 7n3}
[edit: corrected truths to agree with daj95376; my original edit of Xsudo output was wrong]
Last edited by ronk on Tue Jul 10, 2012 12:10 am, edited 1 time in total.
ronk
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### Re: Exotic patterns a resume

[Withdrawn: I accept ...

Code: Select all
15 Truths = {124C2 1245C349}
15 Links  = {1r69 2r16 4r18 5r89 2n4 3n9 4n2 5n349 7n3}
Last edited by daj95376 on Mon Jul 09, 2012 8:57 pm, edited 2 times in total.
daj95376
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### Re: Exotic patterns a resume

Champagne. thanks for your response giving an alternative approach to puzzle 1. Recently my focus has been on re-formulating my spreadsheet for colouring Shark cell sets, not on JExcocets. I've been using your puzzles to help with this, and have wondered if your solver still couldn't find the multi-fish I've been locating as I had thought it was quite powerful.

Although puzzle 1 can be solved as you say, I never even checked that because it demonstrates a case I've been looking for where an Almost Shark pattern can be used in conjunction with another almost pattern.

DPB
David P Bird
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### Re: Exotic patterns a resume

David P Bird wrote:Champagne. thanks for your response giving an alternative approach to puzzle 1. Recently my focus has been on re-formulating my spreadsheet for colouring Shark cell sets, not on JExcocets. I've been using your puzzles to help with this, and have wondered if your solver still couldn't find the multi-fish I've been locating as I had thought it was quite powerful.

Although puzzle 1 can be solved as you say, I never even checked that because it demonstrates a case I've been looking for where an Almost Shark pattern can be used in conjunction with another almost pattern.

DPB

Hi David,

Coding is an heavy task and I have still on my to do list a lot of key things to do.

Some new ideas can rush on the top of the list, but this is limited to what appears as a break trough in the logic with new solving capabilities.

In that case, the known properties are enough to solve the puzzle, so I just politely follow the new idea, trying to catch the moment when the conditions to change my mind are there

I must confess that I have not yet a clear view of your new concept, but I will see if new solving capabilities appear

champagne
champagne
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### Re: Exotic patterns a resume

daj95376 wrote:[Withdrawn: I accept ...

Code: Select all
15 Truths = {124C2 1245C349}
15 Links  = {1r69 2r16 4r18 5r89 2n4 3n9 4n2 5n349 7n3}

And again, for the same reason as in the row solution, a pattern my solver does not study.
This will likely be the next improvement in my code.

I like that writing showing clearly the column C2 where one digit is missing.
champagne
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### Re: Exotic patterns a resume

I'm still trying to get a handle on Multi-Fish patterns. In champagne's file "03 NN ...", there are a few puzzles that seem to be "template friendly" -- including the first puzzle. So, I tried to manually construct a Multi-Fish pattern for it. Please review/critique!

Code: Select all
1....6.......8.2....97....5.3.9....4..5....9.....2.1....4.....7.9.3...4.8.....6..

# 1582;elev;567;11.30;1.20;1.20;914

+--------------------------------------------------------------------------------+
|  1       24578   2378    |  245     3459    6       |  34789   378     389     |
|  34567   4567    367     |  145     8       13459   |  2       1367    1369    |
|  2346    2468    9       |  7       134     1234    |  348     1368    5       |
|--------------------------+--------------------------+--------------------------|
|  267     3       12678   |  9       1567    1578    |  578     25678   4       |
|  2467    124678  5       |  1468    13467   13478   |  378     9       2368    |
|  9       4678    678     |  4568    2       34578   |  1       35678   368     |
|--------------------------+--------------------------+--------------------------|
|  2356    1256    4       |  12568   1569    12589   |  3589    12358   7       |
|  2567    9       1267    |  3       1567    12578   |  58      4       128     |
|  8       1257    1237    |  1245    14579   124579  |  6       1235    1239    |
+--------------------------------------------------------------------------------+
# 181 eliminations remain

1268 R34578\c56+c16+c15+c67 + r3c28,r4c38,r5c249,r7c248,r8c39

The above was derived using my template analyzer's output ... and manually coloring cells using Simple Sudoku.

Code: Select all
<1268>   accepted = 94 template combinations   -- no   UR test
<1268>   accepted = 63 template combinations   -- with UR test

<1268>   <>1  r2c6,r9c56
<1268>   <>2  r9c6
<1268>   <>6  r2c1
<1268>   <>8  r1c7,r6c6

<1268>   <>3  r37c8,r5c9
<1268>   <>4  r3c2,r5c24
<1268>   <>5  r4c8,r7c248
<1268>   <>7  r4c38,r5c2,r8c3

r3c28,r4c38,r5c249,r7c248,r8c39   locked for candidates <1268>

Hopefully, this puzzle hasn't already been presented elsewhere.

[Edit: corrected typo found by ronk. Thanks!]
Last edited by daj95376 on Sun Jul 15, 2012 4:02 pm, edited 1 time in total.
daj95376
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### Re: Exotic patterns a resume

daj95376 wrote:I'm still trying to get a handle on Multi-Fish patterns. In champagne's file "03 NN ...", there are a few puzzles that seem to be "template friendly" -- including the first puzzle. So, I tried to manually construct a Multi-Fish pattern for it. Please review/critique!

Code: Select all
1....6.......8.2....97....5.3.9....4..5....9.....2.1....4.....7.9.3...4.8.....6..

# 1582;elev;567;11.30;1.20;1.20;914

1268 R34578\c56+c16+c15+c56 + r3c28,r4c38,r5c249,r7c248,r8c39

<1268>   <>1  r2c6,r9c56
<1268>   <>2  r9c6
<1268>   <>6  r2c1
<1268>   <>8  r1c7,r6c6

<1268>   <>3  r37c8,r5c9
<1268>   <>4  r3c2,r5c24
<1268>   <>5  r4c8,r7c248
<1268>   <>7  r4c38,r5c2,r8c3

r3c28,r4c38,r5c249,r7c248,r8c39   locked for candidates <1268>

Your <1268>-starfish checks out in Xsudo, just the one typo (cover 8c56 should be 8c67). As you probably know, applying uniqueness isn't productive for this particular multi-fish.

For the list of covers (links), using both '+' and ',' for separators doesn't make a great deal of sense. How about all commas?

Code: Select all
1268r34578\1c56,2c16,6c15,8c67,r3c28,r4c38,r5c249,r7c248,r8c39
1268c23489\1r29,2r19,6r26,8r16,r3c28,r4c38,r5c249,r7c248,r8c39

3457r1269,9r129\3c89,4c24,5c48,7c38,9c9,r1c57,r2c16,r6c6,r9c56
3457c1567,9c567\3r37,4r35,5r47,7r58,9c7,r1c57,r2c16,r6c6,r9c56

The four multi-fish above are equivalent, i.e., all four produce the same exclusions. Note that the cell covers for the first two are the same. Ditto for the last two.
ronk
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### Re: Exotic patterns a resume

ronk wrote:Your <1268>-starfish checks out in Xsudo, just the one typo (cover 8c56 should be 8c67). As you probably know, applying uniqueness isn't productive for this particular multi-fish.

For the list of covers (links), using both '+' and ',' for separators doesn't make a great deal of sense. How about all commas?

The four multi-fish above are equivalent, i.e., all four produce the same exclusions. Note that the cell covers for the first two are the same. Ditto for the last two.

Thanks for catching the typo. Yes, except for the number of accepted template combinations (ATC), the results from using UR detection is the same as not using UR detection. I now cross-check the UR results with the non-UR results. If the results are equivalent, then I manually merge the common results -- as above.

For readability and compactness, I prefer the mixed format of plus and comma characters that I used.

Hmmm. My analyzer didn't find the <3457> pattern. It may have been blocked by finding the <1268> pattern. Something to check.
daj95376
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