The New Sudoku Players' Forum

by **daj95376** » Sun Dec 23, 2007 10:52 pm

I've learned (and been shown) a few things while searching for new fish -- i.e., ones that don't match ronk's Oct, 24 2007 Exemplars.

1) Many unfinned fish degenerate -- at least the ones I've encountered.
2) Some unfinned fish eliminate all candidate values in a unit. Not good!

[Edit: now I've been shown ...]

3) Degeneration can be far more complex in scope than I care to tackle.

by **ronk** » Mon Dec 24, 2007 12:44 am

daj95376 wrote:I decided to post a few fish that I know/believe don't degenerate once the fin cells are removed.

Based on just a quick scan, it looks like most of your fish patterns are non-sashimi, but here are two exceptions for the jellyfish:

Code: Select all: finned mutant Jellyfish r39c5b6\r6c7b27 +-----------------------------------+ | . . . | * X * | * . . | | . . . | * X * | * . . | | / # / | X / X | X / / | |-----------+-----------+-----------| | . . . | . / . | X / / | | . . . | . / . | X / / | | * * * | * X * | * X X | |-----------+-----------+-----------| | * * * | . / . | * . . | | * ** * | . # . | * . . | | X X X | / / / | X / / | +-----------------------------------+ # sdaj_07_69b ak 4

This degenerates to an (unfinned) mutant swordfish r3c5b6\r6c7b2.

Code: Select all: finned mutant Jellyfish r2c8b58\r67c36 +-----------------------------------+ | . . * | . . * | . / . | | / / X | / / X | / / / | | . . * | . . * | . / . | |-----------+-----------+-----------| | . . * | / / X | . / . | | . . * | / / X | . / . | | * * * | X X * | * X * | |-----------+-----------+-----------| | * * * | X X * | * X * | | . . * | / / X | . / . | | . . ** | # # X | . # . | +-----------------------------------+ # sdaj_12_16c aq 4

This degenerates to an (unfinned) mutant swordfish c8b58\r67c6

by **daj95376** » Mon Dec 24, 2007 5:38 am

Yes ronk, your (Remora) unfinned Swordfish exist within my larger unfinned Jellyfish. Too bad they don't include the critical elimination cells as well.

Code: Select all: unfinned mutant Jellyfish r39c5b6\r6c7b27 +-----------------------------------+ | . . . | * X * | * . . | | . . . | * X * | * . . | | / / / | X / X | X / / | |-----------+-----------+-----------| | . . . | . / . | X / / | | . . . | . / . | X / / | | * * * | * X * | * X X | |-----------+-----------+-----------| | * * * | . / . | * . . | | * * * | . / . | * . . | | X X X | / / / | X / / | +-----------------------------------+ # sdaj_07_69b ak 4, [r8c2]<>X unfinned mutant Swordfish r3c5b6\r6c7b2 +-----------------------------------+ | . . . | * X * | * . . | | . . . | * X * | * . . | | / / / | X / X | X / / | |-----------+-----------+-----------| | . . . | . / . | X / / | | . . . | . / . | X / / | | * * * | * X * | * X X | |-----------+-----------+-----------| | . . . | . / . | * . . | | . . . | . / . | * . . | | . . . | . / . | * . . | +-----------------------------------+

Code: Select all: unfinned mutant Jellyfish r2c8b58\r67c36 +-----------------------------------+ | . . * | . . * | . / . | | / / X | / / X | / / / | | . . * | . . * | . / . | |-----------+-----------+-----------| | . . * | / / X | . / . | | . . * | / / X | . / . | | * * * | X X * | * X * | |-----------+-----------+-----------| | * * * | X X * | * X * | | . . * | / / X | . / . | | . . * | / / X | . / . | +-----------------------------------+ # sdaj_12_16c aq 4, [r9c3]<>X unfinned mutant Swordfish c8b58\r67c6 +-----------------------------------+ | . . . | . . * | . / . | | . . . | . . * | . / . | | . . . | . . * | . / . | |-----------+-----------+-----------| | . . . | / / X | . / . | | . . . | / / X | . / . | | * * * | X X * | * X * | |-----------+-----------+-----------| | * * * | X X * | * X * | | . . . | / / X | . / . | | . . . | / / X | . / . | +-----------------------------------+

by **ronk** » Mon Dec 24, 2007 5:56 am

daj95376 wrote:Yes ronk, your (Remora) unfinned Swordfish exist within my larger unfinned Jellyfish. Too bad they don't include the critical elimination cells as well.

I don't recall "critical elimination cell" being part of the definition for "degenerate" or "sashimi." Where did you see that :?:

The "critical cells" are eliminated indirectly anyway ... via locked candidates (the 1st case) and a hidden single (the 2nd case).

Moreover, we unfin a fish primarily to determine (test) whether it is sashimi. Therefore I don't believe "remora" is a proper term to use during that determination.

by **daj95376** » Mon Dec 24, 2007 7:06 pm

ronk wrote:The "critical cells" are eliminated indirectly anyway ... via locked candidates (the 1st case) and a hidden single (the 2nd case).

Would you please show how you eliminated the original/critical '%' cells.

Code: Select all: after unfinned mutant Swordfish r3c5b6\r6c7b2 eliminations +-----------------------------------+ | . . . | / . / | / . . | | . . . | / . / | / . . | | / / / | . / . | . / / | |-----------+-----------+-----------| | . . . | . / . | . / / | | . . . | . / . | . / / | | / / / | / . / | / . . | |-----------+-----------+-----------| | . . . | . / . | / . . | | . % . | . / . | / . . | | . . . | . / . | / . . | +-----------------------------------+

Code: Select all: after unfinned mutant Swordfish c8b58\r67c6 eliminations +-----------------------------------+ | . . . | . . / | . / . | | . . . | . . / | . / . | | . . . | . . / | . / . | |-----------+-----------+-----------| | . . . | / / . | . / . | | . . . | / / . | . / . | | / / / | . . / | / . / | |-----------+-----------+-----------| | / / / | . . / | / . / | | . . . | / / . | . / . | | . . % | / / . | . / . | +-----------------------------------+

by **ronk** » Mon Dec 24, 2007 8:08 pm

daj95376 wrote:
ronk wrote:The "critical cells" are eliminated indirectly anyway ... via locked candidates (the 1st case) and a hidden single (the 2nd case).

Would you please show how you eliminated the original/critical '%' cells.

Let's go back to your original fish patterns. The first ...

Code: Select all: finned mutant Jellyfish r39c5b6\r6c7b27 +-----------------------------------+ | . . . | * X * | * . . | | . . . | * X * | * . . | | / # / | X / X | X / / | |-----------+-----------+-----------| | . . . | . / . | X / / | | . . . | . / . | X / / | | * * * | * X * | * X X | |-----------+-----------+-----------| | * * * | . / . | * . . | | * ** * | . # . | * . . | | X X X | / / / | X / / | +-----------------------------------+ # sdaj_07_69b ak 4

... degenerates via mutant swordfish r3c5b6\r6c7b2. This swordfish eliminates the candidate in r9c7 leaving the 1-fish r9\b7 for r78c123<>X.

The second ...

Code: Select all: finned mutant Jellyfish r2c8b58\r67c36 +-----------------------------------+ | . . * | . . * | . / . | | / / X | / / X | / / / | | . . * | . . * | . / . | |-----------+-----------+-----------| | . . * | / / X | . / . | | . . * | / / X | . / . | | * * * | X X * | * X * | |-----------+-----------+-----------| | * * * | X X * | * X * | | . . * | / / X | . / . | | . . ** | # # X | . # . | +-----------------------------------+ # sdaj_12_16c aq 4

... degenerates via mutant swordfish c8b58\r67c6. This swordfish eliminates the candidate in r2c6 leaving the hidden single r2c3.

Therefore both your fish are sashimi.

I've examined all four of your Jellyfish and all but two of your Starfish ... and have yet to find a non-sashimi. Unfortunately that means my GFF implementation of issashimi() is woefully inadequate ... at least for "exemplars."

by **daj95376** » Tue Dec 25, 2007 12:16 am

Interesting and Impressive :!:

I didn't checked for degeneration beyond: Hidden Single, Locked Candidate (1), Locked Candidate (2), and basic unfinned X-Wing, Swordfish, and Jellyfish. Indeed, most (new) unfinned fish prove to be degenerate/Sashimi by using just these techniques. At least, that's true for most of the 3,224 fish that I scanned to create my table of 265 HPc14n entries. Now, the 18 remaining fish from that table have fallen.

ronk wrote:Unfortunately that means my GFF implementation of issashimi() is woefully inadequate ... at least for "exemplars."

It's beginning to look like (almost) everything beyond basic fish are degenerate/Sashimi. That implies that it would be more meaningful to only flag fish that don't qualify as degenerate/Sashimi.

by **daj95376** » Tue Dec 25, 2007 7:21 am

[Withdrawn: A bookeeping error was found. Sorry!!!]

by **daj95376** » Tue Dec 25, 2007 8:08 pm

Obvious things that I've learned the hard way about base and cover sectors in unfinned fish.

1) If a base sector doesn't intersect the cover set, then every cell in that sector must be empty. This makes the fish invalid.

2) If a cover sector doesn't intersect the base set, then every cell in that sector must be eliminated. This makes the fish invalid.

3) If every cell in a box belongs to non-intersecting base and cover sectors, then every cell in that box is either empty or eliminated. This makes the fish invalid.

[b2] contains base sectors [c56], cover sector [c4], but [r123b2] are not part of either the base or cover set.

Code: Select all: invalid 5-Fish r6c3567\r578c4b6 +-----------------------------------------------+ | . . / | * / / | / . . | | . . / | * / / | / . . | | . . / | * / / | / . . | |---------------+---------------+---------------| | . . / | * / / | . * * | | * * . | * . . | * * * | | / / / | . / / | / . . | |---------------+---------------+---------------| | * * . | * . . | . * * | | * * . | * . . | . * * | | . . / | * / / | / . . | +-----------------------------------------------+

by **ronk** » Tue Dec 25, 2007 9:32 pm

daj95376 wrote:Obvious things that I've learned the hard way about base and cover sectors in unfinned fish.

1) If a base sector doesn't intersect the cover set, then every cell in that sector must be empty. This makes the fish invalid.
2) If a cover sector doesn't intersect the base set, then every cell in that sector must be eliminated. This makes the fish invalid.
3) If every cell in a box belongs to non-intersecting base and cover sectors, then every cell in that box is either empty or eliminated. This makes the fish invalid.

An unfinned sashimi is not an actual fish, so discovering that some unfinned sashimi are "invalid" is meaningless IMO.

by **ronk** » Wed Dec 26, 2007 12:39 am

ronk wrote:
daj95376 wrote:Yes ronk, your (Remora) unfinned Swordfish exist within my larger unfinned Jellyfish. Too bad they don't include the critical elimination cells as well.

I don't recall "critical elimination cell" being part of the definition for "degenerate" or "sashimi." Where did you see that

daj95376, I now think your "critical elimination cell" requirement might be correct.

It's not a requirement of "degeneration" per se, but the elimination is only true if 1) it's an elimination if the unfinned fish is true, AND 2) it's an elimination if any one fin cell is true.

Is that how you're looking at it :?:

by **daj95376** » Wed Dec 26, 2007 1:33 am

ronk wrote:I now think your "critical elimination cell" requirement might be correct.

It's not a requirement of "degeneration" per se, but the elimination is only true if 1) it's an elimination if the unfinned fish is true, AND 2) it's an elimination if any one fin cell is true.

Is that how you're looking at it?

Basically, yes. However, I feel that degeneration should eliminate the same cells as the finned fish. Otherwise, degeneration of the unfinned fish fails to satisfy condition (1) and is meaningless in my opinion.

As you demonstrated, my unfinned 5-Fish can degenerate through your unfinned 4-Fish and perform the critical eliminations. (Thanks for the enlightenment!)

by **ronk** » Wed Dec 26, 2007 5:47 pm

daj95376 wrote:
Code: Select all
finned mutant Starfish r367c2b3\r1c159b4 +-----------------------------------+ | * X * | * * * | X X * | | * / . | . * . | / / X | | X / / | / X / | / / # | |-----------+-----------+-----------| | * X * | . * . | . . ** | | * X * | . * . | . . * | | * / X | / X / | / / X | |-----------+-----------+-----------| | X / / | / X / | / / X | | * / . | . * . | . . * | | * / . | . * . | . . * | +-----------------------------------+

I assume you're not illustrating r1589<>X because your single-digit PM doesn't have candidates there but, for the general case, wouldn't the pattern look like the below :?:

Code: Select all: finned mutant Starfish r367c2b3\r1c159b4 +-----------------------------------+ | * X * | * * * | X X ** | | * / . | . * . | / / X | | X / / | / X / | / / @ | |-----------+-----------+-----------| | * X * | . * . | . . ** | | * X * | . * . | . . ** | | * / X | / X / | / / X | |-----------+-----------+-----------| | X / / | / X / | / / X | | * / . | . * . | . . ** | | * / . | . * . | . . ** | +-----------------------------------+

My specific reason for the question is to see if you agree that double-covered candidate r1c9 -- before counting the fin sector -- is a valid elimination.

by **daj95376** » Wed Dec 26, 2007 7:13 pm

ronk wrote:I assume you're not illustrating r1589<>X because your single-digit PM doesn't have candidates there but, for the general case, wouldn't the pattern look like the below?:
Code: Select all
finned mutant Starfish r367c2b3\r1c159b4 +-----------------------------------+ | * X * | * * * | X X ** | | * / . | . * . | / / X | | X / / | / X / | / / @ | |-----------+-----------+-----------| | * X * | . * . | . . ** | | * X * | . * . | . . ** | | * / X | / X / | / / X | |-----------+-----------+-----------| | X / / | / X / | / / X | | * / . | . * . | . . ** | | * / . | . * . | . . ** | +-----------------------------------+

My specific reason for the question is to see if you agree that double-covered candidate r1c9 -- before counting the fin sector -- is a valid elimination.

Yes, my example is from a real candidate grid ... in a real PM ... from a real puzzle. My GFF output is as much diagnostic as general in scope. I wanted to make sure that it was working properly with real data.

Yes, I agree with your general grid representation using my fin cell. That includes [r1c9].

Code: Select all: Obi-Wahn base/cover counts for unfinned fish +-----------------------------------------------+ | 0/2 1/1 0/1 | 0/1 0/2 0/1 | 1/1 1/1 1/2 | | 0/1 1/0 0/0 | 0/0 0/1 0/0 | 1/0 1/0 1/1 | | 1/1 2/0 1/0 | 1/0 1/1 1/0 | 2/0 2/0 2/1 | |---------------+---------------+---------------| | 0/2 1/1 0/1 | 0/0 0/1 0/0 | 0/0 0/0 0/1 | | 0/2 1/1 0/1 | 0/0 0/1 0/0 | 0/0 0/0 0/1 | | 1/2 2/1 1/1 | 1/0 1/1 1/0 | 1/0 1/0 1/1 | |---------------+---------------+---------------| | 1/1 2/0 1/0 | 1/0 1/1 1/0 | 1/0 1/0 1/1 | | 0/1 1/0 0/0 | 0/0 0/1 0/0 | 0/0 0/0 0/1 | | 0/1 1/0 0/0 | 0/0 0/1 0/0 | 0/0 0/0 0/1 | +-----------------------------------------------+

Code: Select all: Obi-Wahn counts converted to standard representation -- except '*' for '*X' +-----------------------------------------------+ | * X * | * * * | X X * | | * / . | . * . | / / X | | X / / | / X / | / / / | |---------------+---------------+---------------| | * X * | . * . | . . * | | * X * | . * . | . . * | | * / X | / X / | / / X | |---------------+---------------+---------------| | X / / | / X / | / / X | | * / . | . * . | . . * | | * / . | . * . | . . * | +-----------------------------------------------+

In retrospect, I should have edited my results and removed the fin cell, just showed the unfinned fish. I'll do that now.

by **daj95376** » Thu Dec 27, 2007 12:26 am

I've been thinking about the implications of smaller unfinned fish in the degeneration of an unfinned fish. Below is an example. There are 22 eliminations directly attributable to the fish. There isn't any sign of a Hidden Single, Locked Candidate (1), or Locked Candidate (2) remaining after the eliminations occur.

Code: Select all: 5-Fish r378c37\r2c14b49 ... <> X [r1c14],[r2c1245689],[r456c124],[r9c1489] 5-Fish r3c37b78\r29c14b4 ... <> X [r1c14],[r2c1245689],[r456c124],[r9c1489] +-----------------------------------+ | * . / | * . . | / . . | | * * . | * * * | . * * | | . / / | . / / | / / / | |-----------+-----------+-----------| | * * . | * . . | / . . | | * * . | * . . | / . . | | * * . | * . . | / . . | |-----------+-----------+-----------| | . / / | . / / | / . . | | . / / | . / / | / . . | | * . / | * . . | . * * | +-----------------------------------+ # sdaj_11_77b ah 5 (unfinned)

However, when I factor in smaller fish eliminations associated with the hidden pattern, then I get 4 additional eliminations. A Hidden Single at [r2c7] and a Locked Candidate (2) at [c3b4] are now obvious.

Code: Select all: 3-Fish r378\c14b9 F ... <> X [r12456c14],[r9c14789] 3-Fish r3b78\r9c14 ... <> X [r12456c14],[r9c14789] 4-Fish r378b6\c1489 F ... <> X [r129c1489],[r456c14] 4-Fish r378c7\c14b39 ... <> X [r129c1489],[r456c14] 4-Fish r3c7b78\r9c14b3 ... <> X [r129c1489],[r456c14] 4-Fish r378c7\r2c14b9 ... <> X [r1456c14],[r2c12345689],[r9c1489] 4-Fish r3c7b78\r29c14 ... <> X [r1456c14],[r2c12345689],[r9c1489] +-----------------------------------+ | * . / | * . . | / * * | | * * * | * * * | . * * | | . / / | . / / | / / / | |-----------+-----------+-----------| | * * . | * . . | / . . | | * * . | * . . | / . . | | * * . | * . . | / . . | |-----------+-----------+-----------| | . / / | . / / | / . . | | . / / | . / / | / . . | | * . / | * . . | * * * | +-----------------------------------+

Bottom Line: I went to an awful lot of effort to duplicate the Template eliminations for the original hidden pattern.

Suddenly, I have this urge to place restrictions on how an unfinned fish is allowed to degenerate! I'm beginning to understand why ronk's latest definition of Sashimi doesn't contain smaller fish like his earlier definition.

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