The New Sudoku Players' Forum

by **Mike Barker** » Thu Dec 14, 2006 5:36 am

Ron suggested separating out Kraken Fish from the Ultimate Fish Guide to compartmentalize the topics somewhat. I've collected up most of what already exists here. Future posts on Kraken Fish can be made here and appropriate links to the Guide made.

Here's a contribution to the thread on Kraken fish based mostly on the posts in Ruud's ARC thread and Luke's finned X-wing thread. I figure this can serve as a starting point for discussions of style and content for this thread.

In a fish, defined by the cells of "n" units (rows, columns, and/or boxes) containing a given digit (the fish digit), a candidate is eliminated from a cell (the candidate elimination cell or CEC) when its existance allows only n-1 or fewer fish digit candidates to be placed in the "n" units. In a standard fish the CEC directly sees sufficient cells of the fish to prevent placement. In a Kraken fish the CEC can also prevent placement if it is linked to elements of the fish via its tentacles: stong links, grouped strong links, bivalue cells or other ALS, or any other linking element. A single link or a chain of links may be used. In addition, multiple (one, two, or more) links/chains can be used to link to different elements of the fish. When such links are used it is possible for a candidate which is not the fish digit to be eliminated, in which case it is also possible for the CEC to be part of the fish.

In the following examples the fish is r25c25 with fin r8c2 and "x" is the fish digit. In the first example, a strong link and a "direct link" are used to link the fish to possible CECs, r25c9. In this case, either both members of the covering set, c25, must contain a cell from the fish with the fish digit or the fin and one member of the covering set must. One way to view this elimination is that either the fin contains the digit or it does not. If the fin does then c9c8=x because of the strong link. If the fin does not, then the fish is reduced to a basic fish and r25c9<>x. In either case r25c9<>x. In a more general view of the elimination, any cell which is seen by the fin and all fish elements of one of the covering sets, either directly or indirectly, can not contain the fish digit. In this case r8c2-x-r7c3=x=r7c9-r25c9 and either r2c25-x-r2c9 or r5c25-x-r5c9 and the same eliminations occur.

Code: Select all: . . . | . . . | . . . . X . | . X . | . . * . | . | . | . | . . . ---|---+---|---+------- . | . | . | . | . . . . X . | . X . | . . * . | . | . . . | . . . ---|---+-------+------- . | x================x . # . | . . . | . . . . . . | . . . | . . .

In the next example, a grouped strong link and a bivalue cell link the fish to the CECs, r79c9: r8c2=y=r8c78-y-r79c9 and r5c25-x-r5c9-r79c9. In this example the candidate to be eliminated, "y", is not the fish digit.

Code: Select all: . . . | . . . | . . . . X . | . X . | . . . . | . | . | . | . . . ---|---+---|---+------- . | . | . | . | . . . . X . | . X . | . . xy . | . | . . . | . . . ---|---+-------+------- . | . | . . . | . . * . #y=============y y y . . . | . . . | . . *

In the last example, two bivalue/ALS chains link the fish to the CEC, r5c5: r5c2-x-r68c1-z-r8c5-y-r5c5 and r8c2-x-r9c3-w-r8c1-z-r8c5-y-r5c5. In addition, because the CEC directly replaces a fish element "y" is again eliminated. Note that since each fish-to-CEC link estabilishes an independent truth condition, individual links/chains can overlap without restriction.

Code: Select all: . . . | . . . | . . . . X . | . X . | . . . . | . | . | . | . . . ---|---+---|----+------ . | . | . | . | . . . . X . | . Xy . | . . . xw | . | . . . | . . . ---|---+--------+------ . | . | . . . | . . . zw # . | . yz . | . . . . . wx| . . . | . . .

Kraken fish have been used in the past to solve published puzzles. Myth Jellies used a strong link with a 2 finned Swordfish to perform the elimination in Unsolvable #4. The fins of the fish, r5c7 and r9c4, connect to the CEC, r4c8, directly and via the strong link, r9c4-7-r4c6=7=r7c6-7-r4c8.

Code: Select all: +-----------------+--------------------+------------------+ | 179* 489 5 | 3 89 24 | 6 127* 279* | | 1689 2 3 | 5689 7 569 | 159 4 59 | | 679 49 679 | 569 1 24 | 2579 3 8 | +-----------------+--------------------+------------------+ | 3 5 8 | 4 69 679@ | 279 26-7 1 | | 79* 6 4 | 2 5 1 | 379# 8 379* | | 2 1 79 | 679 3 8 | 579 567 4 | +-----------------+--------------------+------------------+ | 4 3 69 | 156789 2 5679@ | 1578 157 567 | | 568 7 2 | 1568 4 56 | 1358 9 356 | | 569 89 1 | 5679# 689 3 | 4 257* 2567* | +-----------------+--------------------+------------------+

Anne Morelot used a Kraken Fish, a two finned swordfish, to advance #5000 from Ruud's Top 50000. In this case the fins/body of the fish connects to the CEC, r4c9, via an ALS, r4c4-9-r4c35-8-r4c9, and a bivalue, r9c2|r8c7-9-r9c8-8-r4c9.

Code: Select all: +--------------------+-------------------+---------------------+ | 3589 589* 35689 | 2579* 2379 1 | 4 3689 2358 | | 7 589* 34589 | 259* 6 345 | 23589* 1 2358 | | 1 2 34569 | 8 359 345 | 7 369 35 | +--------------------+------------------+--------------------+ | 4 3 589@ | 1569* 59@ 2 | 1568 7-8 1578 | | 6 17 2 | 157 8 357 | 135 4 9 | | 589 17 589 | 4 3579 3567 | 13568 2 1358 | +--------------------+------------------+--------------------+ | 238 68 1 | 267 247 9 | 238 5 23478 | | 2359 4 359 | 257 1 578 | 2389# 3789 6 | | 2589 5689# 7 | 3 245 4568 | 128 #89 1248 | +--------------------+------------------+--------------------+

Here are some additional examples. The first eliminates a cell of the fish:

Code: Select all: 1-link Kraken Column X-Wing (c14) (r5c4|r5c1-6-r5c3-1-, r4c4-6-r4c25689-1-): r145c14=6 => r4c1<>1 +-----------------------+--------------------+----------------------+ | 146* 147 8 | 156* 1367 2 | 345 347 9 | | 149 5 124 | 179 1378 1378 | 2348 6 23478 | | 3 279 26 | 4 6789 589 | 1 278 2578 | +-----------------------+--------------------+----------------------+ | 45689-1* 148& 7 | 2569* 1268& 18& | 23489 12348& 23468& | | 1689# 3 16@ | 12679# 4 178 | 289 5 268 | | 2 1489 1456 | 3 1689 1589 | 7 148 468 | +-----------------------+--------------------+----------------------+ | 458 248 9 | 27 237 6 | 23458 23478 1 | | 148 6 1234 | 127 5 1347 | 2348 9 23478 | | 7 124 12345 | 8 1239 1349 | 6 234 2345 | +-----------------------+--------------------+----------------------+

Code: Select all: 1-link Kraken Row X-Wing: r38/c1b2,fins=r8c34 (r8c4|r3c6|r3c5-3-r12c4-8-, r8c3=8=r8c8-8-): r3c156|r8c134=3 => r2c8<>8 8...2.1.......9....651...2....5....3.3..61....874......1.24.3......169.4......7.. +--------------------+------------------+----------------------+ | 8 479 349 | 36@ 2 3457 | 1 34579 5679 | | 1234 247 1234 | 368@ 3578 9 | 4568 34567-8 5678 | | 349* 6 5 | 1 378* 3478* | 48 2 789 | +--------------------+------------------+----------------------+ | 12469 249 12469 | 5 789 278 | 2468 46789 3 | | 2459 3 249 | 789 6 1 | 2458 45789 5789 | | 2569 8 7 | 4 39 23 | 256 569 1 | +--------------------+------------------+----------------------+ | 79 1 89 | 2 4 578 | 3 568 568 | | 237* 25 238#$ | 37# 1 6 | 9 58$ 4 | | 346 45 3468 | 389 3589 358 | 7 1 2 | +--------------------+------------------+----------------------+ . . . | . . . | . . . . . . | . . . | . * . X . / | . X X | / / / ------+-------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ------+-------+------ . . . | . . . | . . . X / # | # / / | / / / . . . | . . . | . . . 1-link Kraken Column X-Wing: c57/r3b6,fins=r1c7,r6c5 (r45c7|r6c5-4-r6c8|r45c9-5-, r1c7-4-r1c28-5-) => r1c9<>5 ..7..8.....6.2.3...3......9.1..5..6.....1.....7.9....2........4.83..4...26....51. +------------------+---------------------+----------------------+ | 1459 245$ 7 | 1356 39 8 | 246# 245$ 16-5 | | 14589 459 6 | 1457 2 1579 | 3 4578 158 | | 1458 3 128 | 4567 47* 1567 | 24678* 24578 9 | +------------------+---------------------+----------------------+ | 3489 1 289 | 23478 5 237 | 4789* 6 38@ | | 34689 249 289 | 234678 1 2367 | 4789* 345789 358@ | | 34568 7 58 | 9 48# 36 | 1 348@ 2 | +------------------+---------------------+----------------------+ | 7 59 159 | 125 368 125 | 68 38 4 | | 15 8 3 | 15 67 4 | 29 29 67 | | 2 6 4 | 378 3789 379 | 5 1 378 | +------------------+---------------------+----------------------+ . . . | . / . | # . * . . . | . / . | / . . . . . | . X . | X . . ------+-------+------ . . . | . / . | X . . . . . | . / . | X . . . . . | . # . | . . . ------+-------+------ . . . | . / . | / . . . . . | . / . | / . . . . . | . / . | / . . 1-link Kraken Row Swordfish: r258/c356,fins=r2c2,r5c8,r8c9 (r2c2=7=r1c3-7-, r5c8=7=r5c7-7-, r8c3-3-r1c3-7-, r8c9=7=r2c9-7-): r2c256|r5c68|r8c3569=3 => r1c7<>7 .5..9......12.......6..73.8....2...4...98...53.....91.7.....6...4.8..1..1.8.7.... +-------------------+----------------------+---------------------+ | 248 5 37@% | 346 9 3468 | 24-7 2467 1 | | 489 37#@ 1 | 2 3456* 34568* | 45 4679 679& | | 249 29 6 | 145 145 7 | 3 2459 8 | +-------------------+----------------------+---------------------+ | 569 1679 579 | 13567 2 1356 | 8 36 4 | | 26 126 24 | 9 8 134* | 27$ 2367#$ 5 | | 3 8 2457 | 4567 456 456 | 9 1 26 | +-------------------+----------------------+---------------------+ | 7 239 2359 | 1345 1345 123459 | 6 8 239 | | 2569 4 2359* | 8 356* 23569* | 1 2579 2379#& | | 1 369 8 | 356 7 23569 | 245 2459 239 | +-------------------+----------------------+---------------------+ . . . | . . . | * . . / # . | / X X | / / / . . . | . . . | . . . ------+-------+------ . . . | . . . | . . . / / . | / . X | / # / . . . | . . . | . . . ------+-------+------ . . . | . . . | . . . / / X | / X X | / / # . . . | . . . | . . .

This one is interesting since it is not only cannibalistic, but also uses part of the fish in creating the nice links.

Code: Select all: 1-link Kraken Column Swordfish: c346/r1b58,fins=r3c6,r9c3 (r346c6|r9c3-7-r9c6-4-, r6c4-7-r128c4-4-): r19c3|r1678c4|r34679c6=7 => r7c4<>4 6....38......2...7..95.....96.18....7.........8.....49.........3.2.95...1..6..2.5 +--------------------+----------------------+------------------------+ | 6 12457 157* | 479*$ 147 3 | 8 1259 124 | | 458 1345 13458 | 489$ 2 14689 | 134569 13569 7 | | 248 12347 9 | 5 1467 14678# | 1346 1236 12346 | +--------------------+----------------------+------------------------+ | 9 6 345 | 1 8 247* | 357 2357 23 | | 7 12345 1345 | 2349 3456 2469 | 1356 123568 12368 | | 25 8 135 | 237* 3567 267* | 13567 4 9 | +--------------------+----------------------+------------------------+ | 458 4579 6 | 2378-4* 1347 12478* | 3479 3789 348 | | 3 47 2 | 478*$ 9 5 | 1467 1678 1468 | | 1 479 478# | 6 347 47*@ | 2 3789 5 | +--------------------+----------------------+------------------------+ . . X | X . . | . . . . . / | / . / | . . . . . / | / . # | . . . ------+-------+------ . . / | . . X | . . . . . / | . . . | . . . . . / | X . X | . . . ------+-------+------ . . / |*X . X | . . . . . / | X . . | . . . . . # | . . X | . . .

Here are examples of Kraken Mutant X-wings. In the first, the links connect r5c13 and the fin, r2c5, to the candidate elimination cell, r3c3 resulting in the elimination.

Code: Select all: Kraken Mutant X-Wing: r5c5/b45,fin=r2c5 (r5c134|r246c5=5) (r5c1-5-r1379c1-8-, r5c3-5-r24c3-8-, r2c5=8=r2c3-8-) => r3c3<>8 +---------------------+------------------+-------------------+ | 157@ 3457 13457 | 457 2 179 | 6 8 1459 | | 9 6 458$% | 3 58#% 14 | 7 145 2 | | 1578@ 2 1457-8 | 4578 6 1479 | 3 1459 1459 | +---------------------+------------------+-------------------+ | 28 9 458$ | 124 345* 6 | 145 135 7 | | 257* 1 457* | 245* 379 34 | 8 3469 469 | | 3 457 6 | 147 579* 8 | 145 2 1459 | +---------------------+------------------+-------------------+ | 167@ 37 9 | 467 478 5 | 2 146 1348 | | 4 357 2 | 678 1 37 | 9 56 358 | | 156@ 8 135 | 9 34 2 | 145 7 13456 | +---------------------+------------------+-------------------+ . . . | . / . | . . . . . . | . # . | . . . . . * | . / . | . . . ------+-------+------ . . . | . X . | . . . X / X | X / / | / / / . . . | . X . | . . . ------+-------+------ . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . .

Code: Select all: 1-link Mutant X-Wing (r37) (r3c5-8-r12c4|r2c5-3-, r7c7|r3c9-8-r9c9-3-): r3c159|r7c17=8 => r2c9<>3 +------------------+------------------+---------------------+ | 5 3 468 | 468@ 1 9 | 7 2 468 | | 1468 7 9 | 3468@ 48@ 2 | 3458 1345 4568-3 | | 468* 14 2 | 5 478* 367 | 9 134 3468* | +------------------+------------------+---------------------+ | 1349 19 345 | 2 457 137 | 6 8 3457 | | 7 2 4563 | 3468 458 36 | 345 9 1 | | 1346 8 3456 | 346 9 1367 | 2 345 3457 | +------------------+------------------+---------------------+ | 38* 6 1 | 7 2 45 | 348* 345 9 | | 49 459 7 | 1 3 8 | 45 6 2 | | 2 45 38 | 9 6 45 | 1 7 38$ | +------------------+------------------+---------------------+

And an example from DAJ of a Kraken Mutant Swordfish:

Code: Select all: # [r7c2]-2-(Swordfish [r467C358])=2=([r2c3]|[r3c8])-2-[r3c1]=2=[r9c1]-2-[r7c2] *---------------------------------------------------* | 39 4 5 | 2 7 89 | 1 6 38 | | 7 128 #128 | 3 4 6 | 25 9 258 | | 239 289 6 | 1 58 589 | 4 #23 7 | |-----------------+----------------+----------------| | 15 3 9 | 6 *12 78 | 257 *258 4 | | 8 27 4 | 5 9 3 | 27 1 6 | | 15 6 *27 | 78 *12 4 | 3 *258 9 | |-----------------+----------------+----------------| | 4 17-2 *12 | 9 6 57 | 8 *235 235 | | 6 5 78 | 78 3 2 | 9 4 1 | | 29 289 3 | 4 58 1 | 6 7 25 | *---------------------------------------------------*

by **ronk** » Fri Dec 29, 2006 7:27 pm

Although this doesn't do much to advance the puzzle, I think it's a good illustration of my concept of a kraken fish.

Code: Select all: 4...5..3997..6.2.5..3...6...4.2.3.5.5...9...4.3.6.5.7...5...4..7.4.3..2636..8...7 #B049 1 After Simple Sudoku's Technique Set (SSTS): 4 128 6 | 18 5 128 | 7 3 9 9 7 18 | 3 6 148 | 2 148 5 128 5 3 | 14789 127 14789 | 6 148 18 -------------------+-------------------+------------------ 6 4 1789 | 2 17 3 | 189 5 18 5 12 127 | 178 9 178 | 3 6 4 18 3 189 | 6 4 5 | 189 7 2 -------------------+-------------------+------------------ 128 189 5 | 179 127 6 | 4 189 3 7 189 4 | 159 3 19 | 158 2 6 3 6 12 | 1459 8 1249 | 15 19 7 Looking at just digit 8: . 8 . | 8 . 8 | . . . . . 8 | . . 8 | . 8 . *8 . . | 8 . 8 | . 8 *8 ---------+----------+---------- . . -8 | . . . | 8 . *8 . . . | 8 . 8 | . . . #8 . *8 | . . . | *8 . . ---------+----------+---------- *8 8 . | . . . | . 8 . . *8 . | . . . | #8 . . . . . | . . . | . . . r68c19\r3b467 plus fins r6c1 and r8c7 imply r4c3<>8 r68c19\r3b467-8-r4c3 (if all fins are false) r6c1-8-r4c3 (if direct fin r6c2 is true) r8c7-8-r6c7=8=r6c13-8-r4c3 (if kraken fin r8c7 is true)

It is a deduction made on the basis of just one digit, and the exclusion is true even when all fins are false.

Note that r6c1 is a fin because it is in the intersection of base sectors r6 and c1. Even though box 4 is a cover sector, r6c1 must still be considered a fin.

Also note that the strong-link used by the kraken cell chain is wholly contained within the unfinned jellyfish. This probably has no significance, but it seemed noteworthy.

P.S. This is the same puzzle generated by daj95376 which yielded a mutant leviathan.

by **Mike Barker** » Sat Dec 30, 2006 4:16 pm

Kraken Fish with deductions made on just the fish digit have a certain appeal, but I wouldn't limit them to just using one digit. In this case, the elimination can be made with a "simple" mutant Jellyfish (a Kraken fish is not required).

Code: Select all: Mutant Jellyfish: r68c9b1/r3c237/fins=r6c1,r4c9: r6c137|r8c27|r34c9|r3c1|r1c2|r2c3 => r4c3<>8 +------------------+--------------------+----------------+ | 4 128* 6 | 18 5 128 | 7 3 9 | | 9 7 18*@ | 3 6 148 | 2 148 5 | | 128* 5 3 | 14789 127 14789 | 6 148 18* | +------------------+--------------------+----------------+ | 6 4 179-8 | 2 17 3 | 189 5 18#@ | | 5 12 127 | 178 9 178 | 3 6 4 | | 18#@ 3 189*@ | 6 4 5 | 189* 7 2 | +------------------+--------------------+----------------+ | 128 189 5 | 179 127 6 | 4 189 3 | | 7 189* 4 | 159 3 19 | 158* 2 6 | | 3 6 12 | 1459 8 1249 | 15 19 7 | +------------------+--------------------+----------------+

by **ronk** » Sat Dec 30, 2006 4:38 pm

Mike Barker wrote:In this case, the elimination can be made with a "simple" mutant Jellyfish (a Kraken fish is not required).

Very nice, but what are the '@'s for?

Kraken Fish with deductions made on just the fish digit have a certain appeal, but I wouldn't limit them to just using one digit.

I expect we'll never agree on that.

But to me it's simple. Multi-digit kraken deductions, like kraken house or kraken cell, that use a fish just aren't the same as a kraken fish.

by **Mike Barker** » Sat Dec 30, 2006 4:55 pm

The "@" show which cells are affected by the candidate elimination cell (useful for finding fins and the covering set). Normally I delete them, but didn't this time.

How about we split Kraken Fish - those that use general exclusions and those that use only the fish digit. We could call the later Ronken Fish

.

by **ronk** » Sat Dec 30, 2006 5:44 pm

Mike Barker wrote:How about we split Kraken Fish - those that use general exclusions and those that use only the fish digit. We could call the later Ronken Fish .

How about calling the latter YAFIN? -- as in "Yet Another Fish Name", or YASUTEN -- as in Yet Another Sudoku Technique Name?" ;-)

Seriously, I want no part of creating another name for a fish type. I'd rather disagree forever on the definition of kraken fish -- or just call it "single-digit kraken fish."

Stepping back and looking at the big picture, I was rather hoping the definitions would eventually allow us to say that all the fish -- basic, franken and kraken -- yielded eliminations equivalent to Nishio and templates. IOW fish were logical alternatives to what are essentially elimination-by-contradiction (EBC) techniques.

CAVEAT: As I've implemented neither Nishio nor templates, I could be wrong about my EBC viewpoint.

[edit: added YASUTEN back in since Mike "quoted" me mid-edit]

by **Mike Barker** » Sat Dec 30, 2006 6:20 pm

I agree we should probably save YASUTEN and YAFIN for one of Danny's eliminations

. I see your point about wanting only single digit eliminations, but with mutant fish I'm not sure how viable a sd-Kraken Fish is. It seems like most sd-Kraken Fish will reduce to a possibly larger mutant fish. Consider Myth's solution, it can also be expressed as a Mutant Jellyfish. I'd rate this simpler than a Kraken Swordfish. Having said that we should emphasize sd-Kraken Fish in the ultimate guide. We'll need to come up with some good examples.

Code: Select all: Mutant Jellyfish: r159,c6/c189,b8/fins=r4c6,r5c7: r1c189|r5c179|r9c489|r47c6 => r4c8<>7 +-----------------+--------------------+-------------------+ | 179* 489 5 | 3 89 24 | 6 127* 279* | | 1689 2 3 | 5689 7 569 | 159 4 59 | | 679 49 679 | 569 1 24 | 2579 3 8 | +-----------------+--------------------+-------------------+ | 3 5 8 | 4 69 679# | 279 26-7 1 | | 79* 6 4 | 2 5 1 | 379# 8 379* | | 2 1 79 | 679 3 8 | 579 567 4 | +-----------------+--------------------+-------------------+ | 4 3 69 | 156789 2 5679* | 1578 157 567 | | 568 7 2 | 1568 4 56 | 1358 9 356 | | 569 89 1 | 5679* 689 3 | 4 257* 2567* | +-----------------+--------------------+-------------------+

by **daj95376** » Sat Dec 30, 2006 6:34 pm

Hey, I resemble that!!!

So, would this finned sd-Kraken Swordfish be a good example?

by **Mike Barker** » Sat Dec 30, 2006 7:22 pm

Actually, it is also a mutant jellyfish:

Code: Select all: Mutant Jellyfish: r17,c69/r6,c2,b29/fins=r1c1,r3c9: r1c125|r7c27|r26c6|r368c9 => r3c2<>9 +------------------+----------------+-------------------+ | 159# 29* 7 | 15 1259* 3 | 8 6 4 | | 159 8 4 | 7 6 129* | 1259 159 3 | | 6 23-9 359 | 8 1259 4 | 7 1259 159# | +------------------+----------------+-------------------+ | 59 7 1 | 3 4 8 | 6 59 2 | | 3 4 59 | 2 159 6 | 159 7 8 | | 2 6 8 | 15 7 19* | 3 4 159* | +------------------+----------------+-------------------+ | 4 139* 2 | 6 13 5 | 19* 8 7 | | 7 19 69 | 4 8 12 | 1259 3 1569* | | 8 5 36 | 9 123 7 | 4 12 16 | +------------------+----------------+-------------------+

by **ronk** » Sat Dec 30, 2006 9:10 pm

Mike Barker wrote:I see your point about wanting only single digit eliminations, but with mutant fish I'm not sure how viable a sd-Kraken Fish is. It seems like most sd-Kraken Fish will reduce to a possibly larger mutant fish.

That would be OK with me. But perhaps you would explain how viewpoint A makes viewpoint B non-viable. How many names do we have for an x-cycle of cycle length five? Does any one of them make the others non-viable?

Consider Myth's solution, it can also be expressed as a Mutant Jellyfish. I'd rate this simpler than a Kraken Swordfish.

Many are franken rather than mutant. Reconsider Myth's solution, it can also be expressed as a franken jellyfish. I'd rate this simpler than a mutant jellyfish.

Code: Select all: *7 . . | . . . | . *7 *7 . . . | . . . | . . . 7 . 7 | . . . | 7 . . ---------+-----------+---------- . . . | . . #7 | 7 -7 . *7 . . | . . . | #7 . *7 . . 7 | *7 . . | 7 7 . ---------+-----------+---------- . . . | 7 . 7 | 7 7 7 . . . | . . . | . . . . . . | *7 . . | . *7 *7 franken jellyfish r159b5\c1489 plus fins r4c6 and r5c7, implies r4c8<>7

Having said that we should emphasize sd-Kraken Fish in the ultimate guide.

Maybe, I'll give that some thought. But I still rather like this test:

If an elimination cell is a peer of all the fin cells -- that is, the elimination cell "sees" all the fin cells, it's not a kraken fish. Otherwise, it is.

Mike Barker wrote:I agree we should probably save YASUTEN and YAFIN for one of Danny's eliminations .

I don't see how someone can agree to what another didn't say ... and I'm not referring to YASUTEN.

by **Mike Barker** » Sat Dec 30, 2006 10:31 pm

Ronk wrote:That would be OK with me. But perhaps you would explain how viewpoint A makes viewpoint B non-viable. How many names do we have for an x-cycle of cycle length five? Does any one of them make the others non-viable?

I think we are agreeing that we want to keep technique names to a minimum. If most sd-Kraken Fish are also Franken or Mutant Fish then distinguishing between sd and regular Kraken Fish maybe of little consequence.

Ronk wrote:Many are franken rather than mutant. Reconsider Myth's solution, it can also be expressed as a franken jellyfish. I'd rate this simpler than a mutant jellyfish.

I agree - I still look for Franken Fish with a box in the base set and Mutant Fish with the same algorithm so didn't catch the simpler fish.

Ronk wrote:I don't see how someone can agree to what another didn't say ... and I'm not referring to YASUTEN.

The reference was to not creating another name for Kraken Fish - saving YASUTEN for one of DAJ's fish was just a hyperbole. As far as not refering to YASUTEN - there must have been a glitch in the Matrix, because at one time I would have sworn that you did

.
[Edit - another glitch - YASUTEN is back - is it possible you are the One?]

by **daj95376** » Sat Mar 03, 2007 9:10 pm

An expanded cross-post from The Ultimate Fish Guide.

Code: Select all: .47.6.8...1...8...9..7...6..61....4.83..4..97.9....63..8...9..6...6...8...4.1.75. #E091 2 # After SSTS and (necessary) XYZ-Wing for [r3c9]<>2 *-----------------------------------------------------------* | 23 4 7 | 9 6 15-2 | 8 12 1235 | | 23 1 6 | 245 35-2 8 | 9 7 2345 | | 9 5 8 | 7 23 124 | 123 6 134 | |-------------------+-------------------+-------------------| | 7 6 1 | 3 9 25 | 25 4 8 | | 8 3 25 | 125 4 6 | 125 9 7 | | 4 9 25 | 125 8 7 | 6 3 12 | |-------------------+-------------------+-------------------| | 15 8 3 | 245 7 9 | 14-2 12 6 | | 15 7 9 | 6 25 245 | 1234 8 123 | | 6 2 4 | 8 1 3 | 7 5 9 | *-----------------------------------------------------------*

There have been several solutions posted to explain the three eliminations in <2>. I have my own approach.

First elimination [r1c6]<>2:

Code: Select all: # finned X-Wing r34/c67 *-----------------------------------* | 2 . . | . . -2 | . 2 2 | | 2 . . | 2 2 . | . . 2 | | . . . | . #2 *2 | *2 . . | |-----------+-----------+-----------| | . . . | . . *2 | *2 . . | | . . 2 | 2 . . | 2 . . | | . . 2 | 2 . . | . . 2 | |-----------+-----------+-----------| | . . . | 2 . . | 2 2 . | | . . . | . 2 2 | 2 . 2 | | . 2 . | . . . | . . . | *-----------------------------------*

Now, I add a row and a column to get elimination [r7c7]<>2:

Code: Select all: # finned Swordfish r348/c567 *-----------------------------------* | 2 . . | . . 2 | . 2 2 | | 2 . . | 2 2 . | . . 2 | | . . . | . *2 *2 | *2 . . | |-----------+-----------+-----------| | . . . | . . *2 | *2 . . | | . . 2 | 2 . . | 2 . . | | . . 2 | 2 . . | . . 2 | |-----------+-----------+-----------| | . . . | 2 . . | -2 2 . | | . . . | . *2 *2 | *2 . #2 | | . 2 . | . . . | . . . | *-----------------------------------*

For elimination [r2c5]<>2, I choose to simply rename the above fish and observe that all three eliminations can now be explained with it.

Code: Select all: # Kraken Swordfish r348/c567 w/cell [r8c9] # (2) [r8c9] => ![r6c9] => [r45c7] => ![r37c7] => [r3c56] => !([r1c6],[c2c5]) *-----------------------------------* | 2 . . | . . -2 | . 2 2 | | 2 . . | 2 -2 . | . . 2 | | . . . | . *2 *2 | *2 . . | |-----------+-----------+-----------| | . . . | . . *2 | *2 . . | | . . 2 | 2 . . | 2 . . | | . . 2 | 2 . . | . . 2 | |-----------+-----------+-----------| | . . . | 2 . . | -2 2 . | | . . . | . *2 *2 | *2 . #2 | | . 2 . | . . . | . . . | *-----------------------------------*

To paraphrase Obi-Wahn ... the candidate in [r8c9] is an obstacle because it prevents the Swordfish and doesn't directly see two of the three exclusion candidates. However, I'm perfectly happy to know that [r8c9] indirectly forces the other two eliminations through a simple, single-digit, implication chain.

Note: The Kraken Swordfish performs all of the eliminations in the following pattern proposed by Obi-Wahn.
How? [r8c9] => [r456c7] => [r3c56], which overlaps the base Swordfish in the same cells as marked (*) in Obi-Wahn's pattern.

Code: Select all: Mutant Squirmbag r348c8b1\r12c567b9 with one fin sector . . . | . * * | * . . . . . | . * * | * . . / / / | / . . | . / / -------+-------+------- / / / | / . . | . / / . . . | . . . | . / . . . . | . . . | . / . -------+-------+------- . . . | . . . | * . . / / / | / . . | . / . . . . | . . . | * . . / = empty cell . = cell may or may not contain a candidate * = possible exclusions

by **daj95376** » Sun Mar 11, 2007 3:09 am

Here are two (single-digit) Kraken Swordfish with the same fin (#) and remote (^) cells.

Code: Select all: # Kraken Swordfish c189/r258 w/remote cell [r4c9] # (9) [r4c9] => ![r5c8] => [r8c8] => ![r8c3] *-----------------------------------* | . 9 9 | . . . | 9 . . | | *9 9 9 | . . . | . . *9 | | . . . | . 9 . | . . . | |-----------+-----------+-----------| | . 9 . | . . . | 9 . ^9 | | *9 9 9 | . . . | 9 *9 *9 | | . . . | . . 9 | . . . | |-----------+-----------+-----------| | #9 9 . | . . . | 9 . . | | *9 . -9 | . . . | . *9 . | | . . . | 9 . . | . . . | *-----------------------------------*

Code: Select all: # Kraken Swordfish r147/c237 w/remote cell [r4c9] # (9) [r4c9] => ![r5c8] => [r8c8] => ![r8c3] *-----------------------------------* | . *9 *9 | . . . | *9 . . | | 9 9 9 | . . . | . . 9 | | . . . | . 9 . | . . . | |-----------+-----------+-----------| | . *9 . | . . . | *9 . ^9 | | 9 9 9 | . . . | 9 9 9 | | . . . | . . 9 | . . . | |-----------+-----------+-----------| | #9 *9 . | . . . | *9 . . | | 9 . -9 | . . . | . 9 . | | . . . | 9 . . | . . . | *-----------------------------------*

Now, very few people are interested in Kraken Fish, but more people seem to be interested in anything with the word Almost in it. So, my question is: Does the remote cell qualify as a link between two Almost Finned Swordfish?

Yes, I know, Almost doesn't work this way. Darn!!!

For Carcul:

Code: Select all: # (9) ![r8c8] => ([r2c9],[r5c8],[r7c7]) => !([r2c1],[r5c1],[r7c1]) => [r8c1] => ![r8c3] *-----------------------------------* | . 9 9 | . . . | 9 . . | | !9 9 9 | . . . | . . +9 | | . . . | . 9 . | . . . | |-----------+-----------+-----------| | . 9 . | . . . | 9 . 9 | | !9 9 9 | . . . | 9 +9 9 | | . . . | . . 9 | . . . | |-----------+-----------+-----------| | !9 9 . | . . . | +9 . . | | +9 . -9 | . . . | . !9 . | | . . . | 9 . . | . . . | *-----------------------------------*

by **daj95376** » Mon Oct 29, 2007 6:10 pm

Code: Select all: Puzzle sdaj_02_15: +-----------------------+ | 1 . . | . 5 . | 7 . . | | . 5 . | 7 . 9 | . 2 1 | | . 9 7 | . . . | 4 3 . | |-------+-------+-------| | . . . | 3 . . | . 7 . | | . . 1 | . 4 . | 2 . . | | . 7 . | . . 2 | . . . | |-------+-------+-------| | . 1 2 | . . . | 3 6 . | | 5 3 . | 2 . 1 | . 4 . | | . . 4 | . 7 . | . . 2 | +-----------------------+

Code: Select all: after SSTS +-----------------------------------------------------------------------+ | 1 2 3 | 48 5 468 | 7 89 689 | | 4 5 68 | 7 3 9 | 68 2 1 | | 68 9 7 | 1 2 68 | 4 3 5 | |-----------------------+-----------------------+-----------------------| | 2 4 589 | 3 189 58 | 15689 7 689 | | 689 68 1 | 5689 4 7 | 2 589 3 | | 3 7 5689 | 5689 1689 2 | 1589 1589 4 | |-----------------------+-----------------------+-----------------------| | 7 1 2 | 45 89 45 | 3 6 89 | | 5 3 689 | 2 689 1 | 89 4 7 | | 689 68 4 | 689 7 3 | 15 15 2 | +-----------------------------------------------------------------------+

A finned Jellyfish will eliminate [r6c5]<>8 and a finned mutant Starfish will eliminate [r1c9]<>8 and [r6c7]<>8. However, as a fan of sd-Kraken fish, I prefer to do all three eliminations at once.

Code: Select all: sd-Kraken Jellyfish r2478\c3579 w/remote cell [r5c6] [r5c6]=8 => [r1c4]=8 => [r2c7]=8 ===> [r1c9],[r6c57]<>8 +-----------------------------------+ | . . . | 8 . 8 | . 8 -8 | | . . *8 | . . . | *8 . . | | 8 . . | . . 8 | . . . | |-----------+-----------+-----------| | . . *8 | . *8 @8 | *8 . *8 | | 8 8 . | 8 . . | . 8 . | | . . 8 | 8 -8 . | -8 8 . | |-----------+-----------+-----------| | . . . | . *8 . | . . *8 | | . . *8 | . *8 . | *8 . . | | 8 8 . | 8 . . | . . . | +-----------------------------------+

by **wintder** » Tue Oct 30, 2007 7:43 pm

Mike Barker wrote:In the next example, a grouped strong link and a bivalue cell link the fish to the CECs, r79c9: r8c2=y=r8c78-y-r79c9 and r5c25-x-r5c9-r79c9. In this example the candidate to be eliminated, "y", is not the fish digit.
Code: Select all
. . . | . . . | . . . . X . | . X . | . . . . | . | . | . | . . . ---|---+---|---+------- . | . | . | . | . . . . X . | . X . | . . xy . | . | . . . | . . . ---|---+-------+------- . | . | . . . | . . * . #y=============y y . . . . | . . . | . . *

Would this be a more general, and valid, form?

(Where at least one of the capital "Y"s is a candidate in the pattern.)

Code: Select all: . . . | . . . | . . . . X . | . X . | . . . . | . | . | . | . . . ---|---+---|---+------- . | . | . | . | . . . . X . | . X . | . . xy . | . | . . . | . . . ---|---+-------+------- . | . | . . . | . . * . #y=============Y Y Y . . . | . . . | . . *

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