## Kraken Fish

Advanced methods and approaches for solving Sudoku puzzles

### Kraken Fish

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
(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 / # | # / / | / / /
. . . | . . . | . . .

(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 . .
. . . | . # . | . . .
------+-------+------
. . . | . / . | / . .
. . . | . / . | / . .
. . . | . / . | / . .

(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
(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   |
*---------------------------------------------------*
Last edited by Mike Barker on Wed Oct 31, 2007 9:01 am, edited 2 times in total.
Mike Barker

Posts: 458
Joined: 22 January 2006

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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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  |
+------------------+--------------------+----------------+
Mike Barker

Posts: 458
Joined: 22 January 2006

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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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 .
Mike Barker

Posts: 458
Joined: 22 January 2006

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]
Last edited by ronk on Sat Dec 30, 2006 5:15 pm, edited 1 time in total.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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* |
+-----------------+--------------------+-------------------+
Mike Barker

Posts: 458
Joined: 22 January 2006

Hey, I resemble that!!!

So, would this finned sd-Kraken Swordfish be a good example?
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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  |
+------------------+----------------+-------------------+
Mike Barker

Posts: 458
Joined: 22 January 2006

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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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?]
Mike Barker

Posts: 458
Joined: 22 January 2006

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
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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  .  .  |  .  .  .  |
*-----------------------------------*
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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  .  .  |  .  .  .  |
+-----------------------------------+
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Kraken Fish

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
.  . . | . . . | . .  *
wintder

Posts: 297
Joined: 24 April 2007

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