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2025-07-20T15:37:30Z

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A '''Kraken Fish''' is a [[fish]] pattern which is connected to a [[candidate elimination cell]] ([[CEC]]) in such a way that placing this [[candidate]] would reduce the [[secondary set]] to a size smaller than the [[defining set]].

Here is a diagram depicting a '''Kraken X-Wing'''. It has 2 CECs.

[[image:kraken x-wing.png]]

There is a potential [[X-Wing]] in [[column]]s 2 & 5 and [[row]]s 2 & 5. The candidate in '''r8c2''' acts as a [[fin]], but because it does not share a [[box]] with one of the candidate forming the X-Wing, it does not cause any eliminations that would normally occur in a [[Finned X-Wing]]. The pattern has 2 columns covering 3 rows.

Now consider what would happen if either '''r2c8''' or '''r5c8''' would contain digit '''X'''. Both would eliminate all candidate on their own row and through the [[strong link]] in row 9, the candidate in '''r8c2''', leaving a pattern with 2 columns covering 1 row, an impossible situation.

'''A Kraken-related Extended 2-String Kite Example'''

Next consider the example below. This is identical to the Kraken X-wing example except the candidate has benn removed from cell r2c2. The resultant pattern is a 2-string kite consisting of conjugate pairs AB and CD and an additional conjugate pair EF. This is an example of a more general technique called the extended 2-string kite technique.

.-------.-------.-------.
| . - . | . - . | . . . |
| . - . | . F . | . * . |
| . - . | . - . | . . . |
:-------+-------+-------:
| . - . | . - . | . . . |
| . D . | . E . | . * . |
| . - . | . - . | . . . |
:-------+-------+-------:
| . - . | . - . | . . . |
| . C . | . - . | . . . |
| - - A | - - - | - B - |
'-------'-------'-------'

How it works. Since A and C are peers, at most only one of them can be X. This means that either or both of their conjugates B and D must be X. If B is X then r25c8 cannot be X. If B is not X, then D must be X and its peer E must be not X. Therefore E's conjugate F must be X. Therefore r25c8 cannot be X. So you get the same eliminations as the Kraken X-wing. A similar argument holds if r5c2 had been eliminated instead of r2c2. This means that either r2c2 or r5c2 but not both can be eliminated from the Kraken X-wing pattern without changing the results. The extended 2-string kite pattern occurs more often then the Kraken X=wing in puzzles.

== Connection Types ==

In the example, the CECs are connected to the pattern with a direct [[weak link]] and an indirect connection via a strong link. However, there are several other methods to connect the CEC to the fish pattern.

* Strong links
* Grouped strong links
* [[Almost Locked Set]]s

As a result, the CEC does not even need to be a candidate for the same digit as the pattern. The following diagram shows how an X-Wing pattern for digit '''X''' can eliminate a candidate for digit '''Y'''.
. - . | . - . | . . .
. X . | . X . | . XY .
. - . | . - . | . . .
---------+----------+---------
. - . | . - . | . . .
. X . | . X . | . . .
. - . | . - . | . . .
---------+----------+---------
. - . | . - . | . . .
. X . | . - . | . . .
. - XY | . - . | . CEC .
In this example, a similar Finned X-Wing is present, but '''r2c8''' and '''r9c3''' are both [[bivalue]] cells with candidates '''XY'''. Placing '''Y''' in the CEC at '''r9c8''' would force both these cells to '''X''' and reduce the fish pattern to a single row and 2 columns.

== External Link ==
* [http://forum.enjoysudoku.com/viewtopic.php?t=5143 Kraken Fish] (New Sudoku Players' Forums)

== See Also ==
* [[Fish]]

[[Category:Solving Techniques]]
{{example}}

Kraken Fish - Revision history

Rooted: Created page with "A '''Kraken Fish''' is a fish pattern which is connected to a candidate elimination cell (CEC) in such a way that placing this candidate would reduce the sec..."