Mirrored from **Sudopedia**, the Free Sudoku Reference Guide

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.

There is a potential X-Wing in columns 2 & 5 and rows 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.

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 Sets

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.

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