Finned X-Wing (2-Fish)

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A Finned X-Wing is a size-2 Finned Fish.

How to spot it

• For each candidate x from 1 to 9, select two rows (or columns) containing x as the base set, and two columns (or rows) as the cover set.
• Check every occurrence of x in each base row (or column). Treat any occurrence outside the cover set as a fin, and ensure that there is at least one fin. All fin cells must see one another; otherwise no target cell within the cover set and outside the base set can see every fin. The remaining occurrences of x in the base set must form an X-Wing.
• Eliminate candidate x from any cell in the two cover columns (or rows) that lies outside the base set and sees every fin cell.

How it works

For a target cell within the cover set, outside the base set, that sees every fin cell, there are only two possibilities:

• All fins are false: all base candidates lie within the cover set, forming a basic or degenerate X-Wing, so the target cell cannot contain x.
• At least one fin is true: the target sees every fin cell, so it cannot contain x, regardless of which fin is true.

The target cannot contain x in either case, so candidate x can be eliminated from that cell.

Examples

On the board above, for candidate 5, rows {1, 6} form the base set, and columns {2, 9} form the cover set. The fin is at R1C8.

Candidate 5 can be eliminated from R2C9, since this cell lies within the cover set, outside the base set, and sees every fin cell.

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On the board above, for candidate 7, rows {3, 5} form the base set, and columns {2, 5} form the cover set. The fins are at R5C4 and R5C6.

Candidate 7 can be eliminated from R6C5, since this cell lies within the cover set, outside the base set, and sees every fin cell.

Sashimi X-Wing

The pattern outside the fins can be a degenerate fish, as shown on the boards below: