Finned Swordfish (3-Fish)

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A Finned Swordfish is a size-3 Finned Fish.

How to spot it

• For each candidate x from 1 to 9, select three rows (or columns) containing x as the base set, and three 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 a Swordfish.
• Eliminate candidate x from any cell in the three 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 Swordfish, 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 4, columns {2, 4, 7} form the base set, and rows {2, 3, 4} form the cover set. The fin is at R6C2.

Candidate 4 can be eliminated from R4C3, 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 3, rows {1, 3, 7} form the base set, and columns {2, 6, 9} form the cover set. The fin is at R7C4.

Candidate 3 can be eliminated from R8C6 and R9C6, since these cells lie within the cover set, outside the base set, and see every fin cell.

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On the board above, for candidate 6, rows {2, 4, 7} form the base set, and columns {4, 6, 7} form the cover set. The fins are at R4C8 and R4C9.

Candidate 6 can be eliminated from R6C7, since this cell lies within the cover set, outside the base set, and sees every fin cell.

Sashimi Swordfish

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