Swordfish (3-Fish)

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A Swordfish is a size-3 basic fish.

How to spot it

• For each candidate x from 1 to 9, find three rows (or columns), each containing between 2 and 3 occurrences of x.
• Check all occurrences of x in those three rows (or columns): together, they must be confined to exactly three columns (or rows). The selected rows (or columns) form the base set, and those columns (or rows) form the cover set.
• Eliminate candidate x from all cells in the three cover columns (or rows) outside the base set.

How it works

Each of the three base rows (or columns) must eventually contain one placed digit x, for a total of 3 placements. All of them lie in the three cover columns (or rows). Since a column (or row) cannot contain two xs, these placements must occupy different columns (or rows), with exactly one in each.

Therefore, no cell in the cover set outside the base set can contain x, so candidate x can be eliminated from those cells.

Examples

On the board above, for candidate 1, rows {3, 6, 9} form the base set, and columns {2, 4, 5} form the cover set. All occurrences of 1 in the base set lie within the cover set.

Candidate 1 can be eliminated from R1C5, R4C5, R5C2, R5C4, and R5C5, since these cells lie in the cover set outside the base set.

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On the board above, for candidate 5, columns {2, 6, 8} form the base set, and rows {2, 4, 7} form the cover set. All occurrences of 5 in the base set lie within the cover set.

Candidate 5 can be eliminated from R2C9, R4C1, R4C3, R4C9, and R7C5, since these cells lie in the cover set outside the base set.