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Swordfish (Size-3 Fish)

A Swordfish is a size-3 fish.

When a candidate digit d in three rows or columns (the base set) falls only in three columns or rows (the cover set), then no matter how d is placed, each of the three cover-set houses must contain exactly one digit d. Therefore, candidate digit d can be eliminated from all other cells in the cover set.

For example, in the board below, take three rows as the base set. Look at candidate digit 1 in row 3, row 6, and row 9: it appears only in column 2, column 4, and column 5. So regardless of how these three 1s are arranged within row 3, row 6, and row 9, column 2, column 4, and column 5 must each contain one digit 1. Therefore, in those three columns, candidate digit 1 can be eliminated from every cell except the intersections of the base set and the cover set.

Note that in row 3 and row 9, candidate digit 1 does not appear exactly three times, but that does not prevent them from participating in a size-3 fish. It is enough that all occurrences of candidate digit 1 in the entire base set lie within the cover set.

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For another example, in the board below, take three columns as the base set. Look at candidate digit 5 in column 2, column 6, and column 8: it appears only in row 2, row 4, and row 7. So regardless of how these three 5s are arranged within column 2, column 6, and column 8, row 2, row 4, and row 7 must each contain one digit 5. Therefore, in those three rows, candidate digit 5 can be eliminated from every cell except the intersections of the base set and the cover set.

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