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Swordfish

Medium· L6
Elimination

A Swordfish is an X-Wing with three lines instead of two.

In three rows, one digit only appears in the same three columns (or three columns with the same three rows). The digit is locked to that 3×3 fish pattern.

Before this: Learn X-Wing first.

Why it works

Counting proof: three rows each need the digit. They must cover three columns without sharing a column. If a victim killed one of those columns, three digits could not fit in the two columns left.

Reduction proof: assume any fish cell is true → the remaining pattern collapses to an X-Wing you already trust — and that X-Wing still clears the same victims.

Same ownership idea as X-Wing — just a bigger fish. Incomplete corners still count if the structure holds.

Demonstration

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Pick a digit. Look for three rows whose candidates for that digit stay inside the same three columns.

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The green cells lock 3 to this 3×3 fish. Each of the three rows must place the digit in one of the three columns.

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They cannot pile into fewer than three columns. Counting (or reducing to an X-Wing) shows all three columns get 3. That pattern is a Swordfish.

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Eliminate 3 from the rest of those columns (red). The three fish columns are already spoken for.

Example 1

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For one digit, find three lines sharing the same three crossing lines.

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This is a Swordfish on 7.

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Remove 7 from the rest of those lines (red). Three rows need three columns — a victim would leave too few homes.

Example 2

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For one digit, find three lines sharing the same three crossing lines.

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This is a Swordfish on 5.

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Remove 5 from the rest of those lines (red). Three rows need three columns — a victim would leave too few homes.

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