XY-Wing
Prerequisites: Naked Pair
Overview
An XY-Wing uses three bivalue cells -- a hinge and two wings -- to eliminate a candidate from cells that see both wings.
How It Works
An XY-Wing consists of a hinge cell with candidates (A,B) connected to two wing cells: one with (A,C) and one with (B,C). The hinge must see both wings (share a row, column, or box). If the hinge is A, the (A,C) wing must be C. If the hinge is B, the (B,C) wing must be C. Either way, one wing is always C -- so C can be eliminated from any cell that sees both wings.
When To Use It
Look for XY-Wings when you see multiple bivalue cells (cells with exactly two candidates). They are especially effective when simpler techniques are exhausted.
How To Detect It
Find a cell with exactly two candidates (A,B) (the hinge). Look for two other bivalue cells it can see: one with (A,C) and one with (B,C). If found, eliminate C from cells that see both wings.
Visual Example
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Chains of Bivalue Cells
An XY-Wing uses three bivalue cells — a hinge and two wings — to force a candidate's elimination. The key insight: no matter what the hinge holds, the same digit ends up in one of the two wings.
Practice
An XY-Wing is hiding here. Find the hinge and its two wings, then eliminate and fill the Naked Single.