XY-Wing

Hard

What is it?

An XY-Wing consists of a pivot cell with candidates {X,Y} and two wing cells: one with {X,Z} and one with {Y,Z}, where each wing sees the pivot. Any cell that sees both wings can have Z eliminated, because one wing must contain Z.

When to use it

Look for a cell with exactly two candidates (the pivot) that sees two other bi-value cells. The three cells should collectively hold three distinct values, with each pair sharing one value.

Why it works

The pivot is either X or Y. If it is X, the {Y,Z} wing must be Z. If it is Y, the {X,Z} wing must be Z. Either way, one wing contains Z. Any cell seeing both wings cannot be Z.

Interactive Demo

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Let's find an XY-Wing. We start by looking for a pivot cell with exactly two candidates. R1C1 has candidates {3, 5} — this is our pivot.

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