Solving techniques

XY-Wing

XY-Wing is a short chain of three cells. Once you know the shape, it is easy to spot.

Short answer

An XY-Wing uses a pivot cell with candidates X and Y, and two wing cells it sees: one with X and Z, the other with Y and Z. Whichever way the pivot goes, one wing becomes Z, so Z can be removed from any cell that sees both wings.

The logic

The pivot holds two candidates, say 7 and 9. Suppose the pivot is 7: the wing with 7 and 2 sees it, so that wing must be 2. Suppose the pivot is 9: the wing with 9 and 2 sees it, so that wing must be 2. Either way, a 2 lands in one of the two wings. Any cell that sees both wings cannot be 2.

Real example: the pivot R7C1 holds 7 and 9. The wings are R1C1 (2 9) and R7C6 (2 7). Cell R1C6 sees both wings, so 2 can be removed from it (red).

Open this position in the step-by-step solver

How to find an XY-Wing

Find a cell with exactly two candidates (the pivot), such as 7 and 9.
Find a cell that sees the pivot with candidates 9 and 2 (one pivot digit plus a new digit).
Find a second cell that sees the pivot with candidates 7 and 2 (the other pivot digit plus the same new digit).
Remove the new digit (2) from every cell that sees both wings.

Common mistakes

Using wings that do not see the pivot.
Not checking that both wings share the same third digit.
Removing the digit from cells that see only one wing.

The partner chain technique is simple coloring. Both are needed for Extreme puzzles. Practice X-Wing first.

Frequently asked questions

What is an XY-Wing?

A pattern of three cells with two candidates each (a pivot and two wings) that eliminates a shared digit from cells seeing both wings.

Why does it work?

Whatever the pivot becomes, one of the wings must take the shared digit.

Which level uses it?

Extreme.