XY-Wing

Level 7 · Green Belt

Strategy:

Wings

Requires:

Naked Pair

Learn after:

XYZ-Wing

Overview

XY-Wing uses three bi-value cells arranged so each pair shares a candidate. The pivot cell sees both wing cells, and the common candidate of the wings can be eliminated from cells that see both wings.

How It Works

  1. Find a pivot cell with candidates {X,Y} that sees two wing cells.
  2. One wing has candidates {X,Z}, the other has {Y,Z}.
  3. If pivot is X, one wing is Z. If pivot is Y, the other wing is Z.
  4. Eliminate Z from any cell that sees both wings.

Example

Starting position

Look for XY-Wing.

1

Pivot r3c5 with two wings

Find a two-candidate pivot cell r3c5 connected to two wing cells.

2

Wings share the elimination digit

The wings r3c9 and r7c9 share a candidate not in the pivot - this is the elimination digit.

3

This is an XY-Wing

This is an XY-Wing - the shared candidate is eliminated from common peers.

4

Remove 8 from r7c5

One wing must contain 8, so remove that candidate from cells seeing both wings: r7c5.

5

Result

Result after applying the technique.

Tips & Patterns

  • All three cells must be bi-value (exactly 2 candidates).
  • The pivot 'sees' both wings; wings may or may not see each other.
  • Look for bi-value cells and check if they form the XY-YZ-XZ pattern.