XY-Wing

Level 6 · Orange Belt (Green Stripe)

Strategy:

Requires:

Learn after:

XY-Chain 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

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

Example

Look for XY-Wing.

Sudoku grid showing the initial puzzle state for Look for XY-Wing.

1

XY-Wing

Find a pivot cell r7c2 with two candidates, connected to two 'wing' cells.

Sudoku grid illustrating step 1: XY-Wing — Find a pivot cell r7c2 with two candidates, connected to two 'wing' cells.

2

XY-Wing

The wings r9c3 and r9c7 share a candidate not in the pivot - this is the elimination digit.

3

XY-Wing

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

Sudoku grid illustrating step 3: XY-Wing — This is an XY-Wing - the shared candidate is eliminated from common peers.

4

XY-Wing

Either wing must contain 8, so eliminate from cells seeing both wings: r7c7, r7c8 and r9c1.

Sudoku grid illustrating step 4: XY-Wing — Either wing must contain 8, so eliminate from cells seeing both wings: r7c7, r7c8 and r9c1.

5

Result after applying the technique.

Sudoku grid showing the 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.