XYZ-Wing

Level 7 · Green Belt

Strategy:

Requires:

Learn after:

Overview

XYZ-Wing extends XY-Wing by having the pivot cell contain three candidates. The pivot has {X,Y,Z}, while wings have {X,Z} and {Y,Z}. Z can be eliminated from cells seeing all three.

How It Works

Find a pivot cell with candidates {X,Y,Z}.
Find two wings: one with {X,Z}, another with {Y,Z}.
The pivot sees both wings.
Eliminate Z from cells that see all three cells.

Example

Look for XYZ-Wing.

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

1

XYZ-Wing

Find a pivot cell r4c6 with THREE candidates (XYZ), connected to two wing cells.

Sudoku grid illustrating step 1: XYZ-Wing — Find a pivot cell r4c6 with THREE candidates (XYZ), connected to two wing cells.

2

XYZ-Wing

The wings r6c4 and r8c6 each have two candidates that are subsets of XYZ.

Sudoku grid illustrating step 2: XYZ-Wing — The wings r6c4 and r8c6 each have two candidates that are subsets of XYZ.

3

XYZ-Wing

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

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

4

XYZ-Wing

One of the three cells must contain 9, so these cells seeing all three cannot keep it: r5c6.

Sudoku grid illustrating step 4: XYZ-Wing — One of the three cells must contain 9, so these cells seeing all three cannot keep it: r5c6.

5

XYZ-Wing

Remove 9 from the cells that see all three: r5c6.

Sudoku grid illustrating step 5: XYZ-Wing — Remove 9 from the cells that see all three: r5c6.

6

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

The pivot has 3 candidates; wings have 2 each.
Eliminations are limited to cells seeing all three pattern cells.
This is often more restrictive than XY-Wing but still useful.