XYZ-Wing

Level 8 · Blue Belt

Strategy:

Wings

Requires:

XY-Wing

Learn after:

WXYZ-Wing

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

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

Example

Starting position

Look for XYZ-Wing.

1

Find the XYZ-Wing pivot r2c6

Find a three-candidate pivot cell r2c6 connected to two wing cells.

2

Wing cells r1c6 and r2c2 fit within XYZ

The wings r1c6 and r2c2 each have two candidates that are subsets of XYZ.

3

XYZ-Wing pattern

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

4

Cells seeing all three lose 6

One of the three cells must contain 6, so these cells seeing all three cannot keep it: r2c5.

5

Remove 6 from common peers

Remove 6 from cells that see the pivot and both wings: r2c5.

6

Result

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.