Mirrored from **Sudopedia**, the Free Sudoku Reference Guide

# XYZ-Wing

The **XYZ-Wing** is an extension of the XY-Wing. The pivot cell also carries the **Z** candidate.

Upto 2 candidates can be eliminated by an XYZ-Wing, because they need to share an intersection with the pivot. The following diagram shows how it works:

.-----------.----------.----------.
| * * XYZ | . . . | YZ . . |
| . . . | . . . | . . . |
| XZ . . | . . . | . . . |
:-----------+----------+----------:

The pivot has candidates **XYZ**. The implications of each option are:

- X
- the
**XZ** pincer will contain digit **Z**. This digit is eliminated from the starred cells.
- Y
- the
**YZ** pincer will contain digit **Z**. This digit is eliminated from the starred cells.
- Z
- the pivot eliminates
**Z** in the starred cells.

Under all circumstances, the starred cells will lose their candidates for digit **Z**.

## ALS Alternative

The XYZ-Wing can be replicated by an ALS-XZ move.

Consider set r1c37. 2 cells, digits XYZ.
Consider set r3c1. 1 cell, digits XZ.
X is common restricted. It cannot appear in both sets at the same time. One of these sets will be locked for the remaining digits.
r1c12 can see all candidates for digit **Z** in both sets. Since one of these sets will be locked with digit **Z**, we can eliminate digit **Z** from r1c12.

This is the Eureka notation for the ALS alternative:

(Z)r1c12-(Z=YX)r1c37-(X=Z)r3c1-(Z)r1c12 => r1c12<>Z

XYZ-Wings can also be replicated by Aligned Pair Exclusion, by pairing one of the target cells with the **XYZ** cell.

## See Also

This page was last modified 06:55, 7 November 2006.