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# 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:

the XZ pincer will contain digit Z. This digit is eliminated from the starred cells.
the YZ pincer will contain digit Z. This digit is eliminated from the starred cells.
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.