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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:

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

• WXYZ-Wing

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

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