127.0.0.1: Created page with "The '''XYZ-Wing''' is an extension of the XY-Wing. The pivot cell also carries the '''Z''' candidate. Up to 2 candidates can be eliminated by an XYZ-Wing, bec..."

2021-10-25T15:42:22Z

Created page with "The '''XYZ-Wing''' is an extension of the XY-Wing. The pivot cell also carries the '''Z''' candidate. Up to 2 candidates can be eliminated by an XYZ-Wing, bec..."

New page

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

Up to 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]]

[[Category:Solving Techniques]]

XYZ-Wing - Revision history

127.0.0.1: Created page with "The '''XYZ-Wing''' is an extension of the XY-Wing. The pivot cell also carries the '''Z''' candidate. Up to 2 candidates can be eliminated by an XYZ-Wing, bec..."