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The '''WXYZ-Wing''' is an extension of the [[XYZ-Wing]], and is sometimes called '''XYZW-Wing'''. Seeing the extension of XYZ-Wing to WXYZ-Wing, one can further extend the [[technique]] to VWXYZ-Wing, UVWXYZ-Wing and so on.

== Simplest form of the WXYZ-Wing ==

.-----------.----------.----------.
| * * WXYZ| . XZ . | YZ . . |
| . WZ . | . . . | . . . |
| . . . | . . . | . . . |
:-----------+----------+----------:

Similar to the XYZ-Wing, the [[pivot]] has the [[candidates]] '''WXYZ'''. In all possible options for the pivot [[cell]], '''Z''' will be [[eliminate]]d from the starred cells.

== Extended form of the WXYZ-Wing ==

The idea from the extended form of the WXYZ-Wing comes from the following observation:
* If the '''WZ''' is '''W''', then the '''WXYZ''' (which becomes '''XYZ'''), '''XZ''' and '''YZ''' cells form a [[naked subset]], and so '''Z''' can be eliminated from the starred cells.
* If the '''WZ''' is '''Z''', then obviously '''Z''' can also be eliminated from the starred cells.

Put another way, observe that there are two [[almost locked set]]s: (a) '''WXYZ''', '''XZ''' and '''YZ'''; and (b) '''WZ'''. Then the [[ALS-XZ]] rule can be applied with '''W''' being the restricted common, so '''Z''' can be eliminated from the starred cells.

=== Type 1 ===

.-----------.----------.----------.
| * * WXYZ| . XYZ. | XYZ. . |
| . WZ . | . . . | . . . |
| . . . | . . . | . . . |
:-----------+----------+----------:

We can perform the same eliminations for '''Z''' on the starred cells so long:
* The '''WXYZ''' and the two '''XYZ''' cells form an [[almost locked set]].
* The '''WXYZ''' and '''WZ''' cells belong to the same box.
* Each of the four cells may contain a subset of the candidates as shown, e.g. the '''WXYZ''' cell may contain only '''XZ'''.
* One of the '''XYZ''' cells may appear in the same box as '''WZ''', in which case the '''XYZ''' cell may also have '''W''' as a candidate.

=== Type 2 ===

.-----------.----------.----------.
| * * WXYZ| . . . | WZ . . |
| XYZ. . | . . . | . . . |
| . XYZ. | . . . | . . . |
:-----------+----------+----------:

We can perform the same eliminations for '''Z''' on the starred cells so long as:
* The '''WXYZ''' and the two '''XYZ''' cells form an [[almost locked set]].
* The '''WXYZ''' and '''WZ''' cells belong to the same line.
* Each of the four cells may contain a subset of the candidates as shown, e.g. the '''WXYZ''' cell may contain only '''XZ'''.
* One of the '''XYZ''' cells may appear in the same line as '''WZ''', in which case the '''XYZ''' cell may also have '''W''' as a candidate.

== Example ==

This is a Type 1 WXYZ-Wing (marked yellow) which leads to the elimination of 4 from the blue cell.

[[Image:WXYZWing.png]]

== WXYZ-Wing as an ALS-XZ ==

The WXYZ-Wing can be replicated as an [[ALS-XZ]] move by considering the '''XZ''' cell as an [[ALS]] and the other three cells as the other ALS, with '''W''' as a [[restricted common]].

== External link ==

* [http://forum.enjoysudoku.com/extension-of-xyz-wing-t1169.html Extension of xyz-wing]

== See also ==

* [[XYZ-Wing]]
* [[ALS-XZ]]

[[Category:Solving Techniques]]

WXYZ-Wing - Revision history

Rooted: Created page with "The '''WXYZ-Wing''' is an extension of the XYZ-Wing, and is sometimes called '''XYZW-Wing'''. Seeing the extension of XYZ-Wing to WXYZ-Wing, one can further extend the t..."