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

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.

## Contents |

.-----------.----------.----------. | * * 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 eliminated from the starred cells.

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 sets: (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.

.-----------.----------.----------. | * * 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.

.-----------.----------.----------. | * * 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.

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

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.