WXYZ-Wing

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-Wing, Sudoku solving technique,picture 1

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.

Extended form of the WXYZ-Wing

The idea from the extended form of the WXYZ-Wing comes from the following observation:

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.

Type 1

WXYZ-Wing, Sudoku solving technique,picture 2

We can perform the same eliminations for Z on the starred cells so long:

Type 2

WXYZ-Wing, Sudoku solving technique,picture 3

We can perform the same eliminations for Z on the starred cells so long:

Example

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

WXYZ-Wing, Sudoku solving technique,picture 4

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.

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