The WXYZ-Wing is an extension of the XYZ-Wing. The objective of using this technique is to eliminate a certain candidate instead of finding out a solution to a cell. Similar to XYZ-Wing, one of the cells (pivot) has the candidates WXYZ.

1. If WXYZ=W, then WZ=Z, so * cannot be Z. (Same block)
2. If WXYZ=X, then XZ=Z, so * cannot be Z. (Same column)
3. If WXYZ=Y, then YZ=Z, so * cannot be Z. (Same column)
4. If WXYZ=Z, then * cannot be Z. (Same block)

So whichever value is in WXYZ, the marked cell can never be Z. Here is an example:

In the puzzle above, suppose W=2, X=4, Y=6, and Z=5. So [A8] is WXYZ, [A9] is WZ, [F8] is XZ, and [G8] is YZ. Based on the analysis above, the candidate 5 can be eliminated from the candidates in cell at [B8].

The WXYZ-Wing pattern can also be like this:

Below is an example in this type:

In the puzzle above, suppose W=2, X=3, Y=7, and Z=1. So [G3] is WXYZ, [I1] is WZ, [G5] is XZ, and [G7] is YZ. Based on the analysis above, the candidate 1 can be eliminated from the candidates in cell at [G2].

Here are some more examples that apply this technique:

See also: ««  Direct Elimination Techniques  »» ««  Candidates Elimination Techniques  »»