This is an extension of XYZ-Wing that uses four cells instead of three. Each possible value of the hinge cell results in a Z value in one of the cells in the WXYZ-Wing pattern, thus leaving no room for a Z on any cell all four can 'see'.

13th April 2013. A larger discussion fo these wings and some excellent variants by strmckr are posted on this page. I will be attempting to learn from these in the next update of the solver.

Its name derives from the four numbers W, X, Y and Z that are required in the hinge. The outer cells in the formation will be WZ, XZ and YZ, Z being the common number.

WXYZ-Wing theory

In this example our four-value hinge is B4 marked in brown. The three outlier cells, marked in yellow each contain a 3 (our Z) plus one other number unique to themselves and the hinge. It's important that these extra numbers really are common only to the hinge and there are no pairs like 3/6 and 3/6 in two of the yellow cells. There is only one cell that all four of the WXYZ can see - C4. It has a 3 which can be removed. No matter what number is the final solution in the hinge, one of the WXYZ must be a 3. Note (10 Oct 2011): Due to changes in the solver the previous example became outdated without turning off lots of strategies. This new example seems 'necessary' in the sense that no prior strategies make progress - and its therefore quite interesting.

WXYZ-Wing example: Load Example or : From the Start