

WXYZWing
This is an extension of XYZWing that uses four cells instead of three. A.k.a. Bent Quads.
I am grateful to SudoNova posting below and StrmCkr who posted about this strategy way back when on this page. I only got round to appreciating the insights recently but the much expanded version of WXYZ is now in version 1.96+ of the solver. Previously I'd restricted the scope to a very narrow definition. Using one of my test libraries, the 50k set from Ruud, I increased the detection from 299 instances to 8313, so it is definitely worth looking out for.
I'm going to start with my narrow definition if only to show how this is an extension of the threecell XYZWing.
Its name derives from the four numbers W, X, Y and Z that must be in exactly four cells. In my narrow definition we need a hinge cell containing all four candidates WXYZ and three outlier cells each containing a pair wZ, xZ and yZ  Z being the common number.
The easy principle is that each possible value of the hinge cell results in a Z value in one of the cells in the WXYZWing pattern, thus leaving no room for a Z on any cell all four can 'see'.

WXYZWing theory 
That's the narrow definition and a glance at XYZ Wing will show you its the same idea plus one more cell. You could expand it to a five cell pattern and five numbers.
Now, lets consider StrmCkr's more general definition: WXYZWings can be considered as a group of 4 cells and 4 digits, that has exactly one nonrestricted common digit. We use that digit (Z) to eliminate since at least one of Z will be the solution.
So what is a nonrestricted common digit?
Well, a restricted digit is one where all the instances of candidate N in the pattern can see each other. On the diagram to the left I have connected the W candidates  because they share the same box, and I can connect the Xs and Ys as they share a row. Only Z is nonrestricted because some of the Zs  ie the one in C1 CANNOT see the Zs in B4 and B5.

NonRestricted Common Digit 
In the first example I show a classic WYXZ wing  in that it has all four candidates (1/2/5/9) in the hinge cell D3 marked in brown. The three outlier cells, marked in yellow each contain a 9 (our Z) plus some of the other four candidates.
I have also marked in rings the spread of candidates 1, 2 and 5. You will see that both 1s can 'see' each other because they are in the same box. The 2s can 'see' each other because they are on the same row and the three 5s can all see each other since they share the same row as well. That makes 1, 2 and 5 restricted in the four cell pattern.
Candidate 9 is different. At least one 9 (in F1) cannot see at least one other 9 (infact both 9s in D4 and D5). That makes it the only nonrestricted candidate.

WXYZWing example 1: Load Example or : From the Start 
Any WXYZ elimination will always be made on the nonrestricted candidate. We are looking for a 9 elsewhere that can see every 9 in the four cells of our WXYZ pattern. That 9 is on D2.
It is important to note is that StrmCkr's rule says nothing about the hinge requiring four candidates and the other cells two. Like Quads, we need in total four candidates in four cells. This is a fourcell Locked Set. StrmCkr makes this point in his second corollary, So lets look at some examples where the is a thinner spread of four candidates.
Interestingly, where Z is present in less than four cells, ie three or just two cells of the four  more eliminations are possible because there are less cells that the eliminated candidates need to 'see'. I believe my new implementation WXYZ gives more variants than the 10 StrmCkr lists as exemplars.
The second WXYZ example is orientated in columns rather than rows, but works the same. The hinge cell in D6 conspicuously fails to contain the nonrestricted candidate 5, but no matter. Whatever the final solution of D6 a 5 is forced into either E5 or one of the two cells G6/J6. The outliers are nice easy pairs  like my original narrow definition, but the improvement is not needing 5 (Z) in the hinge every time.
The solver tells us WXYZ Wing The four cells {D6,E5,G6,J6} contain in total 2/5/6/9. Candidate 5 determines the 'wing' cells (in yellow) and one or other of those 5s must be true. Therefore... 5 can be taken off F6 5 can be taken off G5 5 can be taken off J5

WXYZWing example 2: Load Example or : From the Start 
Here is an example where the nonrestricted common digit is present in just two pincer cells. We don't have to worry about 3s 'seeing' the brown cells as they don't have a 3 in them. Consider how the hinge cell in C1 solves when each digit is looked at. Suppose C1 is 4. That makes C8 contain 3/5. C8 + C3 + B2 now becomes an XYZWing  and eliminates 3s in the same way. Interesting!
The solver returns WXYZ Wing The four cells {C1,B2,C8,C3} contain in total 3/4/5/9. Candidate 3 determines the 'wing' cells (in yellow) and one or other of those 3s must be true. Therefore... 3 can be taken off B7 3 can be taken off B8 3 can be taken off B9

WXYZWing example 3: Load Example or : From the Start 
I'm ending this article with a nice Sudoku puzzle that has four YWings an XYZWings and four WXYZWings. Here is the first of the later. It is worth following this through on the solver from the start.

WXYZWing example 4: Load Example or : From the Start 
Where next? StrmCkr's gives a theory example of a "double restricted common in a WXYZWing when spanning the same band using boxbox restraints" which I will explore at a future date. We can also go in the direction of a five cell VWXYZWing but I think the next step is to exactly define the overlap and relationship with Almost Locked Sets  since a number of people have pointed out that these XWings are simple examples of ALSs.


