WXYZ-Wing
The WXYZ-Wing — sometimes called a Bent Quad — is the four-cell big brother of the XYZ-Wing. It's an expert-level pattern, seldom needed, but it rounds out the wing family and handles grids where nothing smaller moves.
What is a WXYZ-Wing?
Take four cells that between them use exactly four candidates — call them W, X, Y and Z. The four cells are "bent": they span one box and one line, so they don't all lie in a single unit. Pick the digit Z that is not restricted to a single unit within the group (it appears in cells across both the box and the line). The logic of the bent set guarantees that Z must be placed somewhere inside the group — so any cell outside the group that can see every Z-candidate cell within it cannot be Z.
In plain terms: like the XYZ-Wing, one of the group's cells must take the shared digit, and that forces Z out of the cells that see all its possible homes.
A WXYZ-Wing on digits 1–4: four cells — r1c1{3,4}, r1c5{1,3}, r3c1{2,4}, r3c2{1,2} — bent across row 1 and box 1. Digit 1 (Z, amber) is the one not locked to a single unit; the set forces a 1 into r1c5 or r3c2, so r1c2 — seeing both — loses its 1.
Where it sits
The WXYZ-Wing is really a small, readable case of a much more general technique, ALS-XZ (almost locked sets). The whole wing family — XY, XYZ, WXYZ — are increasingly large bent sets sharing a single "restricted common" digit. If you enjoy these, ALS techniques are the natural next step.
Is it worth learning?
For most solvers, the XY- and XYZ-Wings cover the ground you'll actually meet. The WXYZ-Wing is one for enthusiasts and for the hardest hand-crafted puzzles — worth knowing exists, and satisfying when you spot one, but rarely the only way through a grid.
Common mistakes
- More than four candidates. The four cells must use exactly four digits between them.
- Wrong Z. The shared digit must be the one that isn't locked to a single unit within the group.
- Target doesn't see all Z cells. The elimination only holds for cells seeing every possible home of Z in the group.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.