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.

Works Classic Sudoku An expert wing for the toughest Classic grids. → Limited Killer Sudoku Almost never reached in Killer. → Limited Sudoku X Simpler patterns usually win first. → Limited Samurai Sudoku Overkill for Samurai. →

Where to practise this

This technique starts paying off at Evil, which is where puzzles first stop yielding to anything simpler. Reading about a pattern and spotting it on a live grid are different skills - the second one only comes from playing.

Play Evil Sudoku About Evil Sudoku

Related techniques

XYZ-Wing Sudoku Technique Explained A pivot with three candidates and two bi-value pincers remove the shared digit from any cell that sees all three wing cells. Jellyfish - the Order-4 Sudoku Fish One digit confined to the same four columns across four rows (or vice versa) - eliminate it from the rest of those columns. Finned Swordfish - Sudoku Fish Variation An almost-Swordfish with one extra candidate; the digit is eliminated only from cover cells that also see the fin. BUG+1 - Bi-Value Universal Grave Technique When all cells but one are bi-value, the extra candidate in that one cell must be the solution, or the puzzle would have two answers.