WXYZ-Wing
Short answer: a cell holding four shapes, plus three two-shape cells that all see it and all contain the same one of those four. Between them the four cells use exactly four shapes. Any cell that sees all four of them cannot hold the shared shape.
What a WXYZ-Wing looks like
The wings grow one cell at a time. An XY-Wing is a two-shape pivot with two wings; an XYZ-Wing gives the pivot a third shape; a WXYZ-Wing gives it a fourth and adds a third wing. The count is always the same: n cells using n shapes, all hinged on one cell.
Here is why it works. Suppose the target cell really were the shared shape. It sees all four pattern cells, so it takes that shape away from every one of them — and each wing then collapses onto its other shape. Those three are all different, they all see the pivot, and the pivot has nothing left to be. That is a contradiction, so the target is not the shared shape.
How to use a WXYZ-Wing
- Start from a four-candidate cell. These are uncommon enough to be a good anchor. Note its four shapes — that is the whole vocabulary the pattern is allowed to use.
- Collect wings that see it. Look for two-candidate cells that see the pivot and whose shapes are both among the pivot’s four. You need three of them.
- Check the arithmetic. One shape must appear in all three wings — that is the shape you will strike. The wings’ other three shapes must all be different, so the four cells together use exactly four shapes and no more.
- Find a cell that sees all four. Remove the shared shape from any cell that sees the pivot and all three wings. Seeing three of the four is not enough: the pivot holds the shape too, so a cell that misses it is untouched.
If only two wings line up, you have an XYZ-Wing — worth checking first, because its elimination is easier to find. Solvers also recognise a looser ALS form of the WXYZ-Wing, where the four cells need not be a pivot and three bivalue wings at all; it eliminates more, but there is nothing to draw and nothing to hinge on, so this page teaches the tight version.
WXYZ-Wing vs XYZ-Wing
Same argument, one size up, and the same tightening comes with it. An XY-Wing eliminates from cells seeing both wings; an XYZ-Wing needs the pivot too, because the pivot also holds the shared shape; a WXYZ-Wing needs all four for the same reason. Each extra cell buys you a rarer pattern and a smaller target zone, which is why the family is worth learning in order rather than skipping to the end.
Find WXYZ-Wing in your own grid
Paste a puzzle and this page will look for WXYZ-Wing in it — the same pattern shown above, in your grid instead of ours. Nothing is uploaded; it runs in your browser.
Frequently asked questions
Must the target see the pivot?
Yes, and this is the usual mistake. The pivot holds the shared shape as well, so a cell that sees the three wings but not the pivot has no argument against it — the pivot could simply take the shape instead. The target must see all four cells.
Do the wings have to see each other?
No. Only the pivot needs to see each wing. The wings can be anywhere as long as each one sees the pivot and holds two of the pivot’s four shapes.
What if two wings hold the same pair?
Then the four cells do not use four shapes between them, and the pattern is not a WXYZ-Wing. It may still be something else — two identical pairs are a naked pair, which is a much easier move.
Is this the same as an almost locked set?
The general version is: a WXYZ-Wing can be described as a four-cell set with one shape too few, joined to a bivalue cell. That form is more powerful and eliminates more, but it has no pivot and no clean picture, so it belongs to solver software more than to a person with a pencil.