XYZ-Wing
Short answer: an XYZ-Wing is an XY-Wing whose pivot carries the shared shape too. The pivot holds three candidates, each wing holds two, and all three cells could be the shared shape. So one of the three must be it — and any cell seeing all three loses that shape.
What an XYZ-Wing looks like
Written out, the pivot is XYZ, one wing is XZ and the other YZ. Z is in all three cells, which is the whole difference from an XY-Wing: there, the pivot could not be Z, so only the wings mattered. Here the pivot is in the running too, and the elimination has to account for it.
That extra candidate makes the pattern weaker, not stronger. The target now has to see three cells instead of two, which is a much harder condition to satisfy — in practice it usually means the target sits in the same box as the pivot.
How to use an XYZ-Wing
- Start from a three-candidate cell. Take a cell with exactly three candidates as the pivot. This is the one wing technique that does not begin with a two-candidate cell, which is partly why it gets overlooked.
- Find two wings inside it. Look for two two-candidate cells the pivot can see, each of whose candidates are both among the pivot’s three. Between them the wings must use all three shapes.
- Identify the shared shape. The shape both wings have in common is Z — the one that will be eliminated. It is necessarily in the pivot as well, since the wings only use the pivot’s candidates.
- Strike where all three can be seen. Remove Z from every cell that sees the pivot and both wings. Because that is a strict condition, look first in the box the pivot sits in.
If your pivot has only two candidates you are looking at an XY-Wing instead, which eliminates more freely. Both are worth learning as one habit — the search overlaps almost entirely.
XYZ-Wing vs XY-Wing
The pattern is nearly identical, and the difference is entirely in the pivot. In an XY-Wing the pivot cannot be Z, so only the two wings can supply it and a target only has to see those two. In an XYZ-Wing the pivot can be Z as well, so a target has to see all three cells to be ruled out. More candidates in the pattern means fewer eliminations from it — which is a good general instinct for these techniques.
Find XYZ-Wing in your own grid
Paste a puzzle and this page will look for XYZ-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
Why does the target have to see all three cells?
Because all three could be Z. The elimination says "one of these cells is Z", and a cell is only ruled out if it shares a unit with every candidate for that claim. Miss one and the shape might be sitting in the cell you did not check.
Where do the eliminations usually land?
Almost always in the pivot’s box. Seeing three specific cells at once is restrictive, and the common arrangement has the pivot and one wing in the same box, with the target joining them there. If you cannot find a target, the pattern is real but idle.
Do the wings need to be different from each other?
Yes — between them they must use all three of the pivot’s shapes. Two wings with identical candidates would just be a pair, and would tell you something simpler and stronger about the unit they share.
Is there a WXYZ-Wing too?
There is — a four-candidate pivot with three wings, following the same logic again. It is genuinely rare and rarely necessary; by the time you are hunting for one, a colouring chain will usually have cracked the grid already.