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The XYZ-Wing
Learn the XYZ-Wing: a three-candidate pivot with two bi-value pincers sharing a digit Z, eliminating Z from any cell that sees all three.
The XYZ-Wing is the XY-Wing with a heavier pivot. The pivot cell holds three candidates {X,Y,Z}, and it sees two bi-value pincers, {X,Z} and {Y,Z}, that share the digit Z. All three cells contain Z.
Whatever value the pivot takes, one of the three cells is forced to be Z — so any cell that can see the pivot and both pincers cannot be Z, and you remove it there. Because the eliminating cell must also see the pivot, the targets are usually inside the pivot’s box.
It is a small but powerful step up from the XY-Wing and often appears on the same expert boards. The example highlights the trivalue pivot, its two pincers and the Z it removes.
Practise the XYZ-Wing
The best way to learn a technique is to use it. Play a puzzle at the level where it first appears, or drop a tricky board into the solver to watch it in action.
Frequently asked questions
What is an XYZ-Wing?
A pivot cell {X,Y,Z} that sees two bi-value pincers {X,Z} and {Y,Z}. Since one of the three cells must be Z, any cell seeing all three loses Z.
How is an XYZ-Wing different from an XY-Wing?
In an XY-Wing the pivot has two candidates and does not itself contain Z, so eliminations only need to see both pincers. In an XYZ-Wing the pivot also holds Z, so the eliminated cell must see the pivot too — making the targets fewer and closer.
Where are XYZ-Wing eliminations found?
Usually in the box shared by the pivot and a pincer, because the victim must see all three pattern cells at once.
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