XYZ-Wing
An XYZ-Wing is a three-cell, three-digit ALS-XZ construction. It combines a two-cell ALS A with a one-cell ALS B. Here X is the restricted common candidate (RCC), Z is the elimination digit, and Y is the third distinct digit. Z is a candidate in all three cells. A weak link on X connects the two sets and guarantees Z in at least one of them. An outside cell that sees all three cannot contain Z.
What is an XYZ-Wing?
An almost locked set (ALS) is a group of unsolved cells in one house — a row, column or box — with one more distinct candidate digit than cells. Read this XYZ-Wing as four parts:
- ALS A: the {X,Y,Z} cell and the {Y,Z} cell. They share a house and contain three distinct candidate digits across two cells.
- ALS B: the single {X,Z} cell. This bivalue cell is the smallest possible ALS: two candidate digits in one cell.
- RCC X: it occurs in the {X,Y,Z} cell of ALS A and the {X,Z} cell of ALS B. These cells see each other, giving a weak link (weak inference) between the two X occurrences. X can be placed in one set or neither, but never in both.
- Elimination digit Z: Z is a candidate in all three cells. A target outside both ALSs must see all three.
How to spot it
Build ALS A first: find a {X,Y,Z} cell and a {Y,Z} cell in one house. Next find ALS B, a {X,Z} cell that sees the {X,Y,Z} cell. This visibility establishes the RCC X and its weak link. Finally look for an outside Z candidate whose cell sees all three cells, because each of them has a Z candidate.
The logic
ALS B is a single {X,Z} cell, so it must contain either X or Z. If it contains Z, the construction already has Z. If it contains X, the weak link rules out X in ALS A. ALS A is then left with Y and Z for its two cells and must use both digits. In either case, at least one of the three cells must contain Z.
An outside cell that sees all three possible Z positions cannot contain Z: whichever position uses Z would conflict with it. Remove Z from that outside cell, not from the ALS cells themselves.