XY-Chain
A chain of linked bivalue cells; if both ends contain z, a cell that sees both ends cannot be z.
Rule
A chain of bivalue cells whose two ends both contain z → remove z from cells that see both ends.
A chain of bivalue cells
A chain of 4 cells r8c8, r3c8, r1c9 and r5c9: each has only two candidates, and each sees the previous one and shares a digit with it. Both ends of the chain contain 1.
The idea
Each bivalue cell is a switch: if it is not one digit, it is the other. Link cells that see each other and share a digit, and you get a chain that propagates.
Suppose the first cell is not z → it is its other digit a → the next cell (holding a) is not a → it is its other digit b → … → the last cell is z. So if one end is not z, the other end is z: at least one end is z.
An XY-Wing is an XY-Chain of three cells. Longer chains are stronger but harder to find; start from the bivalue cells that see the cell you want to eliminate from.
How to spot it
- Draw the bivalue cells on paper, and connect cells that see each other and share a digit.
- Choose z as the digit at both ends and walk from one end.
Common mistakes
- Each link must go the right way: the digit "out" of one cell must be the digit "in" to the next.
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Related techniques
References
The examples on this page are generated from random puzzles, not taken from these sources.