Tier 5
XY-Chain
A chain through two-candidate cells, entering on one digit and leaving on the other.
Also called XY-Chain.
Link two-candidate cells so that each shares one of its digits with the next. Assume the first cell is not the target digit; it must then be its other candidate, which forces the next cell, and so on down the chain.
If the far end comes out as the target digit, then either the first cell was the target or the last one is. Either way one of the ends holds it, and any cell seeing both ends loses that candidate.
A worked example
A real position, with the pencil marks a solver would have at that point.
the pattern · what it rules out · 5 a candidate that goes
What it proves. XY-Chain on 1: R2C6 → R2C9 → R3C8 forces R2C6 or R3C8 to be 1, so 1 leaves R2C8, R3C4.
Builds on Y-Wing.