XY-Chain
A chain of two-candidate cells; when both ends carry the same spare digit, one of them must be it.
How it works
- 1Use only cells with exactly two candidates. Such a cell is a switch: rule out one of its digits and it must be the other.
- 2Link them into a chain where each pair of neighbours sees each other and shares a digit — that shared digit is what carries the inference from one to the next.
- 3Read it: if the first cell is not its spare digit z, it takes the shared digit, which forces the next cell off that digit and onto its own, and so on down the chain.
- 4Arrange the chain so both ENDS carry the same spare digit z. Then one end or the other must be z.
- 5Any cell seeing both ends loses z — it cannot be the digit that one of those two ends is certainly taking.