XY-Chain: a chain of bi-value cells
The XY-Chain links several cells that each hold exactly two candidates into a chain. It generalises the Y-Wing to any length and cracks spots where every simpler technique fails. Click through an example below.
Interactive example
Click ‘Step’ to see the chain and the elimination.
Try it: XY-Chain
How the XY-Chain works
Build a chain of cells that each hold exactly two candidates. Two consecutive cells must see each other, that is lie in the same row, column or box, and share the digit that links them. If the first and last cell of the chain both have the same digit X as their other candidate, then no matter how you follow the chain, at least one of the two ends carries X. Any cell that sees both ends of the chain therefore cannot hold X and it is removed there. The Y-Wing is the special case of such a chain with exactly three cells.
More techniques
Y-Wing · X-Wing · Skyscraper