XY-Chain and Remote Pairs

Start with a bi-value cell {A,B}. The next cell sees it and holds {B,C}, the next {C,D}, and so on, up to an end cell that contains A. If the start cell is not A, it is B; that makes the second cell C, the third D, and so on, until the end cell must be A. So at least one of the two end cells is A.

Remove A from every cell that sees both ends. A Remote Pair is the special case where every cell of the chain holds the same two digits.

Notation

XY-Chain: 5 can be removed from r3c3. chain: 5 in r3c6 → 3 in r3c6 → 3 in r4c6 → 9 in r4c6 → 9 in r9c6 → 7 in r9c6 → 7 in r9c3 → 5 in r9c3.