XY-Chain

XY-Chain links bivalue cells (cells with exactly 2 candidates) through shared candidates. Each consecutive pair of cells shares a candidate, creating alternating strong and weak inferences that force eliminations.

Technique

1. Find bivalue cells that share a candidate with neighboring bivalue cells.
2. Build a chain where consecutive cells share one candidate, alternating which is the shared digit.
3. The first and last cells must share a common candidate on their strong links.
4. Eliminate that common candidate from cells seeing both endpoints.

Tips

• XY-Chains extend XY-Wing to longer chains.
• Every cell in the chain must have exactly 2 candidates.
• The key insight: the common candidate at the endpoints must be in at least one endpoint, so cells seeing both can't have it.