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Points. An XY-Chain is a chain made of 3 or more cells, each with only 2 candidates (bi-value cells). Each cell is a truth.  A chain of N cells will have N+1 covering links, thus all XY-Chains are rank 1.  The shortest XY-Chain with 3 cells is also called an XY-Wing.


XY-Chain Example 1 An XY-Chain of length 5 (5 cells) connected through two box links, 1 row  link, and 1 column kink. Candidate 9r8c2 sees both ends of the chain and is eliminated.




Reasoning by truths and covers, 5 truths are covered by 6 covers thus anywhere 2 covers overlap will eliminate candidates. In this case r8c2<>9.



XY-Chain Example 2 Another XY-Chain with a length of 5 cells. 

XY-Chain, dual ends. A rather long XY-Chain with a length of 8 cells. The ends of the chain are in cell r3c3 and r8c2. The ends of the chain overlap in two places b1 and b7 to eliminate 3 candidates.