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