XY-Chain

A XY-Chain is a chain of cells which each contain only 2 candidates.

Because the chain is entirely made up by bivalue cells, the link between the 2 candidates in each cell cause strong inference, which allows us to use weak inference between the cells.

The shortest XY-Chain is an XY-Wing with only 3 cells.

A XY-Chain is both a Double Implication Chain and a Alternating Inference Chain.

Example

The following example shows a XY-chain resulting in an elimination.

XY-Chain , How to solve sudoku puzzles - Solving sudoku strategy,picture 1

This chain involves four cells. In Eureka notation:

(5=1)r3c3-(1=6)r7c3-(6=1)r8c1-(1=5)r8c5

What does this XY-chain mean? Note that both ends of the chain involves the digit 5 as a candidate. Now, if r3c3<>5, then we have r3c3=1, which implies r7c3=1 and so r8c5=5. Similarly, by reversing the direction, if r8c5<>5, then r3c3=5. Thus, this is a Double Implication Chain and we showed that either r3c3=5 or r8c5=5. This means that any cell that is seen by both r3c3 and r8c5 cannot contain the digit 5, so we eliminate 5 from r3c5.

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