Mirrored from Sudopedia, the Free Sudoku Reference Guide
The shortest XY-Chain is an XY-Wing with only 3 cells.
The following example shows a XY-chain resulting in an elimination.
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=6 and r8c1=1, 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.
A single inference xy-chain is also useful for finding a wrap rather than a trap as in the above example. To illustrate this consider rows 6 and 7 of a puzzle shown below.
The 3 digits in column 5 are a conjugate pair. Now r7c5 = 3 implies r7c2 = 7 implies r7c8 = 8 implies r6c8 = 7 implies r6c5 = 3, which is a wrap. Therfore r7c5 = 4 and r6c5 = 3.