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XY-Wing

An XY-Wing is a very advanced technique which can eliminate certain candidates from squares. Its name comes from the pattern formed by the numbers and is not related to X-Wing.

We are looking for three squares, each of which contains exactly two numbers. The first square contains XY and we require a buddy of this square to contain XZ. We then require another buddy of the XY square to contain YZ.

Any squares that are buddies to both XZ & YZ cannot contain Z. Why? Because it doesn't matter whether the XY is X or Y, the Z will be in either XZ or YZ and hence can be removed from their buddies.

Sudoku Image

In this Sudoku X=5, Y=7 & Z=3. R3C9 is XY. R6C9 is XZ. R3C5 is YZ. So no buddies of both R6C9 and R3C5 can contain <3>

Sudoku Image

In this Sudoku X=2, Y=5 & Z=3. R4C6 is XY. R6C5 is XZ. R7C6 is YZ. So no buddies of both R6C5 and R7C6 can contain <3>.


 

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