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XYZ-Wing

An XYZ-Wing is a very advanced technique which can eliminate certain candidates from squares and is a very similar technique to XY-Wing.

We are looking for three squares. This time the first square contains XYZ and we require a buddy of this square to contain XZ. We then require another buddy of the XYZ square to contain YZ.

Any squares that are buddies to all three squares, XYZ, XZ & YZ cannot contain Z. Why? Because no matter which way around the numbers go, the Z will be in one of the three squares.

In this Sudoku X=7, Y=8 & Z=9. R4C4 is XYZ. R4C2 is XZ. R6C4 is YZ. So no buddies of all three squares R4C4, R4C2 & R6C4 can contain <9>.

In this Sudoku X=7, Y=3 & Z=2. R3C3 is XYZ. R3C2 is XZ. R8C3 is YZ. So no buddies of all three squares R3C3, R3C2 & R8C3 can contain <2>.