XY-Wing is a more advanced strategy that commonly appears in my more difficult puzzles starting with the Tough volumes. In my experience, this configuration appears more often than X-Wing, but it is also more difficult to spot.
This is effectively a three link xy-chain, or is similar to a short forcing chain consisting of two links for each candidate, but instead of placing a number, it allows for candidate elimination. This a very common pattern in the harder puzzles.
In the partial Sudoku puzzle below, consider the cells that have only the candidates shown:
It can be easily seen that whichever value is in XY, the cell marked with the asterisk cannot be Z.
if XY = X, then XZ = Z, so * cannot be Z
if XY = Y, then YZ = Z, so * cannot be Z
This allows Z to be eliminated from the candidates for the marked cell.
The cells don't need to form a perfect rectangle, but the cells containing XY and XZ
need to be buddies (sharing the same container), and the cells containing XY and YZ
also need to be buddies (sharing a different container). Once you've got this arrangement, you can eliminate Z from
the candidates of all cells that occupy the intersection of the containers containing XZ and YZ.
Other possible combinations:
The astute among you will notice both the above examples have XY, XZ and YZ in the same relative locations, and so can be combined to give:
All the cells marked with an asterisk can have Z removed from their candidates.
In the Sudoku puzzle below, the XY-wing in the green cells allows the 7s marked in blue to be eliminated.
