The XY-Wing pattern may be found in more difficult sudoku puzzles. Despite the similar name with X-Wing, these two techniques have nothing else alike. The XY-Wing Technique allows for candidates elimination instead of placing a number. Here is a typical XY-Wing pattern:
This is a partial puzzle, where XY and XZ must be in the same row but different blocks, while XY and YZ must be in the same column but different blocks. Therefore, the cell masked with an asterisk cannot be Z. This is because:
So we can safely remove Z from the candidates for the marked cell. Here is an example:
In the puzzle above, suppose X=3, Y=9 and Z=5. So [F3] is XY, [F6] is XZ, and [I3] is YZ. Based on the analysis above, the candidate 5 can be eliminated from the candidates in cell at [I6].
There is another XY-Wing pattern which is more common to be seen:
In this pattern, XY and YZ are in the same block. The result is the same, that is all cells marked with an asterisk cannot be placed with Z. It is easy to understand why so we don't explain it more. Let's see an example:
In the puzzle above, suppose X=4, Y=9, and Z=7. So [D7] is XY, [D2] is XZ, and [E8] is YZ. Based on the analysis above, the candidate 7 can be eliminated from the candidates in cells at [E2] and [D8].
Of course, we can also expect the second pattern of XY-Wing has a vertical variation:
Below is an example of this pattern:
In the puzzle above, suppose X=3, Y=2, and Z=6. So [I8] is XY, [B8] is XZ, and [G9] is YZ. Based on the analysis above, the candidate 6 can be eliminated from the candidates in cells at [A9], [B9], [C9] and [H8].
Here are some more examples that apply this techniques:
See Also:
