XY-Wing
XY-Wing uses three cells with two candidates each: a pivot with candidates XY and two wings with XZ and YZ.
Learn the techniqueXYZ-Wing
XYZ-Wing is like XY-Wing, but the pivot has all three candidates: XYZ.
See the technique in practice
Work through the examples step by step. Each step explains what you see on the puzzle and why the conclusion holds.
Example:
- We look at the cell at row 9, column 8. It has three candidates left, and one of them is 2. We call this cell the pivot.
- Look at the neighboring cell at row 9, column 7. It shares one of the pivot's other candidates and has 2 as the only other candidate itself.
- Look at the other neighboring cell at row 1, column 8. It shares the pivot's last candidate and also has 2 as the only other candidate.
- No matter which of the three digits the pivot ends up with, 2 lands either in the pivot itself or in one of the two neighbors. One of the three cells therefore always contains 2.
- Any cell that sees both the pivot and both neighbors therefore cannot have 2 either. We remove it from the notes in row 7, column 8.
How to recognize the pattern
XYZ-Wing looks like XY-Wing, but the pivot has all three candidates X, Y and Z. The wings see the pivot and have X and Z and Y and Z respectively. Because the pivot itself can also become Z, the pattern is slightly weaker than XY-Wing, and the removals apply to fewer cells.
No matter which of the three candidates the pivot ends up with, one of the three cells becomes Z. If the pivot becomes X, the wing with X and Z is forced to Z. If it becomes Y, the other wing is forced. And if it becomes Z, the pivot itself is Z. Therefore, Z can only be removed from cells that see all three, that is, both the pivot and both wings.
Step-by-step procedure
- Find a cell with exactly three candidates and call them X, Y and Z.
- Look for two cells with two candidates that see the pivot, where one has X and Z and the other has Y and Z.
- Find the cells that see the pivot and both wings at the same time.
- Remove Z from these cells.
Common mistakes
- Using XY-Wing removals. In XYZ-Wing, cells must see all three pattern cells, not just the two wings.
- Choosing the wrong shared digit. Z is the digit found in all three cells, and it is only Z that can be removed.
- Missing that all three cells must share an area. For a cell to see all three, the pattern lies in practice around a box, so search there.
When do you need the technique?
Puzzles at Extreme level require techniques that combine three or more cells in logical reasoning of the if-then type. Try your way through the examples below, step by step, using the same tools the solver uses on your own puzzle.
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