The XYZ-Wing is a close cousin of the Y-Wing.
While the Y-Wing uses a pivot with two candidates (XY), the XYZ-Wing uses a pivot with three candidates (XYZ).
It is slightly harder to spot because the "pincers" look less like a clean pair, but the logic is just an extension of the same principle.
Interactive Example
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Click "Apply Logic" to see the strategy in action.
Real Example Explanation
In the example above, look at the Pivot cell R3C5 (Box 2):
- The Pivot:
- R3C5 contains candidates {1, 6, 7} (let's call them X, Y, Z).
- The Wings:
- Wing A: R5C5 contains {1, 7} (XZ). It sees the Pivot via Column 5.
- Wing B: R1C6 contains {6, 7} (YZ). It sees the Pivot via Box 2.
- Notice that both Wings share the "Z" value (7) with the Pivot.
- The Logic:
- The Pivot (R3C5) must be 1, 6, or 7.
- If Pivot is 1: Then Wing A (R5C5) forces 7.
- If Pivot is 6: Then Wing B (R1C6) forces 7.
- If Pivot is 7: Then the Pivot itself is 7.
- Conclusion: No matter what the Pivot is, one of these three cells must be a 7.
- The Elimination:
- Any cell that sees ALL THREE parts of the formation (Pivot, Wing A, and Wing B) cannot be a 7.
- R1C5 sees the Pivot (same box), Wing A (same column), and Wing B (same row).
- Therefore, we can eliminate 7 from R1C5.
How to Spot It
- Find a Pivot: Look for a cell with three candidates (XYZ).
- Find the Wings: Look for two bivalue cells that:
- Share a unit with the Pivot.
- Contain only candidates from the Pivot (one XZ, one YZ).
- Check Visibility: The key difference from a Y-Wing is the elimination zone.
- Eliminate: Identify the cell(s) that see the Pivot AND both Wings. Remove the common digit (Z).
Comparison: Y-Wing vs XYZ-Wing
- Y-Wing: Pivot has 2 candidates. Eliminations are found where the Wings intersect.
- XYZ-Wing: Pivot has 3 candidates. Eliminations are found where Pivot + Wings all intersect (usually just 1 or 2 cells).