The XYZ-Wing is an extension of the Y-Wing technique that involves a pivot cell with three candidates instead of two. The pattern uses one trivalue pivot cell and two bivalue wing cells. The pivot contains candidates {X, Y, Z}, one wing contains {X, Z}, and the other wing contains {Y, Z}. The pivot must be able to see both wing cells, forming the characteristic wing shape.
The logical reasoning mirrors the Y-Wing but with a slight twist. If the pivot is X, the first wing cannot be X, so it must be Z. If the pivot is Y, the second wing cannot be Y, so it must be Z. If the pivot is Z, then Z is already placed at the pivot. In every possible scenario, the digit Z appears in at least one of the three cells (the pivot or one of the wings). Therefore, any cell that can see all three of these cells simultaneously and contains candidate Z can have Z safely eliminated.
Because a cell must see all three XYZ-Wing cells for the elimination to apply, the scope of elimination is more restricted than in a Y-Wing. Typically, the eliminations happen within the box containing the pivot, where cells can see the pivot and both wings. Despite this limitation, the XYZ-Wing is a valuable technique that appears in many hard puzzles. Understanding it deepens your grasp of wing-based logic and prepares you for even more complex patterns like WXYZ-Wings and ALS-based techniques.
Try It Yourself
Walk through each step of the xyz-wing technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Look for an XYZ-Wing pattern. Cell (3,0) has candidates {3,5,8} making it a trivalue pivot. Examine nearby bivalue cells that share candidates with this pivot.
Step-by-Step Guide
Identify cells with exactly three candidates — these are potential pivots.
For a pivot with candidates {X, Y, Z}, find a wing cell visible to the pivot with candidates {X, Z}.
Find a second wing cell visible to the pivot with candidates {Y, Z}.
Confirm the shared candidate Z appears in the pivot and both wings.
Identify any cell that can see all three cells (pivot and both wings) and contains candidate Z.
Eliminate candidate Z from those cells, since Z must be in at least one of the three XYZ-Wing cells.
Imagine three friends who collectively must bring dessert to a party — no matter who forgets, at least one always brings cake, so anyone expecting cake from an outside source is out of luck.
The trivalue pivot creates a three-way case split over X, Y, and Z, and each case forces Z into at least one of the three cells: if the pivot is X, the {X,Z} wing must be Z; if the pivot is Y, the {Y,Z} wing must be Z; if the pivot is Z, Z is already placed. Since all three exhaustive cases guarantee Z occupies at least one of the three cells, any external cell that can see all three simultaneously cannot hold Z without creating a duplicate. The elimination scope is narrower than Y-Wing precisely because the pivot itself is a possible location for Z, requiring visibility to all three cells rather than just the two wings.
When to use: Use XYZ-Wing when you find a trivalue pivot cell where two bivalue wing cells each share two of the pivot's three candidates, and both wings share one common candidate (Z). Look for this when Y-Wing setups almost work but the pivot has three candidates instead of two.
Common Mistakes to Avoid
Eliminating from cells that can only see two of the three XYZ-Wing cells.
Unlike Y-Wing, XYZ-Wing requires the elimination target to see ALL THREE cells (the pivot and both wings), because Z could be in any of them.
Using a pivot with only two candidates instead of three.
The pivot must have exactly three candidates {X, Y, Z}. If the pivot is bivalue, the pattern is a Y-Wing, not an XYZ-Wing.
Confusing which candidate is Z (the elimination target).
Z is the candidate that appears in ALL three cells — the pivot and both wings. The other candidates appear in only two of the three cells.
More Examples
See xyz-wing applied in different puzzle configurations to strengthen your pattern recognition.
XYZ-Wing with Trivalue Pivot
Highlighted cells show the xyz-wing pattern
Practice Puzzles
Apply the xyz-wing technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- A pivot cell with three candidates ABC and two bivalue wings with AB and AC
- Action:
- Eliminate the shared candidate from cells that see all three XYZ-Wing cells
- Look for:
- A three-candidate pivot connected to two bivalue wings