XYZ-Wing
Like an XY-Wing, but the hinge carries three candidates. The eliminations are fewer but the pattern is more common.
What it is
In an XYZ-Wing the hinge holds {X,Y,Z} and the two wings {X,Z} and {Y,Z}. All three cells contain Z, so at least one of them must be Z. Any cell that sees all three — hinge and both wings — can therefore drop Z. Because the elimination must see three cells rather than two, it usually applies to only one or two cells, typically inside the hinge's box.
How to spot it
Find a cell with exactly three candidates and check whether it sees two bi-value cells that each share two digits with it and one with each other. Then look for cells seeing all three, which in practice means the box containing the hinge.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 4/9, 4/8, 7/9
- Digits
- 1, 7, 9
- Eliminations
- 5/9
Press a marked square to point it out on the board above.
Why it matters
The XYZ-Wing extends the wing idea to a three-candidate hinge and fills gaps where an XY-Wing does not fit. Its narrow elimination zone makes it easy to verify once found.
Practise now
Solve a puzzle where this technique decides the game
Frequently asked questions
Why are there fewer eliminations than in an XY-Wing?
Because the target cell must see all three pattern cells, not just the two wings. That is a much stricter condition, so usually only cells in the hinge's box qualify.
How do I tell an XYZ-Wing from an XY-Wing?
Count the hinge's candidates: two makes it an XY-Wing, three an XYZ-Wing. The wings are bi-value in both cases.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
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