A variant of XY-Wing where the pivot has 3 candidates {X, Y, Z} and pincers have 2 candidates {X, Z} and {Y, Z}.

XYZ-Wing is the natural extension of XY-Wing where the pivot expands from 2 candidates to 3 candidates {X, Y, Z}. Pincers, like in XY-Wing, are bi-value cells with {X, Z} and {Y, Z}, sharing units with the pivot. Z can be eliminated from any third cell that simultaneously sees the pivot and both pincers. It occurs more frequently than XY-Wing but is somewhat harder to spot.

Extension from XY-Wing

XYZ-Wing is a natural extension of <a href="/en/glossary/xy-wing/">XY-Wing</a>. The pivot {X, Y} of XY-Wing becomes {X, Y, Z} with Z added. Following the logic: if pivot is X, one pincer {X, Z} excludes X to confirm Z; if pivot is Y, the other pincer {Y, Z} excludes Y to confirm Z; if pivot is Z, the pivot itself is Z. Thus at least one of pivot, pincer A, pincer B must be Z. The elimination target cell must be visible from the pivot and both pincers (a stricter condition than XY-Wing).

Difficulty of Discovery

XYZ-Wing is harder to find than XY-Wing for two reasons. First, the pivot has 3 candidates, making it harder to spot from the candidate list (XY-Wing only requires looking among bi-value cells). Second, the constraint that the elimination target must be visible from the pivot is stringent. Practically, scanning in reverse - starting from 3-candidate cells to look for pincers - is efficient. The standard procedure is: 'when finding a 3-candidate {X, Y, Z} cell, check if both {X, Z} and {Y, Z} bi-value cells exist in its shared units.'

Extension to WXYZ-Wing

Further extension of XYZ-Wing leads to WXYZ-Wing (4-candidate pivot with 3 pincers). The logical structure is the same, but discovery and verification become significantly harder as candidates increase. Practically, XYZ-Wing is the realistic ceiling - beyond that, computational solvers are more appropriate. In Expert+ puzzles, when XY-Wing fails, XYZ-Wing often breaks through. The habit of consciously focusing on 3-candidate cells is key to advancement.