XYZ-wing
A three-cell wing pattern where the pivot has three candidates and each wing has two — eliminating the shared candidate from any cell that sees all three.
The XYZ-wing is the three-candidate cousin of the Y-wing. The shape is the same — one pivot, two wings — but the pivot has three candidates instead of two, and the elimination radius shrinks accordingly.
The shape
- Pivot: candidates {X, Y, Z}, sharing a unit with each wing
- Wing 1: candidates {X, Z}, in a unit shared with the pivot
- Wing 2: candidates {Y, Z}, in a different unit shared with the pivot
Whatever the pivot ends up as, the corresponding wing must take the leftover that produces a Z somewhere. If the pivot is X, wing 1 must be Z. If the pivot is Y, wing 2 must be Z. If the pivot is Z, the pivot itself is Z. So one of those three cells must be Z.
The elimination: any cell that sees all three of those cells (pivot, wing 1, wing 2) cannot be Z. The reason "all three" matters is the pivot itself can be Z, so a cell only sees the wings (the way the Y-wing requires) isn't enough to eliminate Z — it could still be Z because the pivot is Z and the wings are something else.
Why "XYZ"
The naming convention from the Y-wing extends naturally: pivot has candidates {X, Y, Z}, wings have {X, Z} and {Y, Z}. The shared candidate is Z. Every wing-family technique uses similar alphabet-soup naming: WXYZ-wing for the four-cell version, on up.
When you'll see it
XYZ-wings are rarer than Y-wings because the pivot's three-candidate state usually collapses to two via simpler eliminations before the pattern can fire. On expert puzzles they're a respectable workhorse; on hard puzzles they appear occasionally. The visual recognition is similar to the Y-wing but with one extra candidate in the pivot — once the Y-wing is comfortable, the XYZ-wing follows quickly.
For a survey of which wing-family technique to reach for in different stuck states, see Which technique is this puzzle asking for.
See also
- Y-wing (XY-wing)— Three bivalue cells where the pivot shares one candidate with each wing — eliminating the third candidate from any cell that sees both wings.
- X-wing— When a digit's only two cells across two rows form a rectangle in two columns — eliminating that digit from the rest of those columns. Or the same shape rotated 90°.
- Candidate— A digit (1–9) a cell could still legally hold — one not yet ruled out by anything in its row, column, or 3×3 box. Every empty cell has between one and nine.
Read more
- Which technique is this puzzle asking for
How to read a fresh hard Sudoku and predict which intermediate technique will break it open before you've placed a single digit.