XYZ-Wing
An XYZ-Wing is a Y-Wing whose pivot has three candidates. The pivot has X, Y and Z; one wing sees the pivot and has X and Z, the other sees the pivot and has Y and Z. One of the three cells must be Z, so Z can be removed from every cell that sees all three. Because the pivot itself may be Z, the eliminated cell must see the pivot as well as both wings, which limits it to the box or line the cells share. It is an Expert technique in Bare Sudoku.
When to use it
When X-Wing, Y-Wing and Swordfish find nothing. XYZ-Wings are less common than Y-Wings. Look for them when a three-candidate cell sits in a box with a two-candidate cell that shares two of its digits.
How to spot it
Start from cells with exactly three candidates; each is a possible pivot. Among its peers, look for two cells with two candidates each, both taken from the pivot's three, sharing exactly one digit Z. Then look for cells that see the pivot and both wings and contain Z. In practice one wing is in the pivot's box and the other in its row or column, and the eliminated cells are the remaining cells of that box in that row or column.
Example
| c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | |
|---|---|---|---|---|---|---|---|---|---|
| r1 | 6 | 1 | 5 | 4 | 8 | 7 | 23 | 29 | 39 |
| r2 | 27 | 27 | 4 | 9 | 3 | 6 | 5 | 8 | 1 |
| r3 | 9 | 8 | 3 | 2 | 15 | 15 | 6 | 4 | 7 |
| r4 | 2578 | 4 | 9 | 1 | 256 | 258 | 278 | 3 | 568 |
| r5 | 12578 | 27 | 168 | 3 | 9 | 2458 | 278 | 26 | 4568 |
| r6 | 258 | 3 | 68 | 7 | 256 | 2458 | 9 | 1 | 4568 |
| r7 | 18 | 9 | 7 | 6 | 4 | 3 | 18 | 5 | 2 |
| r8 | 4 | 5 | 2 | 8 | 7 | 19 | 13 | 69 | 369 |
| r9 | 3 | 6 | 18 | 5 | 12 | 129 | 4 | 7 | 8 |
Bold digits are given, blue digits were placed while solving, small digits are candidates. Highlighted cells form the pattern, crossed-out candidates are removed, and a circled candidate is the digit to place.
- The pivot r8c9 has three candidates: 3, 6 and 9. It sees r1c9 with 3 and 9, and r8c8 with 6 and 9.
- If r8c9 is 9, done. If it is 3, r1c9 must be 9. If it is 6, r8c8 must be 9. In every case one of the three cells is 9.
- A cell that sees all three cannot be 9. Remove 9 from r9c9.
Common mistakes
- Eliminating from cells that see only the two wings. Unlike a Y-Wing, the pivot can be Z, so the cell must see the pivot too.
- Using wings whose candidates are not both contained in the pivot's three candidates.
- Confusing it with a Y-Wing: the difference is the third candidate in the pivot, and it changes which cells can be cleared.
In Bare Sudoku
Needed from level: Expert
In the game, the hint says: XYZ-Wing
Play this puzzle · Play Sudoku · Sudoku solver
Practice puzzles
In these puzzles, XYZ-Wing is the hardest technique you need. Each link opens the puzzle in the game; the solver link shows every step.
- Expert 4.4 · Sudoku solver
- Expert 4.4 · Sudoku solver
- Expert 4.4 · Sudoku solver
- Expert 4.4 · Sudoku solver
- Expert 4.4 · Sudoku solver
- Expert 4.4 · Sudoku solver
- Expert 4.4 · Sudoku solver
- Expert 4.4 · Sudoku solver
- Expert 4.4 · Sudoku solver
- Expert 4.4 · Sudoku solver
Frequently asked questions
What is an XYZ-Wing in Sudoku?
A pivot with candidates X, Y and Z and two wings, one with X and Z and one with Y and Z, both seeing the pivot. One of the three cells is Z, so Z is removed from cells that see all three.
How is an XYZ-Wing different from a Y-Wing?
The pivot has three candidates instead of two, including Z. That makes the pivot a possible home for Z, so only cells that see the pivot and both wings can lose Z.
How often does an XYZ-Wing appear?
Less often than a Y-Wing: most Expert puzzles in Bare Sudoku are solved without one. The solver looks for it after X-Wing, Y-Wing and Swordfish.
Is there a WXYZ-Wing?
Yes: four cells with four candidates in two crossing units, where one digit is free to sit in more than one of them. Bare Sudoku finds it too and rates it Expert, like the other wings.
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