Overview
- Tier 4
- Fish, wings, chains & uniqueness
- Typical difficulty
- Peak Score 65–75
- Also known as
- XYZ-Hinge Wing
An XYZ-Wing features a 3-candidate pivot and two bivalue wings sharing one common digit. Any cell that sees all three cells cannot contain that shared digit.
The XYZ-Wing is a variation of the XY-Wing where the pivot cell retains all three candidates (for example, 1, 4, and 7) instead of just two. Because the pivot itself could be 7, target cells must be visible to both wings AND to the pivot itself. This restricts the elimination cells to the same 3×3 box as the pivot, but it provides a clean, decisive deduction.
Worked examples
1 / 5
Reading the exampleCells forming the patternCells losing candidatesEliminated candidates
5
347
1
9
37
34
8
2
6
78
6
9
18
178
2
5
4
3
38
34
2
348
5
6
1
9
7
1
5
4
38
9
378
6
37
2
37
2
6
15
4
15
9
37
8
9
8
37
6
2
37
4
5
1
2
19
5
7
6
148
3
18
49
4
139
8
2
13
135
7
6
59
6
137
37
45
138
9
2
18
45
The pivot R8C6 holds {1,3,5}, one wing R8C5 holds {1,3} and the other wing R5C6 holds {1,5}. One of these three cells must be 1, so 1 can be removed from any cell that sees all three.
Removes: 1 from R7C6
How to apply it
Spotting the pattern and making the deduction, in order.
- Find a three-candidate pivot cell (e.g. holding 1, 4, and 7).
- Find two bivalue wing cells that see the pivot: one holding 1 and 7, and the other holding 4 and 7.
- Notice that digit 7 is shared across all three cells.
- If the pivot is 1, the first wing must be 7. If the pivot is 4, the second wing must be 7. If the pivot is 7, it is already 7.
- One of these three cells is guaranteed to be 7.
- Eliminate candidate 7 from any cell in the same 3×3 box that sees the pivot and both wings.
Common mistakes
- Trying to eliminate the target digit from cells that do not see the pivot cell.
- Eliminating the non-shared digits instead of the digit common to all three cells.
Frequently asked questions
- Why are XYZ-Wing eliminations more restricted than XY-Wings?
- Because the pivot can also be the shared digit, any eliminated cell must see the pivot in addition to both wings. This usually means the eliminated cell must share a 3x3 box with the pivot.
Related techniques
Put XYZ-Wing into practice
Try a puzzle from the Tough tier (Peak Score 61–70).