Y-Wing
A Y-Wing, also called XY-Wing, uses three cells with two candidates each. The pivot has candidates X and Y. One wing sees the pivot and has X and Z; the other wing sees the pivot and has Y and Z. Whatever the pivot is, one of the wings must be Z, so Z can be removed from every cell that sees both wings. It is an Expert technique in Bare Sudoku.
When to use it
When a puzzle has several cells with exactly two candidates and no fish is available. Y-Wings are common in Expert puzzles and are found by following the two-candidate cells: each is a potential pivot or wing.
How to spot it
List the cells with exactly two candidates. For each one, treat it as the pivot with candidates X and Y, and look among its peers for a cell with X and another digit Z, and a cell with Y and the same Z. Those two are the wings. Then find cells that see both wings and contain Z. Note that the wings do not need to see each other.
Example
| c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | |
|---|---|---|---|---|---|---|---|---|---|
| r1 | 1389 | 2 | 159 | 359 | 13 | 6 | 7 | 4 | |
| r2 | 4 | 7 | 369 | 269 | 2369 | 8 | 23 | 1 | 5 |
| r3 | 13 | 136 | 1256 | 7 | 4 | 9 | 8 | 23 | |
| r4 | 19 | 3 | 19 | 7 | 4 | 5 | 8 | 2 | 6 |
| r5 | 7 | 4 | 8 | 126 | 26 | 126 | 5 | 39 | 39 |
| r6 | 6 | 2 | 5 | 3 | 8 | 9 | 7 | 4 | 1 |
| r7 | 38 | 9 | 7 | 2568 | 1 | 236 | 4 | 35 | 238 |
| r8 | 5 | 18 | 13 | 4 | 239 | 237 | 23 | 6 | 23789 |
| r9 | 2 | 6 | 4 | 589 | 359 | 37 | 1 | 359 | 3789 |
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 r7c1 has candidates 3 and 8. It sees r3c1, which has 3 and 1, and r8c2, which has 8 and 1.
- If r7c1 is 3, then r3c1 loses 3 and becomes 1. If r7c1 is 8, then r8c2 becomes 1. One of the two wings is 1 in every case.
- A cell that sees both wings can never be 1. Remove 1 from r1c2, r3c2.
Common mistakes
- Choosing wings that do not both see the pivot. Each wing must share a row, column or box with the pivot.
- Removing Z from cells that see only one wing. The eliminated cell must see both wings.
- Removing Z from the pivot. The pivot does not contain Z in a Y-Wing; if it does, the pattern is an XYZ-Wing with different rules.
In Bare Sudoku
Needed from level: Expert
In the game, the hint says: Y-Wing
Frequently asked questions
What is a Y-Wing in Sudoku?
Three two-candidate cells: a pivot with X and Y, a wing with X and Z that sees the pivot, and a wing with Y and Z that sees the pivot. One wing is always Z, so Z is removed from cells that see both wings.
Is Y-Wing the same as XY-Wing?
Yes. The two names describe the same pattern. Bare Sudoku calls it Y-Wing.
Why must one wing be Z?
If the pivot is X, the first wing loses X and becomes Z. If the pivot is Y, the second wing becomes Z. The pivot is one of the two, so one wing is Z.
How many cells does a Y-Wing eliminate?
Usually one or two: only the cells that see both wings and still contain Z. That is enough to create a single.
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