W-Wing
A W-Wing uses two cells that have exactly the same two candidates, X and Z, and do not see each other. They are joined by a strong link on X: a row, column or box in which X has exactly two candidate cells, one seeing each of the two pair cells. If both pair cells were X, that unit would have no place left for X, so at least one of them is Z. Z can therefore be removed from every cell that sees both pair cells. The W-Wing is an Expert technique in Bare Sudoku.
When to use it
When single-digit patterns such as the Skyscraper and the 2-String Kite find nothing. W-Wings are less common than Y-Wings but appear regularly in Expert puzzles. Look for them when two cells far apart show the same pair of candidates.
How to spot it
List the cells with exactly two candidates and look for two with the same pair, say X and Z, that share no row, column or box. For each of the two digits, look for a row, column or box where it has exactly two candidate cells, one seeing each pair cell. If X has such a link, check the cells that see both pair cells: they lose Z. Then try the same with a link on Z, which would remove X.
Example
| c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | |
|---|---|---|---|---|---|---|---|---|---|
| r1 | 48 | 248 | 1 | 5 | 6 | 7 | 9 | 28 | 3 |
| r2 | 6 | 7 | 9 | 138 | 2 | 138 | 5 | 4 | 18 |
| r3 | 5 | 28 | 3 | 18 | 4 | 9 | 6 | 128 | 7 |
| r4 | 147 | 9 | 5 | 78 | 3 | 248 | 278 | 6 | 148 |
| r5 | 147 | 148 | 2 | 6789 | 5 | 468 | 3 | 178 | 1489 |
| r6 | 3 | 6 | 48 | 789 | 1 | 248 | 278 | 5 | 489 |
| r7 | 9 | 18 | 6 | 2 | 7 | 13 | 4 | 38 | 5 |
| r8 | 148 | 5 | 48 | 136 | 9 | 136 | 78 | 378 | 2 |
| r9 | 2 | 3 | 7 | 4 | 8 | 5 | 1 | 9 | 6 |
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.
- r1c1 and r6c3 both have exactly the candidates 4 and 8, and they do not see each other.
- In row 8, digit 4 has only two candidate cells: r8c1, which sees r1c1, and r8c3, which sees r6c3. One of them must be 4.
- If r1c1 and r6c3 were both 4, neither r8c1 nor r8c3 could be 4, and row 8 would have no place for 4. So at least one of r1c1 and r6c3 is 8.
- A cell that sees both r1c1 and r6c3 can never be 8. Remove 8 from r4c1, r5c1.
Common mistakes
- Using a link unit in which X has three or more candidate cells. X must have exactly two places in that unit, one seeing each pair cell.
- Removing X instead of Z. The link is on X, so the digit that is removed is the other candidate, Z.
- Using two pair cells that see each other. They are then a naked pair, a simpler technique that removes both digits from the unit they share.
In Bare Sudoku
Needed from level: Expert
In the game, the hint says: W-Wing
Frequently asked questions
What is a W-Wing in Sudoku?
Two cells with the same two candidates, X and Z, that do not see each other, plus a row, column or box where X has exactly two candidate cells, one seeing each of them. At least one of the two cells is Z, so Z is removed from every cell that sees both.
Why does a W-Wing work?
If both pair cells were X, they would rule X out of both link cells, and the link unit would have nowhere to put X. So at least one pair cell is Z, and a cell that sees both of them cannot be Z.
How is a W-Wing different from a Y-Wing?
A Y-Wing connects its two wings through a pivot cell with two candidates. A W-Wing connects two cells with identical candidates through a strong link, a unit where one of their digits has only two places. Both remove a digit from the cells that see both ends.
Can the link of a W-Wing be in a box?
Yes. The link can be any row, column or box in which X has exactly two candidate cells, as long as one of them sees each pair cell.
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