Overview
- Tier 4
- Fish, wings, chains & uniqueness
- Typical difficulty
- Peak Score 65–80
- Also known as
- W-Wing Dual Bivalue
Two identical bivalue cells connected by a strong link on one of their digits ensure at least one bivalue cell must take the other digit, eliminating it from cells seeing both.
A W-Wing combines two identical bivalue cells (for example, both holding 3 and 8) that do not see each other, bridged by an external strong link on digit 8. If digit 8 can only go in two cells of some row, column, or box, and those two cells each see one of the 3/8 cells, it is impossible for both cells to take 8. Therefore, at least one of them must take 3, eliminating candidate 3 from any cell in the grid that sees both bivalue cells.
Worked examples
1 / 5
Reading the exampleCells forming the patternCells losing candidatesEliminated candidates
35789
5789
3578
1578
157
4
67
126
1279
6
57
2
9
1357
37
8
4
17
4
789
1
2
67
678
3
5
79
5789
5789
4578
57
45679
2679
1
3
258
2
1
45
35
8
39
49
7
6
5789
3
6
157
14579
279
49
28
258
78
4
78
6
2
1
5
9
3
13
6
9
378
37
5
2
18
4
135
2
35
4
39
389
67
168
178
R5C6 and R9C5 both hold only {3,9}. In row 2, the digit 3 can only go in R2C6 and R2C5. If R2C6 is 3, R5C6, which shares column 6 with it, isn't 3; if R2C5 is 3, R9C5, which shares column 5 with it, isn't 3. Either way, one of R5C6 and R9C5 is 9, and 9 can be removed from any cell that sees both.
Removes: 9 from R9C6, R6C5, R4C5
How to apply it
Spotting the pattern and making the deduction, in order.
- Find two separated cells with the exact same two candidates (for example, both holding 3 and 8).
- Look for a strong link on digit 8 somewhere on the board (a row, column, or box where 8 only fits in two spots).
- Check that one end of this strong link sees the first cell, and the other end sees the second cell.
- Since one end of the bridge must be 8, it is impossible for both 3/8 cells to take 8.
- Therefore, at least one of the two cells must take 3.
- Eliminate candidate 3 from any cell that sees both of the original cells.
Common mistakes
- Connecting the strong link on the same digit you are trying to eliminate.
- Failing to confirm that S1 and S2 form a genuine strong link (exactly two occurrences in that house).
- Eliminating from cells that do not see BOTH bivalue cells.
Frequently asked questions
- What is a strong link in Sudoku?
- A strong link means a relationship where if one candidate is false, the other MUST be true. For example, if digit 5 appears in only two cells of a row, those two cells have a strong link on 5.
Related techniques
Put W-Wing into practice
Try a puzzle from the Tough tier (Peak Score 61–70).