W-Wing

W-Wing is an advanced strategy that is relatively easy to spot and highly effective in eliminating candidates.

What is a W-Wing?

The W-Wing involves two cells and a Strong Link:

• Two cells that don’t see each other, both containing the same two candidates (a and b).
• A Strong Link (if one digit is not the answer, the other must be) exists on candidate a, with each end of the link seeing one of the two cells.

Candidate b can be eliminated from any cell that sees both of the original cells.

Observe the image below:

• Cells C3 and F7 are bi-value cells with identical candidates a and b.
• There is a Strong Link on a between cells C5 and F5. C5 sees C3, and F5 sees F7.

Eliminations:

Cells F3 and C7 see both bi-value cells C3 and F7. Therefore, candidate b can be eliminated from F3 and C7.

Why is it true?

• If C5 = a, then C3 = b, and b can be eliminated from F3 and C7.
• If C5 ≠ a, then F5 = a → F7 = b , and b can be eliminated from F3 and C7.

This means that regardless of which side of the strong link holds a, one of the bi-value cells must be b, allowing b to be eliminated from all cells that see both bi-value cells.

Example 1

Observe the image below:

• B7 and E6 are bi-value cells with candidates 4 and 9.
• There is a Strong Link on 9 between cells B4 and E4.

As described, the Strong Link on 9 forces 4 to be the solution in one of the bi-value cells (B7 or E6). Therefore, 4 can be eliminated from B6, as it sees both B7 and E6.

Example 2

In the image below, the orange-highlighted cells are bi-value cells with 2 and 7 as candidates. The pink-highlighted cells represent the Strong Link on 7. This forms a W-Wing setup. As a result, 2 can be eliminated from C1, which sees both bi-value cells.