W-Wing

Walkthrough

Example 01 — W-Wing

Identical bivalue cells r4c6 and r7c4 contain numbers 8 and 9; they do not see each other but are connected by the conjugate pair r1c4 and r1c6 through number 9. Bivalue cell r4c6 only sees one end of the strong link cell r1c6, while bivalue cell r7c4 only sees the other end of the strong link cell r1c4. This allows eliminate the other number 8 from any cell that sees both the bivalue cells, in this case, cells r4c4 and r9c6, as the following explained:

If cell r4c6 is number 8, both cells r4c4 and r9c6 cannot be number 8 because both of them see cell r4c6.

if cell r4c6 is number 9 instead, then one end of the connecting conjugate pair, which is cell r1c6 in this case, cannot be 9, then the other end of the conjugate pair cell r1c4 must be dight 9, which then forces the other bivalue cell r7c4 to be number 8. Because both cells r4c4 and r9c6 also see cell r7c4, so they cannot have number 8

Walkthrough

Example 02 — W-Wing

In this example, bivalue cells are r2c6 and r8c9 with numbers 2 and 4; the strong link is cells r7c6 and r7c9 with number 4, this leads to number 2 to be eliminated from cell r8c6, which sees both bivalue cells(endpoints).

What to notice: W-Wings do not have to look like a literal W on the grid. The important structure is two identical bivalue endpoints plus a strong link on one candidate connecting the two sides.

Mark the strong link clearly, then follow the two cases. If the first endpoint takes X, the opposite end of the strong link is forced to X and the second endpoint is forced to Y. If the first endpoint is already Y, the conclusion is immediate.

Only after the proof is complete should you look for cells that see both endpoints and remove Y.