W-Wing Sudoku Technique
The W-Wing Sudoku technique joins two identical bivalue cells with a strong link and turns the pair into a guaranteed placement. It is easier to spot than most wings because two of the three ingredients look identical, and it often fires on grids where a Y-Wing finds nothing.
What the pattern is
You need three things:
- Two cells holding exactly the same two candidates,
{x,y}, that do not see each other. - A unit (a row, column or box) in which the digit
xhas exactly two possible cells. Two positions in one unit is a strong link, sometimes called a conjugate pair. - One end of that link sees the first bivalue cell, the other end sees the second.
Because the link is strong, one of its two cells really is x. Whichever end it is, that end knocks x out of the bivalue cell it sees, and that cell falls to y.
So at least one of the two matching cells is y. Every cell that sees both of them loses y.
| Y-Wing | W-Wing | |
|---|---|---|
| Pattern cells | three bivalue cells, three digits | two bivalue cells with the same pair |
| What connects them | a pivot that sees both pincers | a strong link on one digit of the pair |
| Digit eliminated | the digit shared by the pincers | the pair's other digit y |
| Where | cells seeing both pincers | cells seeing both bivalue cells |
When to look for it
- Whenever you notice two cells with an identical candidate pair sitting far apart in the grid.
- When a digit is nearly placed and several units are down to two spots for it, and those units are your strong links.
- After the easy patterns dry up but before you start colouring or chaining, because a W-Wing costs one quick scan.
How to apply it, step by step
- Collect the bivalue cells and group them by their digit pair.
- Take two cells from the same group that do not share a row, column or box.
- Pick one of the two digits,
x. Look for a unit wherexhas exactly two candidate cells. - Check the link: one of its two cells must see the first bivalue cell, the other must see the second. One end per cell, not both ends on the same one.
- If it matches, at least one bivalue cell is the other digit
y. - Delete
yfrom every cell that sees both bivalue cells. Then try the same pair again with the roles ofxandyswapped.
A worked example
In the demo the pair cells are D7 and H9, both {2,6}. They share no row, column or box, so neither sees the other.
Column 5 holds a 2 only in D5 and H5, so it is a strong link on 2. D5 sees D7 along row D, and H5 sees H9 along row H.
If D5 is 2, then D7 cannot be 2, so it is 6. If H5 is 2, then H9 cannot be 2, so it is 6. One of the two link cells is always 2, so D7 or H9 is 6.
Three cells see both pair cells: G7, H7 and J7 see D7 through column 7 and H9 through box 9. Erase the 6 from all three.
Common mistakes
- Pair cells that see each other. Then they are a naked pair, and the strong link adds nothing new.
- Both link ends aimed at one cell. The link must reach one bivalue cell from each end, or the case split collapses.
- Eliminating the linked digit. The link is on
x; the digit you erase is alwaysy. - Weak links. The unit must have exactly two positions for
x. Three positions is not a strong link and the argument fails, though it may still work through simple colouring.
Where you meet it
The W-Wing sits in the tough tier alongside the other wings. You will meet it on hard classic Sudoku, typically on grids that are rich in bivalue cells but have no clean fish or Y-Wing available.