Wings
W-Wing
A W-Wing is two cells that hold exactly the same two candidates, {X, Y}, together with a strong link on X somewhere else in the grid. The strong link says X must be in one of its two ends, so at least one of the two {X, Y} cells is forced to Y, and Y can be removed from any cell that sees both of them.
- Level
- Advanced
The pattern
What it does.
The two {X, Y} cells don't need to see each other, which is what separates this from a naked pair. They are connected instead by a strong link: two cells elsewhere that are the only homes for X in their unit.
If the link's first end is X, it removes X from one of the {X, Y} cells, forcing it to Y; if the link's second end is X, the other cell is forced. Either way a Y is placed in one of the two cells.
The strong link is the part that has to be hunted. Two cells that are the only possible homes for a digit in a row, a column or a box are common, and a W-Wing is what happens when both ends of one line up with a matching pair.
Example
A worked example.
Collect the matching pairs
Scan for two-candidate cells and note any two that carry exactly the same pair, wherever they are. They don't have to share a unit.
Pick one digit of the pair
Take X, one of the two digits in the pair, and look for a strong link on it: two cells in one unit that are the only homes for X there.
Connect the link to the pairs
One end of the strong link must see the first {X, Y} cell, and the other end must see the second. If only one end lines up, keep looking; the pattern needs both.
Remove Y where both pairs are seen
Delete Y from every cell that can see both {X, Y} cells at once. As with the other wings, that set is often small, and sometimes empty.
Spotting it
How to spot it.
- Two-candidate cells that hold the same pair are the raw material, exactly as they are for a naked pair. Collect them before looking for the link.
- Look for strong links whose ends happen to see those cells. A digit with only two homes in a unit is where the connection comes from.
- Try both digits of the pair as X. A pattern that fails on one digit frequently works on the other.
- If the two {X, Y} cells do see each other and share a unit, you have a naked pair and should take the stronger elimination instead.
Where it stops working
A W-Wing needs the strong link to be genuine: two cells that are the only homes for X in their unit. If a third cell anywhere in that unit can also take X, the link isn't strong and the elimination is wrong. It also needs complete pencil marks, because both the pairs and the link are read from them and nothing else.
Keep going
Related topics.
New to sudoku? The rules take two minutes to read, and the first-puzzle walkthrough covers the basics that come before any of these.
Beyond the lessons.
The game's lessons stop at X-Wing, so there's no W-Wing lesson. The eight it does teach will get you through almost any puzzle; this page is here for when you run into the pattern anyway.