What is a W-Wing?
A W-Wing is two cells with the same two candidates, X and Y, that don’t share a row, column or box, plus a row, column or box where Y has exactly two spots, each seeing one of the two cells. One of the two cells must be X, so X can be removed from every cell that sees both.
It is the next wing after the Y-Wing and works with notes on two-candidate cells. In Marble Sudoku the notes are small marbles, so you look for two holes showing the same two colors.
Use one in 4 moves
- 1Pair. Find two cells with the same two candidates, X and Y, that don’t see each other.
- 2Link. Find a row, column or box where Y fits in exactly two cells.
- 3Check. Each of those two cells must see one of the pair cells.
- 4Clear. Remove X from every cell that sees both pair cells.
Then look for singles where you removed it.
TRY IT · GUIDED EXAMPLE
Build the W-Wing
Small marbles show the colors each hole can still take, here only in holes with two colors left. Find two matching Orange and Pink holes, connect them through a Pink link, and clear Orange where both can see.
This is the real board from Marble Sudoku. The nine marble colors stand for the numbers 1 to 9.
- Pair
- Link
- Clear
- Place
Build the W-Wing
Read the example in words
Row 6, column 4 and row 8, column 6 can each only be Orange or Pink, and they don’t share a row, column or box. Column 9 has exactly two spots for Pink: row 6 and row 8. Row 6, column 9 sees the first cell along row 6, and row 8, column 9 sees the second along row 8. One of those two spots is Pink, so one of the pair cells loses Pink and must be Orange. Row 4, column 6 sees both pair cells (the center box and column 6), so it can’t be Orange and is left with a single color: Navy. With numbers turned on, Orange is 1, Pink is 3 and Navy is 8.
YOUR TURN · PRACTICE
Spot the W-Wings
Small marbles show holes with two colors left. Find two matching holes that don’t see each other, linked by a color with only two spots in a line, and tap a hole that loses the other color. On Easy the pair and the link glow. On Hard you find them yourself.
Round color:
Why a W-Wing works
Column 9 must place its 3 in row 6 or row 8. Whichever it is, that 3 sees one of the pair cells and takes 3 away from it. A pair cell that loses 3 has only 1 left.
So at least one of the two pair cells is 1. We don’t know which, and we don’t need to: a cell that sees both pair cells would clash with either one, so it can’t be 1.
How to spot W-Wings faster
- Collect two-candidate cells. Note every cell with exactly two candidates and look for two with the same pair that don’t see each other.
- Try both numbers as the link. For a pair XY, look for a line where X has two spots, then a line where Y has two spots. Either can be the link.
- Check each end. One end of the link must see the first pair cell, the other end the second. The ends are never the pair cells themselves.
- Clear the other number. The link’s number stays. You remove the other number of the pair from cells that see both pair cells.
W-Wing vs. Y-Wing vs. XYZ-Wing
| W-Wing | Y-Wing | XYZ-Wing | |
|---|---|---|---|
| Cells used | Two pair cells plus a link | A pivot and two wings | A pivot and two wings |
| Candidates | Both pair cells: XY | Pivot XY, wings XZ and YZ | Pivot XYZ, wings XZ and YZ |
| Removes | X from cells that see both pair cells | Z from cells that see both wings | Z from cells that see all three |
| Difficulty | Advanced | Advanced | Advanced |
Common mistakes
- Pair cells that see each other. If the two cells share a row, column or box, they are a naked pair, not a W-Wing.
- A link with three spots. The link number must have exactly two spots in its row, column or box.
- Removing the link number. You clear the other number of the pair, not the one that forms the link.
- Link ends on the pair cells. The two link spots must be other cells, each seeing one pair cell.
W-Wing FAQ
What is a W-Wing in Sudoku?
A W-Wing is two cells with the same two candidates that don’t see each other, plus a row, column or box where one of those numbers has exactly two spots, each seeing one of the cells. The other number can be removed from every cell that sees both pair cells.
Why is it called a W-Wing?
Draw the pair cells, the link and the lines between them and you get a zigzag like a W. It is one of the wing patterns, together with the Y-Wing and XYZ-Wing.
Is a W-Wing harder than a Y-Wing?
It is usually rated a little harder, because the link is a single number in a line rather than a third two-candidate cell. Once you look for it, it is just as quick to check.
Can the link be in a box?
Yes. The link can be a row, a column or a box, as long as the number has exactly two spots there and each spot sees one of the pair cells.
Does this work in Marble Sudoku?
Yes. Find two holes whose small marbles show the same two colors and that don’t share a line or box. Then look for a line where one of those colors has only two holes left.
When should I look for one?
After singles, pairs, box/line reductions and Y-Wings stop finding moves. W-Wings are common in hard and expert puzzles.
PRACTICE IN THE GAME
Find W-Wings in a real puzzle
When a hard puzzle stalls, look for two holes with the same two colors far apart. A two-hole link between them often breaks the puzzle open.
Next techniqueSimple Coloring
