Y-Wing (XY-Wing) Sudoku Technique
The Y-Wing Sudoku technique, also called the XY-Wing, is built from three cells that hold only two candidate digits each. It is the first pattern most solvers meet that spans three different digits, and it is worth learning early because the wings above it are all variations of the same idea.
What the pattern is
You need three bivalue cells and exactly three digits between them:
- The pivot holds
{x,y}. - One pincer holds
{x,z}and sees the pivot. - The other pincer holds
{y,z}and also sees the pivot.
The two pincers do not have to see each other. What matters is that each of them shares the pivot's row, column or box.
Now follow the pivot. If the pivot is x, the first pincer cannot be x, so it must be z. If the pivot is y, the second pincer cannot be y, so it must be z. The pivot has no other options, so one of the two pincers is always z.
That is the whole payoff: z is guaranteed to sit in one of the pincers, so any cell that sees both pincers can never be z.
| Y-Wing | XYZ-Wing | |
|---|---|---|
| Pivot candidates | two: {x,y} | three: {x,y,z} |
| Pincer candidates | {x,z} and {y,z} | {x,z} and {y,z} |
Where z can hide | one of the two pincers | pivot or either pincer |
You eliminate z from | cells seeing both pincers | cells seeing all three |
When to look for it
- When the grid is stalled and you have several cells with exactly two candidates left.
- When two of those cells share a digit that a third bivalue cell does not have: that third cell is your pivot candidate.
- Especially around box corners, where a row peer and a column peer of the same cell often land in a shared box.
How to apply it, step by step
- Pick a bivalue cell as the pivot and note its two digits
xandy. - Scan its row, column and box for another bivalue cell containing
xbut noty. Call its second digitz. - Scan the pivot's peers again for a bivalue cell holding exactly
{y,z}. - If you find both, you have a Y-Wing. Ignore the pivot from here on.
- List the cells that see both pincers and still carry
z. - Delete
zfrom every one of them, then re-check for new singles.
A worked example
In the demo the pivot G9 holds {7,9}. The pincer G1 holds {5,7} and sees the pivot through row G. The pincer J7 holds {5,9} and sees the pivot through box 9. The pincers do not see each other. The three digits are 7, 9 and 5, so z is 5.
Follow the two cases. If G9 is 7, then G1 loses its 7 and becomes 5. If G9 is 9, then J7 loses its 9 and becomes 5. One of the pincers is a 5 either way.
Two cells see both pincers. G8 sees G1 along row G and J7 through box 9. J1 sees G1 through box 7 and J7 along row J. Neither can be 5, so erase the 5 from G8 and J1.
Common mistakes
- Four digits. If the three cells use four different digits, there is no shared
zand no deduction. Count the digits before anything else. - A pincer that does not see the pivot. Both pincers must be peers of the pivot. Two pincers linked only to each other prove nothing.
- Eliminating everywhere. Only cells that see both pincers are affected. A cell seeing one pincer and the pivot is safe.
- Using cells with three candidates. All three cells must be bivalue. A three-candidate pivot makes it an XYZ-Wing, which eliminates less.
- Missing the second target. Two pincers often share more than one common peer. Sweep the whole intersection, including the box.
Where you meet it
The Y-Wing belongs to the tough tier, and it is one of the most frequently needed patterns at that level. Expect it on hard classic Sudoku, where a stalled grid full of two-candidate cells is almost always hiding one.