Fish patterns like X-Wing and swordfish track one digit across rows and columns. The XY-Wing works completely differently. It tracks three cells, each holding exactly two candidates, and uses the way those candidates overlap to remove a single digit from cells that see two of the three.
It looks fiddly the first few times you find one, but the shape is always the same. One cell, called the pivot, has two candidates, say 3 and 7. Two other cells, each also holding two candidates, share a unit with the pivot: one has candidates 3 and 9, the other has 7 and 9. Those two are called the pincers. Between the three cells, three digits appear (3, 7 and 9 in this example), and one of them, the digit shared by both pincers but not the pivot, can be crossed off any cell that sees both pincers at once.
XY-Wing solves problems that fish patterns cannot touch, because it does not need a digit to be scarce across a whole row or column. It only needs three cells with exactly two candidates each, arranged the right way, which makes it one of the more common advanced techniques once a board is sufficiently full.
Worked example
A real Expert-tier puzzle, reduced to a stuck position after singles. Step through to see the pivot, its two pincers and the elimination.
Finding the pivot and its pincers
Start by hunting for a cell with exactly two candidates. That is your candidate pivot. Now look at its peers, meaning cells that share its row, its column or its box, and check whether any of them also have exactly two candidates. You need two such peers, and their candidate pairs have to relate to the pivot in a specific way: each pincer shares exactly one digit with the pivot, and the digit each pincer does not share with the pivot has to be the same digit in both pincers.
So if the pivot holds {3, 7}, one pincer might hold {3, 9} and the other {7, 9}. The 9 is the digit that appears in both pincers but not the pivot; that is the digit you are trying to eliminate. It helps to write the three candidate pairs down when you are starting out, since keeping track of which digit is shared with which cell in your head gets confusing fast.
The two pincers do not need to see each other. That is the detail that trips up most beginners, who assume all three cells must share a unit pairwise. Only the pivot needs to share a unit with each pincer individually.
Why the shared digit can be removed
Think about what the pivot can actually be. It is either 3 or 7, nothing else. Follow both branches. If the pivot is 3, then the pincer holding {3, 9} cannot also be 3 (same row, column or box as the pivot, so it cannot repeat the digit), which forces that pincer to be 9. If the pivot is 7 instead, the other pincer, holding {7, 9}, cannot be 7 for the same reason, so it is forced to be 9.
Either way, whichever value the pivot turns out to hold, one of the two pincers ends up being 9. You do not know which pincer in advance, and you do not need to. What you know for certain is that at least one of them is 9. Any cell that sees both pincers, meaning it shares a unit with each of them, cannot be 9 in either scenario, because whichever pincer is the 9, that cell would conflict with it. So 9 comes off every cell that sees both pincers, regardless of which branch the puzzle actually takes.
Common mistakes
- Picking a pivot or pincer with three or more candidates. All three cells in the pattern must have exactly two candidates. A cell with three candidates cannot serve as a pivot or a pincer, no matter how promising it looks.
- Forgetting to check that each pincer relates correctly to the pivot. Each pincer needs one digit in common with the pivot and one digit in common with the other pincer; if a pincer's two candidates match the pivot's exactly, it is not a pincer, it is just another copy of the pivot's pair.
- Eliminating from cells that only see one pincer. The elimination only applies to cells that are peers of both pincers at once. A cell that only shares a unit with one of the two keeps the candidate.
- Eliminating the wrong digit. Only the digit common to both pincers (and absent from the pivot) gets removed. The pivot's own two candidates, and the other digit each pincer holds, are untouched by this move.
Where XY-Wing shows up
Look for XY-Wings on Hard and especially Expert puzzles, where the board is crowded enough to have plenty of two-candidate cells but still short of naked or hidden singles. Expert boards here run 23 to 27 givens and are generated fresh with a uniqueness check, so a genuine XY-Wing will always lead somewhere real. Turn on Notes before hunting for one; trying to track three separate two-candidate cells without pencil marks is difficult even for experienced solvers. If you cannot find a pivot with the right pincers, check for an X-Wing instead, since the two techniques tend to unstick different kinds of positions.
Expert boards run 23 to 27 givens and are generated fresh with a guaranteed unique solution. Turn on Notes and hunt for two-candidate cells that share a unit.
Frequently asked questions
An XY-Wing uses three cells with exactly two candidates each: a pivot and two pincers that each share a unit with the pivot. One digit appears in both pincers but not the pivot, and that digit can be removed from any cell that sees both pincers.
No. Only the pivot needs to share a row, column or box with each pincer individually. The pincers themselves can be anywhere on the board relative to each other; what matters is which cells see both of them.
It is the digit that appears in both pincer cells but does not appear in the pivot. If the pivot holds 3 and 7, one pincer holds 3 and 9, and the other holds 7 and 9, the eliminated digit is 9.
No. A naked triple involves three cells in the same unit sharing three candidates between them and eliminates within that one unit. XY-Wing involves three cells that are not all in the same unit and eliminates from cells that see two of the three from different directions.
Because both possible values for the pivot lead to the same conclusion. Whichever one it turns out to be, one specific pincer is forced to the shared digit, so any cell watching both pincers can rule that digit out no matter which branch is correct.
Mostly Expert, with 23 to 27 givens, and occasionally Hard. Easy and Medium puzzles on this site are built to fall to singles alone, so this technique will not come up there.