The XY-wing in sudoku
The XY-wing is where sudoku stops being about units. Three cells, none sharing a row, column or box with all the others, conspire to remove a candidate none of them will take. The raw material is bivalue cells, cells holding exactly two candidates, and a stalled expert board keeps a handful of them waiting.
The pattern
A pivot and two wings. The pivot holds two candidates, call them X and Y. One wing sees the pivot and shares X, plus a third digit Z. The other wing sees the pivot and shares Y, plus the same Z. Below, the pivot holds 3 and 8, the left wing holds 3 and 5, and the top wing holds 8 and 5. The Z here is 5.
Every candidate on this board is checkable against the placed digits, pivot and wings included. The pivot’s row, column and box account for seven digits between them, leaving 3 and 8. Run the same audit on either wing and two candidates survive each time. Bivalue cells are facts you can verify, and the pattern stands on three of them.
Why the elimination works
Test the pivot both ways. If it takes 3, the row wing loses its 3 and becomes 5. If it takes 8, the column wing loses its 8 and becomes 5. The pivot must take one of the two, so one wing or the other ends up as a 5, and you never find out which.
You do not need to. A cell that sees both wings watches every version of the future contain a 5 in one of them. The corner cell top-left shares a column with the row wing and a row with the column wing, so its own 5 can never come true:
One struck candidate looks like thin reward for three-cell logic. Judge it by what follows: on this board the corner cell collapses to a single candidate, and expert positions stall exactly because no cheaper move exists. The XY-wing is often the crack that reopens one.
How to hunt
Catalogue the bivalue cells first; a stalled board rarely holds more than a dozen. Take each as a trial pivot and look at the bivalue cells it sees. You need one neighbor sharing each pivot digit, and both neighbors agreeing on a third. Two wings sharing the pivot’s own digits teach you nothing, so the check that matters is the wings’ other candidates matching.
The site helps here. Selecting a digit lights its candidates board-wide, so testing “do both wings hold a 5” takes one tap. Auto notes keeps the bivalue catalogue honest, and honest marks are the difference between a wing and a mirage.
Near misses
Every cell in the pattern must hold exactly two candidates. Same board, one placed digit removed:
With three candidates, the pivot can dodge both wings: take the 4, and neither wing gets forced to anything. The whole argument needs the pivot cornered between exactly two futures. A pivot that keeps its Z candidate is a different animal, the XYZ-wing, and its weaker elimination only reaches cells that see all three pattern cells. Meet the wings properly and the step up to master’s forcing chains shrinks, because an XY-wing is a three-link chain you learned to see whole.
Frequently asked questions
What is an XY-wing in sudoku?
Three cells with two candidates each, arranged as a pincer. A pivot holding digits X and Y sees two wings: one shares X and holds a third digit Z, the other shares Y and also holds Z. Whichever way the pivot resolves, one wing becomes Z, so any cell that sees both wings cannot be Z.
Is a Y-wing the same as an XY-wing?
Yes. Some books and apps call the pattern a Y-wing, others an XY-wing, and a few use both names for the same three cells. The letters refer to the pivot candidates and the shared wing digit, and nothing about the technique changes with the name.
What is the difference between an XY-wing and an XYZ-wing?
The pivot. An XYZ-wing adds the shared digit Z to the pivot itself, three candidates instead of two. That weakens the conclusion: the pivot might take Z, so the elimination only hits cells that see all three pattern cells rather than just the two wings.
How do you find XY-wings?
Catalogue the cells with exactly two candidates; a stalled board rarely holds more than a dozen. Take each as a trial pivot and check its bivalue neighbors for the X, Y and Z relationship. On this site, selecting a digit highlights its candidates board-wide, which speeds up the neighbor check.