If a digit can go in exactly two cells in each of two rows, and those cells line up in the same two columns, the digit must sit on two opposite corners of that rectangle. Either way it fills both columns, so you can remove it from every other cell in those two columns. It works the same with rows and columns swapped.
X-Wing is the first pattern that follows a single digit across the whole board instead of working inside one unit. It is named after the X that its two possible solutions draw across the rectangle.
You rarely need it before expert difficulty, but when a grid stalls and the pairs are used up, an X-Wing is often the way through.
An X-Wing
Where the pattern lives
The pattern
Candidates removed
Solved as a result
In rows 4 and 7, the 5 fits in just two cells each, and they line up in columns 3 and 5: R4C3, R4C5, R7C3 and R7C5. The 5s go on one diagonal or the other, and both use up columns 3 and 5. So the 5 can be removed from the rest of columns 3 and 5: R1C5. That leaves R1C5 with only one candidate: 3.
Only the 5s are shown, so the pattern stands out.
This position comes from a puzzle generated on this site, after every single has been filled in. Boxes are numbered 1–9 from the top left, row by row; R5C4 means row 5, column 4.
How to spot it
1Pick a digit and look only at its candidates.
2Find a row where that digit has exactly two possible cells. Note their columns.
3Look for a second row where the digit also has exactly two cells, in the same two columns.
4The four cells form a rectangle. Remove the digit from every other cell in those two columns.
5Try the same with columns: two columns, two cells each, in the same two rows. Then clear those rows.
Why it works
Each of the two rows needs the digit exactly once, and each has only two places for it. Put it in the left cell of the first row and the second row is forced to its right cell; put it on the right and the second row is forced to the left. Either way, both columns get the digit from these two rows.
A column holds each digit once, so no other cell in those two columns can have it.
Common mistakes
Using rows where the digit has three or more spots. Each of the two rows must have exactly two (or, the other way round, each of the two columns).
Rectangles that don't line up. The cells in both rows must be in the same two columns.
Clearing the wrong lines: if you started from rows, you clear the columns, and the other way round.
Questions
Why is it called an X-Wing?
The digit can sit in the four corners in only two ways, top left with bottom right or top right with bottom left. Drawn in, the two options cross like an X.
Do the two rows have to be next to each other?
No. Any two rows (or any two columns) anywhere on the board work, as long as the four cells form a rectangle.
What comes after X-Wing?
In real puzzles the next patterns you meet are usually the Skyscraper and the 2-String Kite, which use the same kind of rows with only one end lined up. Swordfish (three rows) and Jellyfish (four) are rarer.
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