Step 13 · Expert
What is X-Wing? How to Solve Killer Sudoku
When a digit has exactly two possible cells in each of two rows, and those cells line up in the same two columns, you can remove that digit from the other cells of those two columns (and the same works with rows and columns swapped).
What it is
Think about one digit only (say 4).
① In two rows, 4 fits in exactly two cells each.
② Those cells line up in the same two columns, so the four cells form the corners of a rectangle.
Then 4 goes in one diagonal pair of the rectangle: top-left + bottom-right, or top-right + bottom-left.
Either way, the 4s for those two columns are used up inside the rectangle. So no other cell in those two columns can be 4.
How to spot it
Pick one digit and find a row where it has exactly two spots. If another row has its two spots in the same two columns, it's an X-Wing (rows and columns can be swapped).
Example
Dotted outlines are cages, with their total in the top-left corner. Yellow cells are where to look, orange cells are the reason, red digits are candidates you can remove, and the green digit is the answer.
Think about 7 only. In both column 5 and column 9, 7 can only go in row 7 or row 8 (R7C5, R8C5, R7C9, and R8C9). These four cells are the corners of a rectangle, and 7 goes in one diagonal pair. Either way, the 7s of row 7 and row 8 are used up by these four cells, so the other cells of row 7 and row 8 (R8C6) can't be 7.