X-Wing
When a digit fits in only two places on each of two rows, and those places line up in the same two columns, it can't go anywhere else in those columns.
The idea
Pick a digit. Find two rows where it can only go in two cells each, and where those cells are in the same two columns. The four cells make a rectangle.
In the first row the digit is in one column or the other. Whichever it is, the second row must use the other column (a column can't hold it twice). So the two columns get their copy of the digit from these two rows, and the digit can be crossed out of every other cell in those two columns.
It works the same way with columns and rows swapped.
How to spot it
- Look at one digit at a time, with notes. Mark the rows where the digit has exactly two places.
- If two of those rows have their places in the same two columns, you have an X-Wing.
- Then do the same with columns.
Worked example
X-Wing on a real puzzle
From our expert puzzle #636 (28 clues), after 12 earlier steps of our solver. Gold cells make the pattern; red notes are the ones it rules out.
How often our puzzles need it
Our solver works like a careful player: it always uses the easiest technique that still makes progress. Counting the puzzles where it had to use x-wing at least once:
- 650 of our 1000 expert puzzles
- 250 of our 1000 master puzzles
The easiest level that can need it is expert Sudoku.