X-Wing
X-Wing · 2×2 fish
Digit d in two rows lies only in the same two columns, so d is removed from the other cells of those columns.
Rule
Two rows have d only in the same two columns → remove d from those columns in every other row (rows ↔ columns also works).
Two matching rows
Digit 3 in row 2 can only go in r2c3 and r2c8; in row 9 only in r9c3 and r9c8 — the same two columns, 3 and 8.
The idea
Pick a digit d. If in row A d has only two places, and in row B d also has only two places in exactly the same two columns, the four cells form the corners of a rectangle.
Each row needs one d, and the two must be in different columns. There are only two ways: along one diagonal or the other — an X. Either way each column already gets its d from row A or row B, so the other cells in those two columns cannot be d.
Rows and columns can swap roles: two columns with d only in the same two rows remove d from those two rows.
How to spot it
- For each digit, list the rows (or columns) with exactly two places left for it.
- Two such rows with the same pair of columns form an X-Wing.
Common mistakes
- Eliminating in the wrong direction: when the base units are rows, eliminate along columns, and vice versa.
- The four corners do not need to be in four different boxes.
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Related techniques
References
The examples on this page are generated from random puzzles, not taken from these sources.