X-Wing

A digit boxed into the corners of a rectangle can be struck out of the two lines that cross it. The first advanced pattern worth learning.

The idea

Find a digit — say 8 — that appears as a candidate in exactly two cells of one row. Now find another row where 8 also appears in exactly two cells, and where those cells sit in the same two columns. The four cells form a rectangle.

Whichever way it resolves, one of those two rows puts its 8 in the left column and the other puts its 8 in the right column. Between them, the two rows use up the 8 in both columns — so no other cell in either column can be an 8.

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The digit is confined to two cells in each of two rows, sharing the same two columns; it can therefore be removed from the marked cell in one of those columns.

It works in both directions

Everything above holds with rows and columns swapped: two columns that each have the digit in exactly two cells, lying in the same two rows, eliminate that digit from the rest of those two rows.

How to hunt for one

Pick a digit and mark every cell where it is still a candidate.
List the rows where it appears exactly twice. Fewer than two such rows means no X-Wing for that digit.
Compare their column positions. Two rows with matching columns give you the pattern.
Repeat with columns instead of rows, then move to the next digit.

This search is much faster with a single digit's candidates in mind. Trying to see an X-Wing while looking at all nine digits at once is why the pattern has a reputation for being hard.

What comes next

A Swordfish is the same argument with three rows and three columns. An XY-Wing is a different shape entirely and is often easier to find in practice. Both show up in expert puzzles.

Common questions

What is an X-Wing in Sudoku?

A pattern where one digit is a candidate in exactly two cells of two different rows, and those cells share the same two columns. The digit can then be removed from the rest of both columns.

Why is it called an X-Wing?

Because the four cells form a rectangle whose diagonals cross like an X — the two possible resolutions are the two diagonals.

When do I need an X-Wing?

On expert puzzles, once singles, locked candidates and pairs have all stopped producing moves.

Does an X-Wing place a digit?

No, it only removes candidates — but those removals typically create a single straight away.