The X-Wing Technique in Sudoku Explained Simply

When you need it

You reach for the X-Wing when singles and pairs have run dry and the board will not budge. It is a technique for hard and extreme puzzles, where the useful deductions live in the relationship between rows and columns rather than inside a single group.

The pattern

Focus on one value. Find two rows in which that value has only two possible cells each. Now check the columns those cells sit in. If the two candidate cells in the first row line up with the two candidate cells in the second row, so they share the same pair of columns, you have an X-Wing. The four cells form the corners of a rectangle.

Why it works

In each of those two rows, the value must go in one of the two shared columns. Follow the logic and you find that the value will end up in opposite corners of the rectangle, either the top left and bottom right, or the top right and bottom left. Either way, both of those columns will get the value from these rows.

That is the payoff. Since both columns already receive the value from the rectangle, the value cannot appear anywhere else in those two columns. You can erase it as a candidate from every other cell in both columns, which frequently unlocks the board.

How to spot one

1. Choose a value that is proving stubborn.
2. Look for two rows where the value has exactly two candidate cells.
3. Check whether those cells share the same two columns.
4. If they do, erase the value from the rest of those two columns.
5. The same works with rows and columns swapped.

Do not force it

The X-Wing only appears sometimes, and that is fine. Run through your simpler techniques first, and reach for it when nothing else moves. When you do find one, it often breaks a puzzle wide open. Load an Extreme board in Shapedoku, keep clean notes, and watch for that rectangle to form.