X-Wing
A digit forming a rectangle across two rows and two columns. One of the two orientations must be correct, which eliminates the digit elsewhere on those lines.
What it is
An X-Wing appears when a digit has exactly two possible cells in each of two rows, and those cells line up in the same two columns. The four cells form a rectangle. Whichever way the digit is placed — top-left and bottom-right, or top-right and bottom-left — both columns end up containing it. The digit can therefore be removed from every other cell in those two columns. The same works with rows and columns swapped.
How to spot it
Choose a digit and find rows where it has exactly two candidate cells. Compare pairs of such rows: if their candidate columns match, you have an X-Wing. Repeat with columns to find the transposed version. Working one digit at a time across the whole grid is far more reliable than scanning visually.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 4/4, 5/4, 4/7, 5/7
- Digits
- 6
- Eliminations
- 4/2, 4/9, 5/2, 5/8
Press a marked square to point it out on the board above.
Why it matters
The X-Wing is the gateway to advanced solving and the first technique that reasons about the grid as a whole rather than a single unit. It is also the most searched-for Sudoku technique, because it is where most solvers hit their first real wall.
Practise now
Solve a puzzle where this technique decides the game
Frequently asked questions
Why is it called an X-Wing?
Because the two valid placements form the diagonals of a rectangle, which trace an X. Only one diagonal is correct, but both cover the same two columns — which is what makes the elimination safe.
Do the four cells have to be in the same boxes?
No. The rectangle can span any two rows and any two columns anywhere on the board. Box boundaries are irrelevant to the pattern.
Where exactly can I remove the digit?
If you found the pattern in two rows, remove the digit from the two columns everywhere except the four rectangle cells. If you found it in two columns, remove it along the two rows instead.
What if a row has three candidate cells instead of two?
Then it is not an X-Wing. Exactly two cells per line are required. With three cells in three lines you may have a Swordfish, which is the next size up.
Put it to use
Where you will meet it
Hard grids are built around moves like this one. That is where it earns its keep.
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