X-Wing Technique
advancedA powerful fish pattern using two rows and two columns to eliminate candidates
The X-Wing is the foundational "fish" pattern in Sudoku. When a candidate appears in exactly two positions in each of two rows, and those positions share the same two columns, you can make powerful eliminations in those columns.
Understanding the Concept
An X-Wing forms when a candidate digit appears exactly twice in two different rows, and those four cells line up on the same two columns, forming a rectangle.
Because of Sudoku constraints, the candidate must occupy exactly two of these four cells — one per row. This means it must fill one of the two diagonal pairs.
Either way, each column gets one instance of the digit from these rows. Therefore, no other cell in those two columns can hold the digit.
The same logic works transposed: if the candidate appears exactly twice in two columns on the same two rows, eliminate from the rest of those rows.
Named "X-Wing" because connecting the four corners diagonally draws an X.
This is the simplest member of the "fish" family (X-Wing = 2x2, Swordfish = 3x3, Jellyfish = 4x4).
Examples
X-Wing on Digit 7 (Rows 0 and 5, Columns 3 and 6)
Candidate 7 appears in row 0 only at columns 3 and 6, and in row 5 only at columns 3 and 6. These four cells form a rectangle. Therefore, 7 can be eliminated from all other cells in columns 3 and 6. Blue cells show the X-Wing corners; red cells show where 7 is eliminated.
Pro Tips
- •Look for a candidate that appears exactly twice in two different rows
- •Check whether those four cells align on just two columns to form a rectangle
- •Eliminations always happen in the perpendicular direction — row-based X-Wings eliminate from columns
- •Pencil marks are essential — always maintain full candidate lists to spot X-Wings
- •X-Wings are relatively rare but very powerful when found
Practice Exercise
Find the X-Wing on digit 7 in the schematic above. It appears exactly twice in rows 0 and 5 at columns 3 and 6. Identify the four corner cells that form the X-Wing rectangle, then determine which cells in columns 3 and 6 lose candidate 7.
