X-Wing
A digit appearing in exactly two cells in two rows, aligned in the same two columns — eliminate from those columns.
What is X-Wing?
X-Wing is one of the most famous and celebrated advanced Sudoku techniques, and mastering it marks a significant milestone in a solver's journey. It occurs when a specific digit appears as a candidate in exactly two cells in each of two different rows, and those four cells form a rectangle — meaning the two rows share the exact same two columns for that digit's candidates. The underlying logic is elegant: in each of the two rows, the digit must go in one of the two candidate cells. Since those cells align in only two columns, the digit in each row must occupy one of the two column positions. This guarantees that both columns will each receive exactly one instance of the digit (one from each row). Consequently, the digit cannot appear in any other cell in those two columns — it can be safely eliminated from all other cells in both columns. The result is often a cascade of new Singles or patterns. X-Wing also has a column-first variant: find two columns where a digit appears in exactly two cells each, both aligned in the same two rows — then eliminate from those rows.
When to Use X-Wing
Use X-Wing when all intersection techniques (Pointing Pairs, Box-Line Reduction) and subset techniques (Naked/Hidden Pairs and Triples) have been exhausted and the puzzle still has unsolvable cells. X-Wing is particularly effective on Hard and Expert puzzles where a single digit has many candidates spread across the grid. Before applying X-Wing, ensure your candidate grid is fully updated and accurate — stale candidates will cause false pattern matches. To search efficiently, for each digit, list all rows that contain exactly two candidate cells for that digit, then check whether any two such rows share the same two columns for those candidates.
How to Apply X-Wing — Step by Step
- 1
Choose a candidate digit and analyze rows
Select a digit (say, digit 4) and go through each row on the board. For each row, count how many cells have digit 4 as a candidate. You are only interested in rows where digit 4 appears in exactly two candidate cells — make a note of those rows and the specific column positions of the two candidates.
- 2
Find two rows sharing the same two columns
From your list of rows (each with exactly two candidate positions for the digit), look for two rows where the two candidate cells fall in the same two columns. For instance, Row 2 has digit 4 candidates in Columns 3 and 7, and Row 6 also has digit 4 candidates only in Columns 3 and 7. These four cells (2×3, 2×7, 6×3, 6×7) form an X-Wing rectangle.
- 3
Verify the pattern is complete
Confirm that digit 4 appears in exactly two cells in each of the two rows, and those cells are in exactly the two identified columns. There must be no other candidate cells for digit 4 in either row. This confirmation is critical — a violation means the X-Wing pattern doesn't hold and eliminations would be incorrect.
- 4
Eliminate from both columns
Since digit 4 must occupy either Column 3 or Column 7 in both Row 2 and Row 6, it cannot appear in any other row along those two columns. Remove digit 4 from every other candidate cell in Column 3 and Column 7 (except for the four X-Wing cells themselves). After elimination, immediately re-scan the entire board for new singles and patterns.
💡 Pro Tip
X-Wing also works "column-first": find two columns where a digit appears in exactly the same two rows, then eliminate from those rows. When scanning for X-Wings, create a quick reference table showing, for each digit, which rows contain exactly 2 candidate cells — and the column positions of those cells. This table makes spotting the pattern almost mechanical. Also, keep in mind that after applying an X-Wing, the newly eliminated candidates often trigger a chain reaction of simpler techniques, so always perform a full re-scan after any X-Wing elimination.
Practice X-Wing Now
Put this technique to the test on a live puzzle. The Practice Mode lets you work through real examples with candidate marking.