X-Wing
Master advanced rectangular elimination patterns to solve complex puzzles through sophisticated candidate elimination.
What Is an X-Wing?
The X-Wing is an advanced Sudoku solving technique that uses rectangular patterns to eliminate candidates. It occurs when a candidate number appears in exactly two positions in each of two rows (or columns), and these positions form a rectangle.
Key Insight
The name "X-Wing" comes from the X-shaped pattern formed by drawing diagonal lines between the four corners of the rectangle. Since the candidate must appear once in each row and column, it can be eliminated from other positions in the affected columns (or rows).
How X-Wing Works
The Process
- 1 Find two rows where a candidate appears in exactly two positions
- 2 Verify these positions are in the same two columns
- 3 The four cells form the corners of a rectangle
- 4 Eliminate the candidate from all other cells in those columns
The Pattern
Row A: [ ][ ][X][ ][ ][X][ ][ ][ ]
Row B: [ ][ ][ ][ ][ ][ ][ ][ ][ ]
Row C: [ ][ ][ ][ ][ ][ ][ ][ ][ ]
Row D: [ ][ ][X][ ][ ][X][ ][ ][ ]
Col: 3 6
Eliminate candidate from all other cells in columns 3 and 6
Example: X-Wing in Action
Here's an X-Wing pattern with the number 5. The candidate appears in exactly two positions in rows 1 and 4, aligned in columns 3 and 6:
Purple cells: The X-Wing corners (5 can only be here in rows 1 and 4)
Red cells: 5 can be eliminated from these cells in columns 3 and 6
Result
The 5 must appear in one of the diagonal pairs: either (Row 1, Col 3) and (Row 4, Col 6), or (Row 1, Col 6) and (Row 4, Col 3). Either way, columns 3 and 6 are "covered" by the X-Wing, so 5 can be eliminated from all other cells in these columns.
When to Use X-Wing
Best Scenarios
- ✓ Hard puzzles that require advanced techniques
- ✓ When intermediate techniques don't reveal progress
- ✓ Rows/columns with exactly two possible positions for a number
- ✓ After exhausting all simpler elimination methods
Common Mistakes
- ✗ Not verifying the rectangle is perfect (exactly 2 in each row)
- ✗ Eliminating from the wrong lines
- ✗ Missing the pattern due to incomplete candidate marking
- ✗ Confusing row-based and column-based X-Wings
Practice Tips
How to Find X-Wings
- 1 Mark all candidates thoroughly
- 2 For each number, find rows with exactly 2 occurrences
- 3 Check if two such rows share the same two columns
- 4 Apply eliminations to other cells in those columns
Related Techniques
- Y-Wing - Chain-based elimination pattern
- Pointing Pairs - Simpler box-line interaction
- Box/Line Reduction - Line-box interaction
Ready to Practice X-Wing?
Look for rectangular patterns in hard puzzles - find candidates that appear exactly twice in two rows!
Practice Now