X-Wing: The Classic Advanced Pattern
Master the X-Wing technique to eliminate candidates using rectangular patterns across rows and columns.
Welcome to X-Wing, one of the most elegant and powerful techniques in Sudoku! This is where solving becomes truly exciting.
What is an X-Wing?
An X-Wing is a rectangular pattern formed by a candidate number appearing in exactly two positions in each of two parallel lines (rows or columns). When you spot this pattern, you can eliminate that candidate from all other intersecting perpendicular lines.
The Pattern
Imagine the corners of a rectangle marked with X's - that's your X-Wing! The pattern looks like:
Row A: X _ _ _ X _ _ _ _
Row B: _ _ _ _ _ _ _ _ _
Row C: X _ _ _ X _ _ _ _
↓ ↓
Col 1 Col 5
How X-Wing Works
If a candidate appears in exactly two cells in two different rows, and those cells align in the same two columns, then:
- The candidate must occupy opposite corners of the rectangle
- You can eliminate that candidate from all other cells in those two columns
The reverse also works for columns!
Row-Based X-Wing
Pattern: Same candidate in exactly 2 positions in 2 rows, aligned in same 2 columns
Elimination: Remove candidate from all other cells in those 2 columns
Example of Row-Based X-Wing:
- Row 2: Candidate 5 in columns 3 and 7
- Row 6: Candidate 5 in columns 3 and 7
- Action: Eliminate 5 from columns 3 and 7 (except rows 2 and 6)
Column-Based X-Wing
Pattern: Same candidate in exactly 2 positions in 2 columns, aligned in same 2 rows
Elimination: Remove candidate from all other cells in those 2 rows
Example:
- Column 1: Candidate 8 in rows 4 and 9
- Column 5: Candidate 8 in rows 4 and 9
- Action: Eliminate 8 from rows 4 and 9 (except columns 1 and 5)
Why It Works: The Logic
The candidate must be placed in opposite corners of the rectangle. Either:
- Configuration A: Top-left and bottom-right corners, OR
- Configuration B: Top-right and bottom-left corners
In both cases, the perpendicular lines (columns for row-based, rows for column-based) are "blocked" by the X-Wing, allowing safe elimination.
How to Find X-Wings
Pick a candidate number
Choose a number that appears frequently but not everywhere - candidates with limited placement work best.
Scan for rows with exactly 2 instances
Look through each row and identify those where your chosen candidate appears in exactly two cells.
Check if two rows align in the same columns
Compare rows to see if any pair has the candidate in the exact same two column positions.
Eliminate from the pattern columns
If you found a match, eliminate the candidate from all other cells in those two columns (except the X-Wing rows).
Repeat for columns
Now do the same process looking at columns instead of rows to find column-based X-Wings.
Common Mistakes
Watch out for these common X-Wing mistakes:
- Requiring all four corners: Only two corners need the candidate - the pattern shows where it CAN be, not where it IS
- Forgetting the "exactly two" rule: Each line must have exactly two positions for the candidate
- Not checking both orientations: Look for both row-based and column-based X-Wings
- Eliminating from the wrong lines: Remove from the perpendicular lines, not the pattern lines
Advanced Recognition
With practice, you'll spot X-Wings by:
- Scanning for candidates with limited placement options
- Looking for symmetrical patterns
- Checking rows/columns with many filled cells
When to Use X-Wing
X-Wing is powerful when:
- Basic and intermediate techniques are exhausted
- A candidate appears in limited positions
- You need to break through a difficult puzzle
Impact on Puzzle Solving
X-Wings often:
- Unlock multiple hidden singles
- Create cascading eliminations
- Provide the breakthrough on hard puzzles
- Lead to quicker solving once spotted
Variations and Extensions
Once you master X-Wing, you can learn:
- Swordfish: The same pattern with three lines instead of two
- Jellyfish: Four lines (very rare!)
- Finned X-Wing: X-Wings with an extra candidate
Practice Tips
- Start by searching for X-Wings with the number 1, then 2, etc.
- Use candidate notation to spot the pattern easier
- Draw rectangles to visualize the pattern
- Check both row-based and column-based in every puzzle
- Don't be discouraged - X-Wings take practice to spot quickly!
The Aha Moment
When you find your first X-Wing and watch the puzzle unlock, you'll experience one of Sudoku's greatest satisfactions. This technique separates casual players from serious solvers.
Next Steps
Ready for more advanced patterns?
- Swordfish - The three-line version of X-Wing
- XY-Wing - A different type of advanced pattern
- Simple Coloring - Using color logic to find eliminations