Advanced Sudoku Strategy
X-Wing Sudoku Technique: Step-by-Step Guide
Learn how to recognise row-based and column-based X-Wing patterns, remove candidates correctly, and use this advanced technique without guessing.
The Four-Corner Pattern
An X-Wing uses one candidate across two rows and two columns. The four candidate positions form the corners of a rectangle.
Complete Notes First
X-Wing depends on accurate candidate positions. Missing notes can create a false pattern.
Scan One Number
Choose one candidate and compare its positions across different rows or columns.
Remove, Then Rescan
After an X-Wing elimination, check for new singles and easier patterns before searching again.
What Is an X-Wing in Sudoku?
An X-Wing is an advanced candidate-elimination technique. It occurs when one candidate appears in exactly two cells in each of two rows, and those four cells line up in the same two columns.
Because the candidate must appear once in each selected row, it must occupy opposite corners of the rectangle. That means no other cell in either of the aligned columns can contain that candidate.
The same logic also works in reverse. Two columns can form an X-Wing when the candidate positions line up in the same two rows.
X-Wing Pattern at a Glance
How a Row-Based X-Wing Works
Choose One Candidate
Select one number, such as candidate 5, and scan all rows for its possible positions.
Find Two Matching Rows
Look for two rows where candidate 5 appears in exactly two cells, and make sure those cells lie in the same two columns.
Confirm the Rectangle
The four candidate positions should form the corners of a rectangle. For example: row 2 columns 3 and 8, and row 7 columns 3 and 8.
Remove the Candidate From the Columns
Remove candidate 5 from every other unsolved cell in columns 3 and 8. Do not remove it from the four X-Wing cells.
Row-Based X-Wing Example
Imagine candidate 7 appears only in columns 2 and 6 of row 3. It also appears only in columns 2 and 6 of row 8.
Candidate Positions
One 7 must go in row 3 and one 7 must go in row 8. Whichever corners are used, columns 2 and 6 will receive their 7 from those two rows. Therefore, candidate 7 can be removed from all other cells in columns 2 and 6.
How a Column-Based X-Wing Works
A column-based X-Wing uses the same logic in the opposite direction. Instead of starting with two rows, you start with two columns.
Column-Based Checklist
- 1. Choose one candidate.
- 2. Find two columns where it appears in exactly two cells.
- 3. Confirm the four cells line up in the same two rows.
- 4. Remove that candidate from other cells in those rows.
For example, if candidate 4 appears only in rows 1 and 6 of column 3, and only in rows 1 and 6 of column 9, remove candidate 4 from other cells in rows 1 and 6.
Why the X-Wing Elimination Is Valid
Suppose two rows form an X-Wing for candidate 9. In the first row, 9 must occupy one of two aligned columns. In the second row, 9 must occupy the other aligned position so that each column receives only one 9.
There are two possible diagonal arrangements, but both arrangements use the same two columns. Therefore, those columns cannot contain another 9 outside the X-Wing.
Key Logic
You do not need to know which two corners are correct. You only need to know that the candidate must occupy two of the four corners and therefore cannot appear elsewhere in the affected lines.
When Should You Look for an X-Wing?
After Basic Techniques Stop
Check singles, locked candidates, and subsets first. X-Wing is most useful when easier methods produce no progress.
When One Candidate Is Restricted
X-Wings are easier to spot when the same candidate appears only twice in several rows or columns.
In Hard and Expert Puzzles
Easy puzzles rarely require X-Wing. Hard and Expert Sudoku are better places to practise it.
When Notes Are Complete
Never search for X-Wing with incomplete candidates. The technique depends on exact candidate counts.
Common X-Wing Mistakes
❌ More Than Two Candidates in a Base Row
For a standard row-based X-Wing, the candidate must appear exactly twice in each selected row.
❌ Columns Do Not Match
The two candidate positions in both rows must line up in the same two columns.
❌ Eliminating From the Wrong Direction
Row-based X-Wings eliminate from columns. Column-based X-Wings eliminate from rows.
❌ Removing the Candidate From a Corner
The four X-Wing cells must keep the candidate. Only remove it from other cells in the affected lines.
X-Wing vs. Similar Sudoku Techniques
How to Practise the X-Wing Technique
1. Turn On Notes
Complete candidate notes across the puzzle before looking for fish patterns.
2. Scan Candidate by Candidate
Check all positions for 1, then 2, then 3, and continue to 9. A systematic scan is more reliable than random searching.
3. Mark Rows With Exactly Two Positions
Compare those rows and look for matching columns. Then repeat the process with columns.
4. Explain the Elimination
Before removing a candidate, identify the two base lines, two cover lines, and four corner cells.
Related Sudoku Learning Pages
🧠 Advanced Sudoku Techniques
Learn locked candidates, subsets, wings, coloring, chains, and more.
📘 Sudoku Strategies
Review essential solving methods before attempting advanced patterns.
🟠 Hard Sudoku
Practise candidate elimination in difficult puzzles.
🔴 Expert Sudoku
Challenge yourself with puzzles that may require X-Wing and other advanced techniques.
Frequently Asked Questions
What is an X-Wing in Sudoku?
An X-Wing is a four-cell pattern involving one candidate, two rows, and two columns. It allows that candidate to be removed from other cells in the aligned lines.
Is X-Wing an advanced technique?
Yes. It usually appears in Hard or Expert Sudoku and requires accurate candidate notes.
Can X-Wing work with columns?
Yes. A column-based X-Wing uses two columns whose candidate positions line up in the same two rows.
Does X-Wing place a number directly?
Usually not. It removes candidates, which may then reveal a naked single, hidden single, or another useful pattern.
What is the difference between X-Wing and Swordfish?
X-Wing uses two rows and two columns. Swordfish expands the same fish-pattern logic to three rows and three columns.
Practise Finding an X-Wing
Open a Hard or Expert Sudoku puzzle, turn on Notes, and scan one candidate at a time. Look for two rows or columns with matching candidate positions.