Introduction

If you can solve easy Sudoku puzzles in a snap, then you're ready to work on more difficult puzzles and use advanced strategies like the X-wing technique. Suitable for intermediate to hard Sudoku puzzles, this technique has you focus on a single candidate that appears in a pattern so you can eliminate candidates and solve puzzles faster and easier.

What Is the X-Wing Technique?

The X-wing technique is a Sudoku strategy named for the X-like pattern it forms when visualized on the Sudoku grid, forming a four-point X-cycle. It helps eliminate candidates by identifying where a specific candidate is restricted to exactly two possible cells in two rows or columns.

Because the candidate must appear in one of these two cells in each row (or column), it cannot appear in any other cell within the same columns (or rows). This allows all other instances of that candidate in the affected columns or rows to be removed, which can lead to a chain reaction of answers or eliminations.

For example, in a grid where the candidate number 3 occurs just twice in rows 1 and 5, but it occurs multiple times in columns F and H, any time 3 occurs in columns F and H outside of the X-wing pattern (F2, F6, H4, H6), it can be eliminated.

Key Points

Essential concepts for the X-Wing technique:

Pattern formation: A candidate appears exactly twice in two rows (or columns), with those occurrences aligned in the same two columns (or rows)
Four-cell rectangle: The pattern forms a rectangle with four cells, where the candidate appears at the corners
Orientation matters: X-Wing can be horizontal (rows) or vertical (columns), determining where eliminations occur
Elimination logic: The candidate must appear in one of the pattern cells, so it cannot appear elsewhere in the shared columns/rows
Requires pencil marks: Complete candidate marking is essential to identify the pattern
Chain reactions: One elimination can lead to multiple subsequent eliminations or placements

How to Find X-Wings

The X-wing technique works by identifying where a specific candidate is restricted to exactly two possible cells in two rows or columns. When these restrictions align in the same two columns (or rows), they form the X-Wing pattern.

An X-wing can be orientated in two ways: horizontally (rows) or vertically (columns). Orientation refers to whether two rows or two columns have exactly two occurrences of the same candidate.

The orientation of the X-wing determines where you can eliminate candidates. In a horizontal X-wing, you eliminate candidates from the two shared columns, and in a vertical X-wing, you eliminate candidates from the two shared rows.

X-Wing with Horizontal Orientation

To find an X-wing with horizontal orientation, you're looking for a row that has just two occurrences of the same candidate. To do so, you need to note all the candidates by using pencil marks or electronic candidate mode and completely fill in all possible candidates.

Although it's an advanced Sudoku technique, you can easily find an X-wing by following these simple steps:

Step 1: Identify a Single Candidate That Appears Only Twice in a Single Row

Scan the first row for a candidate that appears just twice. If you find one, go on to the next step. If not, continue looking in the second row, and so on until you find one. For example, the candidate 4 appears just twice in row 2 (C2, E2).

This step requires complete pencil marks or candidate mode. Without seeing all possible candidates, you cannot identify the pattern. Make sure you've marked all candidates before attempting to find X-Wing patterns.

Step 2: Check to See If That Candidate Appears Only Twice in Another Row and Ensure It's in the Same Two Columns

Once you've found a candidate that appears just twice in a row, look down each column in which it appears. Confirm whether the same candidate appears only once again in each column and that they share the same row. For example, the candidate 4 appears just once again in columns C and E, sharing row 6.

If the candidate does appear only twice in another row, but those two cells aren't aligned in one column, you can use the Sudoku skyscraper technique to eliminate candidates instead.

The key requirement is that the two rows must have the candidate appearing in the same two columns. This alignment creates the rectangle pattern necessary for the X-Wing technique.

Step 3: Eliminate Instances of the Candidate That Aren't Part of the Pattern But Fall Within the Same Columns

If a candidate appears in the pattern, creating the points of an X, then the candidate must be an answer in one of the rows, so it will appear in one of the cells in each column. Therefore, you can eliminate occurrences of that candidate from other cells within those two columns.

For example, any 4s in columns C and E that aren't in rows 2 or 6 can be crossed out and eliminated. Note that cells in an X-wing form a rectangle, with the cells that share the same candidate as the corners, but only the corners forming the X are part of the pattern, not the entire rectangle.

The logic behind this elimination is clear: since the candidate must appear in one of the two cells in each row of the pattern, and those cells are in the same two columns, the candidate cannot appear anywhere else in those columns.

X-Wing with Vertical Orientation

To find an X-wing with vertical orientation, you still need to mark all the candidates in your puzzles using pencil marks or candidate mode. But instead of looking for only two occurrences in a row, you look for two occurrences in a single column, following the same principles as you do for horizontal orientation. Just follow these steps:

Step 1: Circle a Single Candidate That Appears Only Twice in a Single Column

Scan the first column for a candidate that appears just twice. If you find one, go on to the next step. If not, continue looking in the second column, and so on until you find one. For example, the candidate 6 appears just twice in column B (B3, B7).

Vertical X-Wing follows the same logic as horizontal X-Wing, but rotated 90 degrees. Instead of scanning rows, you scan columns for candidates appearing exactly twice.

Step 2: Check to See If That Candidate Appears Only Twice in Another Column and Ensure It's in the Same Two Rows as It Appears in Step 1

Once you've found a candidate that appears just twice in a column, look across each row in which it appears. Confirm whether the same candidate appears again in only one other column and within the same rows. For example, the candidate 6 appears only twice in column D, specifically in rows 3 and 7 (D3, D7).

The alignment requirement is the same as horizontal X-Wing: the two columns must have the candidate appearing in the same two rows. This creates the rectangle pattern, but oriented vertically.

Step 3: Eliminate Instances of the Candidate That Aren't Part of the Pattern But Fall Within the Same Rows

If a candidate appears in the pattern, creating the points of an X, then the candidate must be an answer in one of the columns, so it will appear in one of the cells in each row. Therefore, you can eliminate occurrences of that candidate from other cells within those two rows.

For example, any 6s in rows 3 and 7 that aren't in columns B and D can be crossed out and eliminated. Note that cells in an X-wing form a rectangle, with the cells that share the same candidate as the corners, but only the corners are part of the pattern, not the entire rectangle.

In vertical X-Wing, eliminations occur in the shared rows, whereas in horizontal X-Wing, eliminations occur in the shared columns.

Examples

Example 1: Horizontal X-Wing with Candidate 3

In this example, we're looking for candidate 3:

Row 1: Candidate 3 appears exactly twice in columns F and H (F1, H1)
Row 5: Candidate 3 appears exactly twice in columns F and H (F5, H5)

This creates a horizontal X-Wing pattern. The candidate 3 must appear in one of the two cells in each row, and since both rows have 3 in the same two columns (F and H), we can eliminate candidate 3 from all other cells in columns F and H.

Eliminations: Any 3s in columns F and H outside of rows 1 and 5 (such as F2, F6, H4, H6) can be eliminated.

Example 2: Vertical X-Wing with Candidate 6

In this example, we're looking for candidate 6:

Column B: Candidate 6 appears exactly twice in rows 3 and 7 (B3, B7)
Column D: Candidate 6 appears exactly twice in rows 3 and 7 (D3, D7)

This creates a vertical X-Wing pattern. The candidate 6 must appear in one of the two cells in each column, and since both columns have 6 in the same two rows (3 and 7), we can eliminate candidate 6 from all other cells in rows 3 and 7.

Eliminations: Any 6s in rows 3 and 7 outside of columns B and D can be eliminated.

Example 3: Horizontal X-Wing with Candidate 4

In this example:

Row 2: Candidate 4 appears exactly twice in columns C and E (C2, E2)
Row 6: Candidate 4 appears exactly twice in columns C and E (C6, E6)

This horizontal X-Wing allows us to eliminate candidate 4 from all other cells in columns C and E that are not in rows 2 or 6.

When to Use the X-Wing Technique

The X-Wing technique is most effective in these situations:

Medium to hard puzzles: When basic techniques like singles, pairs, and triples are no longer sufficient
After pencil marking: When you have complete pencil marks or candidate mode showing all possible candidates
When stuck: When you can't find any obvious moves using simpler techniques
Systematic solving: As part of a regular solving routine for advanced puzzles
Pattern recognition: When you notice a candidate appearing frequently but restricted to specific cells

Pro Tip: X-Wing patterns are easier to spot when you have complete pencil marks. Make sure all possible candidates are marked before looking for X-Wing patterns. Also, practice scanning both horizontally and vertically, as the pattern can appear in either orientation.

Common Mistakes to Avoid

When using the X-Wing technique, avoid these common mistakes:

Incomplete pencil marks: Without complete candidate marking, you cannot reliably identify X-Wing patterns
Wrong alignment: The candidate must appear in the same two columns (horizontal) or rows (vertical) in both rows/columns
Eliminating pattern cells: Only eliminate candidates outside the four-cell pattern, not from the pattern cells themselves
Confusing with other techniques: X-Wing requires exactly two occurrences in each row/column; if there are more, consider Swordfish or other techniques
Not checking both orientations: Always scan for both horizontal and vertical X-Wing patterns

How X-Wing Relates to Other Techniques

The X-Wing technique is part of a family of pattern-based elimination techniques:

Swordfish: Extends X-Wing to three rows/columns instead of two
Jellyfish: Extends further to four rows/columns
Skyscraper: Similar pattern but with different alignment requirements
Y-Wing (XY-Wing): Uses three bi-value cells instead of pattern-based elimination

Understanding X-Wing helps you recognize when to look for these more advanced patterns.

Summary

The X-Wing technique is a powerful advanced Sudoku strategy that identifies patterns where a candidate appears exactly twice in two rows (or columns), with those occurrences aligned in the same two columns (or rows). This creates a four-cell rectangle pattern that allows systematic elimination of the candidate from other cells in the shared columns (horizontal X-Wing) or rows (vertical X-Wing).

To find horizontal X-Wing patterns, scan rows for candidates appearing exactly twice, then check if another row has the same candidate in the same two columns. For vertical X-Wing, scan columns for candidates appearing exactly twice, then check if another column has the same candidate in the same two rows.

The technique requires complete pencil marks or candidate mode to identify the pattern accurately. It's most effective in medium to hard puzzles after basic techniques are exhausted. One elimination can lead to chain reactions of further eliminations or placements, making it a valuable tool for solving challenging puzzles.

Whether you're an advanced solver or just getting started with solving techniques, the best way to practice the X-wing strategy is to dig into a puzzle. So play Sudoku online and practice the Sudoku X-wing technique and try out more strategies like the Y-wing technique as you explore our archive for even more variety.

Ready to master X-Wing? Try our Sudoku game, learn more techniques, or practice with expert puzzles to apply the X-Wing technique!

❓ FAQ

Q1: What is the X-Wing technique in Sudoku?

The X-Wing technique is an advanced Sudoku strategy that identifies patterns where a candidate appears exactly twice in two rows (or columns), with those occurrences aligned in the same two columns (or rows). This creates a four-cell rectangle pattern that allows elimination of the candidate from other cells in the shared columns or rows.

Q2: How do I find an X-Wing pattern?

To find a horizontal X-Wing, scan rows for a candidate appearing exactly twice, then check if another row has the same candidate in the same two columns. For vertical X-Wing, scan columns for a candidate appearing exactly twice, then check if another column has the same candidate in the same two rows. Complete pencil marks are essential.

Q3: What's the difference between horizontal and vertical X-Wing?

Horizontal X-Wing uses two rows with a candidate appearing exactly twice in each, aligned in the same two columns—eliminations occur in those columns. Vertical X-Wing uses two columns with a candidate appearing exactly twice in each, aligned in the same two rows—eliminations occur in those rows.

Q4: When should I use the X-Wing technique?

Use X-Wing in medium to hard puzzles after basic techniques are exhausted, when you have complete pencil marks, and when you notice a candidate appearing frequently but restricted to specific cells. It's most effective when you're stuck and need pattern-based eliminations.

Q5: Do I need pencil marks to use X-Wing?

Yes, complete pencil marks or candidate mode are essential to identify X-Wing patterns accurately. Without seeing all possible candidates, you cannot reliably identify where a candidate appears exactly twice in rows or columns.

Q6: Can X-Wing eliminate candidates from the pattern cells themselves?

No, X-Wing only eliminates candidates from cells outside the four-cell pattern. The pattern cells themselves are where the candidate must appear, so you cannot eliminate the candidate from those cells using this technique.

Q7: What happens if the candidate appears more than twice in a row or column?

If a candidate appears more than twice in a row or column, you cannot use X-Wing for that candidate in that unit. However, you might be able to use more advanced techniques like Swordfish (three rows/columns) or Jellyfish (four rows/columns).

Q8: How does X-Wing relate to other advanced techniques?

X-Wing is the foundation for more advanced pattern-based techniques. Swordfish extends X-Wing to three rows/columns, and Jellyfish extends to four. Skyscraper is similar but with different alignment requirements. Understanding X-Wing helps you recognize when to look for these more advanced patterns.

X-Wing Sudoku Technique: Use Cases and Examples