An X Wing is a Sudoku solving technique that lets you reduce the number of candidates in particular columns or rows of the grid.

While X Wings aren’t always required to solve Sudoku puzzles, knowing what they are and how to use them will help speed up your solves.

What is an X Wing in Sudoku?

The best way to take you through what an X Wing is and how they can help you solve a Sudoku is with an example. 

Consider the Sudoku puzzle below. In this example we’ll focus on the 5s by pencil marking in all the possible cells a 5 could appear in all of the boxes without a 5 based on the given values.  

Your first thought might be that there’s no way to know for sure where any of the 5s go as there are no naked singles. (There is no pencil marked 5 in its own column, row, or box without any other pencil marked 5s).  

But on closer inspection, there is an interesting pattern going on with the pencil marked 5s in rows 3 and 7. The reason the pencil marked 5s in these two rows are interesting is because there are only two in each row and they occur in the exact same columns. 

These four pencil marked 5s form an X pattern which is highlighted below.

How do you solve using an X Wing?

It’s one thing to know that an X Wing is formed when pencil marks for a particular value occur exactly twice in the same locations in two rows or columns. It’s another thing to know how this helps you solve a Sudoku puzzle.

To show why X Wings are powerful, let’s consider columns 7 and 8 in example above (the two columns where the X Wing is formed). 

We know, from the basic rules of Sudoku, that these columns must contain only one 5 each. And we also know from the pencil markings that the 5s in rows 3 and 7 (the rows where the X Wing is formed) can only contain 5s in these columns. 

This means these 5s are essentially ‘locked into’ one of two places. Either they occur in the top left and bottom right corners of the X, or they occur in the top right and bottom left corners. 

Because the 5s must occur in one of these two columns for rows 3 and 7, it means that the 5s for columns 7 and 8 must occur in these two rows. 

If, for sake of argument, you placed 5s elsewhere in columns 7 and 8, then there would be no available cell to place 5s in for rows 3 and 7. 

This means we can now eliminate the other 5 pencil markings in columns 7 and 8 as well as in box 3 (the upper right box). This gives the location of the 5 in box 6 (the rightmost box in the center). 

This then allows us to also resolve the 5s in the two upper left boxes. 

While this hasn’t resolved the 5s that formed the X Wing, it has allowed us to place 5s in every other box in the grid. This is a major step to fully solving the Sudoku puzzle.

Summary

Identifying and using X Wings is a powerful technique to solve Sudokus. 

The first step is to identify X Wings is to look for rows or columns that contain candidates of a particular value in only two locations that are repeated for the corresponding row or column. 

Once you’ve identified an X Wing, you can then eliminate all other candidates of the same value along the corresponding rows or columns. 

Helpful points and tips to keep in mind

• While in our example we identified an X Wing by finding two pencil marked 5s in the same locations across two rows, X Wings can also be formed across columns. That is, rows and columns work interchangeably. 
• When forming an X Wing, it’s critical that there are only two locations for the candidates in either the rows or columns. If in the example, there was another pencil marked 5 in either row 3 or 7 (or both) then the X Wing would not help solve the Sudoku.
• When looking for X Wings, it can be easier to think of them as rectangles with the candidates as the corners instead of looking for Xs. 
• It doesn’t matter what other values (if any) are pencil marked into the corners of an X Wing.