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.
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.
FAQs
The X-Wing relies on logic between the four identified cells sharing the same candidate digits. In this case, the number 5 repeats in cells r4c4, r6c4, r4c7 and r6c7. The X in the technique's name is also due to the relationship between these cells. In this case, cell r4c4 is connected to r6c7 while r6c4 is with r4c7.
What is the xy wing strategy in Sudoku? ›
XY wings must involve 3 buddy cells that are bi-value (have only 2 candidates each) so start by searching for 3 bi-value buddy such. Those 3 cells must then have XY, XZ and YZ as candidates. One you find this scenario, look for the buddy cells of both XZ and YZ cells and eliminate Z from those.
How does an X-Wing work? ›
Armed with four laser cannons and two proton torpedo launchers, the X-wing can take on anything the Empire throws at it. Nimble engines give the X-wing an edge during dogfights, and it can make long-range jumps with its hyperdrive and its astromech droid co-pilot.
What is the secret to figuring out Sudoku? ›
The most basic strategy to solve a Sudoku puzzle is to first write down, in each empty cell, all possible entries that will not contradict the One Rule with respect to the given cells. If a cell ends up having only one possible entry, it is a "forced" entry that you should fill in.
What is the triple tactic in Sudoku? ›
"Hidden triples" technique is very similar to "Hidden pairs" and works on the same concept. "Hidden triples" applies when three cells in a row, column, or 3x3 block contain the same three Notes. These three cells also contain other candidates, which may be removed from them.
What is the best trick for Sudoku? ›
5 Best Tips for Playing Sudoku
- Look for the Easy Solutions. Many puzzles will leave one or two blanks either in a line or in a box. ...
- Seek the Missing Numbers. ...
- Keep Scanning the Entire Puzzle. ...
- Constantly Re-Evaluate the Grid. ...
- Be Patient and Enjoy the Hunt.
About Butterfly Sudoku
It involves a unique layout that resembles a butterfly, consisting of four 9x9 grids, arranged in a specific pattern. The challenge is to fill each grid with numbers from 1 to 9 while adhering to the traditional Sudoku rules and some additional constraints that make the puzzle intriguing.
What is the 3 number rule in Sudoku? ›
If three candidates can be found in only the same three Cells of a region (Row, Column or Square), then one of these candidates is the solution for the first of these Cells, a second one is the solution for the second Cell and the last candidate is the solution for the third Cell.
What is the math behind solving Sudoku? ›
To solve a Sudoku puzzle, one needs to use a combination of logic and trial-and-error. More math is involved behind the scenes: combinatorics used in counting valid Sudoku grids, group theory used to describe ideas of when two grids are equivalent, and computational complexity with regards to solving Sudokus.
Is there any formula to solve Sudoku? ›
Rules of Addition Equation Sudoku
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the 9x9 grid. At the bottom and right side of the 9x9 grid are numbers, each of which is the sum of a column or row of unknown digits marked by asterisks. * + * = 9.
Algorithm X is a nondeterministic, recursive algorithm that uses depth-first search for backtracking [9, p. 2]. It was created by Donald Knuth and can be used to find all solutions to the exact cover problem [8, p.
What does the X mean in Sudoku? ›
This is a variant of the popular Sudoku puzzle which contains two extra constraints on the solution, namely the diagonals, typically indicated by grey cells.
What is an X cycle in Sudoku? ›
In this strategy we build loops by alternately chaining Weak Links and Strong Links (also see note at the bottom of this page). Such a loop can be read in both directions; whichever the direction, a Strong Link remains a Strong Link and a Weak Link remains a Weak Link.
What is cross hatching Sudoku rules? ›
Also known as cross-hatching, this method involves looking at all the appearances of a given number, and drawing imaginary lines horizontally and vertically from these numbers. Each number can only appear in each row or column once, so these lines eliminate possibilities for where the number can appear in other boxes.
What is the X chain in Sudoku? ›
X-Chains are chains that use one digit only. X-Chains of length 4 are sometimes called Turbot Fishes and can be found using the appropriate Turbot variants (Skyscraper, 2-String Kite, or Empty Rectangle). The important thing with X-Chains is, that they have to start and end with a strong link.
