What is Sudoku X-Wing Pattern?
The Sudoku X-Wing pattern or technique is one of the most advanced techniques that can be applied to Sudoku puzzles from a medium difficulty level onwards. It is a very forthright method with a simply discernable pattern. It emphasizes one single digit, and its goal is to confine the number of cells that can have that number as a possible candidate. Sudoku X-Wing technique is also a valuable strategy for any player to learn as it branches out into more complex patterns and techniques that are required to solve impossible puzzles.
In this article, I use one of my handcrafted, very difficult puzzles that have a known X-Wing pattern. Go ahead, download and print out this PDF very hard Sudoku puzzle #1. and follow along. I’ll wait. Back? Great. Let’s get started.
Sudoku X-Wing Pattern
You will need to partially solve the puzzle to reach the picture shown. If you have trouble getting to this position, follow the steps I have outlined in my article “How to Solve Sudoku” X-Wing”.
You will need to solve naked singles, hidden singles, a naked pair (4,7) in row 7, a locked candidate (5) in column 7, and a naked triple (2,4,5) in column 1 first. If these terms are not familiar, read my article Sudoku Tips for an illustrative guide.
An X-Wing pattern occurs when two rows (or two columns) each contain only two cells that hold a matching candidate. This candidate must reside in both rows and share the same two columns or vice versa. In the example shown, an X Wing pattern occurs in row 2 and row 5. Each row has the number 4 in only two cells.
In row 2, the cells are (R2, C3) and (R2, C7). In row 5, the cells are (R5, C3) and (R5, C7). These four positions are highlighted in grey. The number 4 can only appear in two of the four positions. The two positions have to be diagonally opposites forming an X (hence the name). This means the 4 will reside in the pair (R2,C3) and (R5,C7) or in the pair (R2,C7) and (R5,C3).
Sudoku rules forbid any other combination. At this point, we do not know which pair the 4 will reside in.
We do know that it must reside in two of the four positions highlighted. Therefore, it is safe to eliminate the 4s from column 3 and column 7 except for the highlighted positions. The cells circled in red may have the number 4 removed from them safely. When you remove the 4s, you now expose a naked single in (R7, C7).
Solve the naked single and the logjam is broken. You will be able to solve the puzzle quickly now.
Congratulations on solving a very difficult Sudoku puzzle. For more difficult puzzles see my collection of printable free sudoku puzzles. They come in five levels of difficulty.