Advanced Solving Sudoku Technique: XY-Wing

5/10/2018

If you want to be a savvy Sudoku solver, this technique is a must to grasp: XY-Wing.

Simply speaking, when one square with candidates {X, Y} is in the same row, column, or box as two squares with candidate numbers {X, Z}, and {Y, Z}, candidate number Z can be eliminated from the squares in the same row, column, or box as these two squares.

Candidate Numbers (or Candidate Values) of a blank/empty square is a list of ‘possible values’ or candidates for this blank/empty cell. Below is an example of using XY-Wing to refine the candidate values of R3C6. Empty Squares are marked with candidate values.

Use basic methods to solve the Sudoku until no further blank/empty square can be inferred to be a number using basic methods (Sole Candidate and Hidden Single).
Write down the candidate values for every blank/empty square.
Apply interaction methods, Subset, SubsetPosition, X-Wing methods if necessary.
Check if one square with candidates X, Y is in the same row, column, or box, two squares with candidates X, Z and Y, Z. If there exists such a blank/empty square, we can eliminate candidate Z from the squares in the same row, column, or box as these two squares.