Sudoku Solving Techniques

X-Wing

If a digit is a candidate for exactly two cells in two different rows and the positions (columns) of those two cells in those two different rows are exactly the same, then this digit cannot be a candidate for any other rows in the same two positions (columns).

Consider the following Sudoku puzzle:

a Sudoku with X-Wing pattern

The four cells in yellow form a X-Wing pattern. The digit 7 is a candidate in exactly two cells in the third and sixth rows. Also the positions in these two rows are exactly the same at the fifth and seventh columns. There are two possible outcomes for the digit 7 in these two rows:

  1. the fifth column in the third row and the seventh column in the sixth row, or
  2. the seventh column in the third row and the fifth column in the sixth row.

Although we do not know which case is correct, it guarantees that the digit 7 must be in the third row or the sixth row at the seventh column. Therefore the 7 in the blue cell can be eliminated as a candidate.

The solution of this puzzle is almost reached after this step. But we need another technique called XYZ-Wing.

Please note that the roles of rows and columns for this technique can be swapped.