Sudoku Algorithms

The picture on the left shows an X-Wing pattern in the columns. The vertices of the rectangle D1-D7-G7-G1 have the hint '6' marked in yellow. Cells D1 and G1 are the only possible positions for the number 6 in column 1. Similarly, cells D7 and G7 are the only possible positions for the number 6 in column 7.
If 6 is in cell D1, then 6 must be in cell G7. In this case, the hint '6' should be removed from cells D5 and D8 (marked in red) in row D, and from cell G8 in row G. Conversely, if 6 is in cell G1, then 6 must be in cell D7. In this scenario, the hints 6 marked in red should also be removed.
Thus, the X-Wing pattern in columns 1 and 7 allows us to eliminate all other hints of 6 in rows D and G.

The picture on the left shows an X-Wing pattern in the rows. The vertices of the rectangle C1-C9-G1-G9 have the hint '3' marked in yellow. Cells C1 and C9 are the only possible positions for the number 3 in row C. Similarly, cells G1 and G9 are the only possible positions for the number 3 in row G. The X-Wing pattern in rows C and G allows us to remove all other hints of '3' marked in red in columns 1 (B1) and 9 (A9, B9, and H9).