X-Wing

The X-Wing is a powerful advanced technique. It applies when a single digit appears as a candidate in exactly two cells in each of two different rows, and those four cells occupy the same two columns. The four cells form a rectangle - The "X-Wing" shape.

Because the digit must go in one pair of diagonal corners or the other, it will always occupy both of those columns. Therefore, the digit can be safely eliminated from all other cells in those two columns.

1. Choose a digit (e.g., 5) and fill in all candidate notes.
2. For each row, note the columns where 5 is a candidate. Keep only rows where 5 appears in exactly two cells.
3. Look for two such rows where the candidate cells are in the same two columns.
4. You have found an X-Wing. The four cells form a rectangle.
5. Eliminate 5 from every other cell in those two columns (outside the X-Wing rows).
6. Check for new Obvious Singles or Hidden Singles created by the elimination.

X-Wings can also be found by scanning columns instead of rows. Find two columns where the digit appears in exactly two cells, and those cells are in the same two rows. Then eliminate the digit from all other cells in those two rows.

Whether you scan rows or columns first, you will find all X-Wings if you check both orientations.