TECHNIQUE · EXPERT
X-Wing — cross-row, cross-column elimination
When a digit appears as a candidate in only two columns across two rows, the four cells form an X pattern. The digit can then be removed from those columns in every other row. Use this on Expert puzzles when Pairs are not enough.
The logic
Suppose digit N is a candidate only in columns X and Y of row A and row B. N must occupy one diagonal: (A,X)+(B,Y) or (A,Y)+(B,X). Either way, columns X and Y cannot hold N in any other row.
How to find it
Pick an unplaced digit and map which columns hold it in each row. If exactly two rows share the same two-column set, you have an X-Wing.
- Choose a digit that still has many candidate cells.
- For each row, note the column positions of that digit.
- If two rows have candidates in exactly the same two columns — X-Wing.
- Remove the digit from those two columns in all other rows.
Column-based X-Wing
The same logic works by columns. If a digit appears in only two rows across two columns, remove it from those rows in every other column.
Practice order
- Pick a digitChoose a digit with many remaining candidate cells.
- Map row positionsRecord which columns hold the digit in each row.
- Find the patternLook for two rows sharing the exact same two-column set.
- Eliminate columnsRemove the digit from those columns in all other rows.
Walk through it step by step
Step 1 of 4
Focus on digit 5. Rows 1 and 4 each have only two candidate cells for 5 — both at columns 2 and 8.