The X-Wing is one of the most famous advanced Sudoku strategies. It allows you to look beyond a single box or line and find a logical connection between different parts of the grid.
The X-Wing (Column) variation looks for a pattern based on columns.
Interactive Example
Click "Apply Logic" to see the strategy in action.
Real Example Explanation
In the interactive example above, focus on the number 1:
- Scan Columns: Look at Column 5 and Column 7.
- Count Candidates:
- In Column 5, the number 1 can only go in Row 3 (R3C5) and Row 5 (R5C5).
- In Column 7, the number 1 can only go in Row 3 (R3C7) and Row 5 (R5C7).
- The Rectangle: Notice that these four spots align perfectly to form a rectangle.
- The Logic:
- If R3C5 is the 1 for Column 5, then R5C7 must be the 1 for Column 7.
- If R5C5 is the 1 for Column 5, then R3C7 must be the 1 for Column 7.
- Either way, the two 1s for these two columns must occupy Row 3 and Row 5.
- The Elimination: Since Rows 3 and 5 are now "taken" by these columns, no other cell in Row 3 or Row 5 can be a 1. We remove the 1s from the red cells (R3C2 and R5C6).
The Core Logic
The X-Wing works because of a "locked set" across two units.
Imagine two vertical chutes (columns). Each chute needs a "ball" (the number 1). The only places for the ball in Chute A are at height X and height Y. The only places for the ball in Chute B are also at height X and height Y.
This creates a closed loop. If top-left has the ball, bottom-right must have it. If bottom-left has it, top-right must have it. In both scenarios, heights X and Y contain a ball. Therefore, nobody else at height X or Y (the horizontal rows) can have a ball.
How to Spot It
- Pick a Number: This strategy works on one specific number at a time (e.g., "Where are all the 7s?").
- Scan Vertical Lines: Look for columns where that number appears as a candidate exactly twice (or sometimes linked strongly).
- Check Alignment: If you find two columns where the candidates are in the exact same two rows, you have an X-Wing.
- Eliminate Horizontally: If you found the pattern in columns, you verify the logic and eliminate from rows.
(Note: If you find the pattern in rows, you eliminate from columns. That is an X-Wing (Row)).
Related Strategies
- Naked Pair: A simpler form of locked candidates.
- Swordfish: The logic expanded to three columns/rows.
- Jellyfish: The logic expanded to four columns/rows.