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X-Wing

Two rows where a digit can only fit in the same two columns. Eliminate that digit from the rest of those columns. (Or swap row/col — the pattern works both ways.)

Advanced sudoku technique

What it is

An X-Wing is one of the first 'fish' techniques in sudoku — patterns spanning two rows and two columns that lock a digit into a 2×2 arrangement. The setup: pick a digit. Find two rows in which that digit's only possible cells lie in the SAME two columns. The four corner cells form an X. Because the digit must appear once per row and once per column, it must occupy two of those four corners — one per row, one per column. Therefore that digit cannot appear in those two columns in any OTHER row. The column-based version is symmetric: two columns sharing the same two rows for a digit prune that digit from the rest of those rows.

When to use it

On hard and expert puzzles when every simpler technique has stalled. Maintain accurate candidates and scan digit by digit for the 2×2 pattern.

Worked example

Digit 7 in rows 2 and 6 can only go in columns 1 and 5. The four cells R2C1, R2C5, R6C1, R6C5 form an X-Wing on 7. Two of those four cells will end up holding 7 (one in each row, one in each column). Therefore 7 cannot appear anywhere else in columns 1 and 5: R1C1, R3C1, R4C1, R5C1, R7C1, R8C1, R9C1 lose 7 as a candidate (and the same nine cells in column 5).

Try it

The Sudoku247Online solver walks you through every move of any puzzle one logical step at a time, naming the technique that justifies each placement. Paste a puzzle to see this technique applied in real time.

Related techniques

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