X-Wing

Hard

A digit confined to the same two columns across two rows forms a rectangle; it can be eliminated from those columns in all other rows.

How It Works

When a digit appears in exactly two columns across two rows, it forms a rectangle. The digit must occupy two diagonally opposite corners, so it can be eliminated from those same two columns in all other rows.

The same logic applies column-wise: two rows and two columns form the X-Wing.

X-Wing is the foundation of the larger "fish" techniques (Swordfish, Jellyfish).

Example

8	7	5	2	9	1	6	4	3
1	2	3	46	46	8	5	7	9
4	69	69	3	5	7	1	2	8
26	4	126	7	3	5	9	8	16
3	5	16	8	2	9	4	16	7
9	8	7	14	14	6	2	3	5
5	1	8	69	7	2	3	69	4
26	3	269	169	8	4	7	5	16
7	69	4	5	16	3	8	169	2

Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Medium26 givensStrict

8	7	5	2	9	1	6	4	3
1	2	3	46	46	8	5	7	9
4	69	69	3	5	7	1	2	8
26	4	126	7	3	5	9	8	16
3	5	16	8	2	9	4	16	7
9	8	7	14	14	6	2	3	5
5	1	8	69	7	2	3	69	4
26	3	269	169	8	4	7	5	16
7	69	4	5	16	3	8	169	2

8	7	5	2	9	1	6	4	3
1	2	3	46	46	8	5	7	9
4	69	69	3	5	7	1	2	8
26	4	126	7	3	5	9	8	16
3	5	16	8	2	9	4	16	7
9	8	7	14	14	6	2	3	5
5	1	8	69	7	2	3	69	4
26	3	269	169	8	4	7	5	16
7	69	4	5	16	3	8	169	2

8	7	5	2	9	1	6	4	3
1	2	3	46	46	8	5	7	9
4	69	69	3	5	7	1	2	8
26	4	126	7	3	5	9	8	16
3	5	16	8	2	9	4	16	7
9	8	7	14	14	6	2	3	5
5	1	8	69	7	2	3	69	4
26	3	269	169	8	4	7	5	16
7	69	4	5	16	3	8	169	2