XY-Wing

Hard

A pivot cell with two candidates {X,Y} sees two wings {X,Z} and {Y,Z}; digit Z is eliminated from cells seeing both wings.

How It Works

A "pivot" cell has candidates {X,Y}. It sees two "wing" cells: one with {X,Z} and one with {Y,Z}. If pivot takes X, the first wing must take Z. If pivot takes Y, the second wing takes Z. Either way, Z must be in one of the wings — so any cell seeing both wings can have Z eliminated.

This technique uses "pincer" logic and is very powerful.

Example

37	37	2	4	9	6	5	1	8
1	4	5	2	3	8	67	67	9
6	8	9	1	5	7	2	3	4
2	1	6	7	4	3	9	8	5
8	37	347	5	6	9	147	2	17
9	5	47	8	1	2	3	47	6
34	6	13	9	7	14	8	5	2
5	2	17	6	8	14	47	9	3
47	9	8	3	2	5	146	46	17

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

37	37	2	4	9	6	5	1	8
1	4	5	2	3	8	67	67	9
6	8	9	1	5	7	2	3	4
2	1	6	7	4	3	9	8	5
8	37	347	5	6	9	147	2	17
9	5	47	8	1	2	3	47	6
34	6	13	9	7	14	8	5	2
5	2	17	6	8	14	47	9	3
47	9	8	3	2	5	146	46	17

37	37	2	4	9	6	5	1	8
1	4	5	2	3	8	67	67	9
6	8	9	1	5	7	2	3	4
2	1	6	7	4	3	9	8	5
8	37	347	5	6	9	147	2	17
9	5	47	8	1	2	3	47	6
34	6	13	9	7	14	8	5	2
5	2	17	6	8	14	47	9	3
47	9	8	3	2	5	146	46	17

37	37	2	4	9	6	5	1	8
1	4	5	2	3	8	67	67	9
6	8	9	1	5	7	2	3	4
2	1	6	7	4	3	9	8	5
8	37	347	5	6	9	147	2	17
9	5	47	8	1	2	3	47	6
34	6	13	9	7	14	8	5	2
5	2	17	6	8	14	47	9	3
47	9	8	3	2	5	146	46	17