Empty Rectangle

Hard

A digit's arrangement in a box forms an "empty rectangle", enabling eliminations via a conjugate pair.

How It Works

When a digit in a box only appears in cells aligned on one row AND one column (forming an L or T shape), the intersection row/column is "empty". Combined with a conjugate pair outside the box, this enables further eliminations.

Visually: The digit's cells in the box must form an L or T shape.

Example

5	3	1	9	2	8	6	4	7
2	4	6	1	3	7	5	8	9
7	8	9	4	5	6	1	2	3
1	2	3	5	4	9	7	6	8
4	5	57	6	8	7	7	9	2
6	9	8	2	7	23	4	1	5
3	1	2	7	9	4	8	5	6
8	67	37	37	1	7	9	3	4
9	67	4	8	6	25	27	7	1

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

5	3	1	9	2	8	6	4	7
2	4	6	1	3	7	5	8	9
7	8	9	4	5	6	1	2	3
1	2	3	5	4	9	7	6	8
4	5	57	6	8	7	7	9	2
6	9	8	2	7	23	4	1	5
3	1	2	7	9	4	8	5	6
8	67	37	37	1	7	9	3	4
9	67	4	8	6	25	27	7	1

5	3	1	9	2	8	6	4	7
2	4	6	1	3	7	5	8	9
7	8	9	4	5	6	1	2	3
1	2	3	5	4	9	7	6	8
4	5	57	6	8	7	7	9	2
6	9	8	2	7	23	4	1	5
3	1	2	7	9	4	8	5	6
8	67	37	37	1	7	9	3	4
9	67	4	8	6	25	27	7	1

5	3	1	9	2	8	6	4	7
2	4	6	1	3	7	5	8	9
7	8	9	4	5	6	1	2	3
1	2	3	5	4	9	7	6	8
4	5	57	6	8	7	7	9	2
6	9	8	2	7	23	4	1	5
3	1	2	7	9	4	8	5	6
8	67	37	37	1	7	9	3	4
9	67	4	8	6	25	27	7	1