Rectangle Elimination

Hard

Hinge-based rectangle pattern using conjugate pair relationships to eliminate candidates.

How It Works

Hinge cells in two boxes form a rectangle pattern. Using conjugate pair relationships through the hinges, candidates are eliminated from other cells in the pattern.

This technique catches eliminations that W-Wing and Skyscraper miss.

Example

7	3	5	8	4	1	9	26	26
1	26	4	3	6	9	26	7	8
6	69	89	2	5	7	16	3	4
2	1	3	4	7	5	6	8	9
4	25	6	9	2	8	3	1	7
8	29	27	1	19	6	29	4	13
3	4	8	5	9	2	7	16	1
5	6	1	7	8	3	4	9	2
9	78	2	6	13	4	18	5	3

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

Hinge cells in two boxes form a rectangle; candidates are eliminated from the opposite corners based on the conjugate pair constraints.

Practice with a Real Puzzle

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

Medium26 givensStrict

7	3	5	8	4	1	9	26	26
1	26	4	3	6	9	26	7	8
6	69	89	2	5	7	16	3	4
2	1	3	4	7	5	6	8	9
4	25	6	9	2	8	3	1	7
8	29	27	1	19	6	29	4	13
3	4	8	5	9	2	7	16	1
5	6	1	7	8	3	4	9	2
9	78	2	6	13	4	18	5	3

7	3	5	8	4	1	9	26	26
1	26	4	3	6	9	26	7	8
6	69	89	2	5	7	16	3	4
2	1	3	4	7	5	6	8	9
4	25	6	9	2	8	3	1	7
8	29	27	1	19	6	29	4	13
3	4	8	5	9	2	7	16	1
5	6	1	7	8	3	4	9	2
9	78	2	6	13	4	18	5	3

7	3	5	8	4	1	9	26	26
1	26	4	3	6	9	26	7	8
6	69	89	2	5	7	16	3	4
2	1	3	4	7	5	6	8	9
4	25	6	9	2	8	3	1	7
8	29	27	1	19	6	29	4	13
3	4	8	5	9	2	7	16	1
5	6	1	7	8	3	4	9	2
9	78	2	6	13	4	18	5	3