Remote Pairs

Hard

A chain of bivalue cells with identical candidates; cells seeing both ends of an even-length chain can have those digits eliminated.

How It Works

A chain of cells all having exactly the same two candidates (e.g. {3,7}), each seeing the next. At an even chain length, both ends must contain the same digit. Any cell seeing both ends of the chain can have both candidates eliminated.

Similar to Simple Colouring but treats two candidates together.

Example

37	5	6	4	1	8	37	9	2
4	9	1	2	6	3	7	8	5
2	18	8	5	29	9	37	4	6
1	2	3	6	4	5	8	7	9
5	4	7	8	9	1	2	6	3
6	8	9	3	2	7	4	5	1
3	1	4	7	5	6	37	2	8
8	6	2	9	14	4	16	1	57
37	29	5	1	38	2	37	3	4

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

Chain: R1C1={3,7}-R1C5={3,7}-R5C5={3,7}-R5C9={3,7} (4 cells, even length). → Any cell seeing both R1C1 and R5C9 can have 3 and 7 eliminated.

Practice with a Real Puzzle

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

Medium26 givens

37	5	6	4	1	8	37	9	2
4	9	1	2	6	3	7	8	5
2	18	8	5	29	9	37	4	6
1	2	3	6	4	5	8	7	9
5	4	7	8	9	1	2	6	3
6	8	9	3	2	7	4	5	1
3	1	4	7	5	6	37	2	8
8	6	2	9	14	4	16	1	57
37	29	5	1	38	2	37	3	4

37	5	6	4	1	8	37	9	2
4	9	1	2	6	3	7	8	5
2	18	8	5	29	9	37	4	6
1	2	3	6	4	5	8	7	9
5	4	7	8	9	1	2	6	3
6	8	9	3	2	7	4	5	1
3	1	4	7	5	6	37	2	8
8	6	2	9	14	4	16	1	57
37	29	5	1	38	2	37	3	4

37	5	6	4	1	8	37	9	2
4	9	1	2	6	3	7	8	5
2	18	8	5	29	9	37	4	6
1	2	3	6	4	5	8	7	9
5	4	7	8	9	1	2	6	3
6	8	9	3	2	7	4	5	1
3	1	4	7	5	6	37	2	8
8	6	2	9	14	4	16	1	57
37	29	5	1	38	2	37	3	4