Nishio Forcing Chains

Expert

Assume a candidate is true and trace consequences; if a contradiction results, the candidate is eliminated.

How It Works

Assume a candidate is correct and trace all consequences. If a contradiction is reached (an empty candidate set, a digit missing from a unit, etc.), the assumption is wrong and the candidate can be eliminated.

This is proof by contradiction — one of the most powerful chain techniques.

Example

6
14
9
27
35
8
15
3
24
5
27
23
14
36
79
68
28
13
8
14
59
7
35
2
46
19
24
37
46
15
16
9
25
8
14
16
83
37
24
15
26
15
9
15
15
28
6
24
3
47
17
37
49
6
47
29
18
25
35
8
47
34
5
19
37
14
1
36
14
15
15
68
39
47
49
2
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)