Simple Colouring

Hard

Conjugate pairs for a digit are alternately colored; cells seeing same-colored cells or both colors have the digit eliminated.

How It Works

Find all "conjugate pairs" for a digit (units where it can only appear in two cells). These form a chain colored alternately A and B. Two rules apply:

1. If two same-colored cells share a unit → That color is wrong; the other color is correct. 2. If an uncolored cell sees both colors → The digit can be eliminated from it.

Example

4
15
27
38
16
29
35
17
4
25
38
16
47
29
15
36
28
47
17
26
39
15
38
47
12
59
36
38
19
57
26
14
38
59
27
16
4
27
4
35
19
26
48
35
4
19
36
28
47
25
19
37
46
25
25
47
16
38
47
25
19
36
28
37
15
49
26
38
17
25
49
13
49
28
4
15
36
47
29
18
35
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Chain for digit 5: R1C3(A)-R1C7(B)-R4C7(A)-R4C2(B). R7C3 sees both R1C3(A) and R4C2(B) → Eliminate 5 from R7C3.

Practice with a Real Puzzle

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

Medium26 givensStrict