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

8
29
3
579
257
4
57
61
19
129
4
579
2567
679
3
57
8
567138249
2
48
1
578
457
39
57
6
35
68
789
467
679
47
12
46
7921
56
45
83
46
14
5382
16
97
73
68
491
68
25
19
189
26
57
57
18
34
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Practice with a Real Puzzle

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

Medium26 givensStrict