Colouring with every number at once. Two-option squares and two-place lines link candidates of different numbers into one chain of two colours. One colour is all true, so anything both colours rule out goes.
123456789
123456789
9
2
3
5
8
7
4
5
156
7
9
48
68
156
3
4
3
56
68
68
7
9
2
58
7
5
8
3
4
156
5
456
456
468
48
7
3
589
9
146
3
7
5
48
168
2
4
1
7
9
3
8
6
6
8
9
3
2
1
5
4
7
3
7
6
2
9
1
The coloured chainLoses a pencil mark
Two kinds of link
Inside a square with two options, one of them is right. Along a line or box where a number has two places, one of them is right. Each link flips the colour.
How to spot one
Start from a two-option square and follow both kinds of link as far as they go. Then look for a square holding one colour that sees the same number in the other.
What it gives you
Removals that simple colouring can't reach, because the chain changes number as it goes.
Practise 3D Medusa
Boards that need it, with the owl's hints when you're stuck.