Follow one number through lines where it has only two places, colouring the places alternately. All of one colour hold the number, so a square that sees both colours can't have it.
123456789
123456789
9
1
4
8
3
7
6
8
7
1
6
3
9
2
4
6
4
3
7
5
2
1
8
9
1
8
9
2
6
3
7
7
6
3
8
1
9
3
23
2
3
9
4
6
7
8
1
5
1
9
6
235
7
4
2
235
8
3
7
3
1
6
4
9
23
9
3
7
6
1
One colourThe other colourLoses a pencil mark
Why it works
Along each link exactly one end is the number. So the colours can't mix: every square of one colour is the number, or every square of the other.
How to spot one
Pick a number and find every row, column and box where it has exactly two places. Where those pairs share a square, they join into a chain.
What it gives you
Removals where a square sees both colours. If two squares of one colour ever see each other, that colour is wrong everywhere.
Practise Simple colouring
Boards that need it, with the owl's hints when you're stuck.