Colouring
How it works
Take one digit and find every unit where it has exactly two possible cells left — in each of those, one of the two is definitely the digit. Chain those pairs together and colour them alternately, and the chain splits into two groups: one group holds the digit everywhere, the other nowhere. Two things follow without ever learning which is which. If a colour would put the digit twice into one unit it must be the wrong group, so the digit goes from every cell wearing it; and any cell outside the chain that sees both colours loses the digit either way.
Try it
Follow digit 1 through the highlighted chain. Each neighbouring pair is a unit where 1 has only those two cells left, so one of the two must be it — pencil them all in first.
3
8
4
5
2
6
2
1
6
5
6
5
2
7
8
9
4
3
7
5
6
2
7
2
5
6
4
1
6
8
9
2
4
3
5
7
5
9
2
6
7
8
4
7
1
5
8
6
2
8
3
6
1
4
2
7
9
5