Overview
========
This is a colouring problem.
Initially you can divide the numbers into the sets [1248], [36], and [579], depending on how they interact with black kropke dots.
Quite quickly, you'll be able to split [1248] into the inner [24] set and the outer [18] set.
Then colour with the 4 colours until you reach the corner which will uniquely disambiguate all the numbers.