Given $n$ circles of possibly different radii, how many distinct regions can there be? For small $n$, I can work it out with pictures. (I'm pretty sure $n=4$ can yield 13 distinct regions, but not positive.)
Just curious what an approach to the problem could be.
E.g. I have considered that is could be a quadratic sequence based on skimpy evidence, but don't know why that would be, or how to prove it.
I would also be interested to know if there was a way of doing this problem with regular $n$-gons. (I am assuming that there would be more regions, but am not sure.)