This is a problem I saw on Peter Winkler's column on communication of the ACM(might be under a pay wall). It is open.
What is the largest $n$, such that you can always cover a given set of $n$ points with $n$ disjoint unit disks?
I believe the current upper bound is $60$.
I would like to know more reference on this problem. Currently I don't even know what field would study problems like this.