1) Let $S$ be a set of $n$ points in $R^d$. Now, given a bounded geometric object $G$, the problem is to check whether $S$ can be contained in $G$.

2) Also, in general setting, the problem is to check whether $S$ can be contained in $k$ translated copies of $G$.

For what values of $n$ and $d$, and for which type of $G$, solution of (1) and (2) are known?

Pls let me know if the question is clear?