Suppose you had $N$ many fixed points $X_1, X_2, ..., X_N$ in some Euclidean space $R^d$ and from these coordinates you had to choose $n$ many of them ($n \leq N$ also being fixed) to form a subset $S$ that maximizes the function $f(S) = \sum_{(i,j) \in S \times S} ||X_i-X_j||^2$. How would you choose $S$? Note that $||\cdot||$ is the usual Pythagorean norm.

Informally, you are choosing the n points so that they are as 'distant' from each other as possible. Is there a solution to this problem or at least an algorithmic approach to this problem?