Given a set of integers, and a length n - can we find the minimum difference between any two sums of combinations of size n?

Question

Actually my question is slightly tougher than the title.

Say we have n sets of n integers of varying size. We make combinations of integers, one and only one integer from each set. So, each combination is of size n.

Is it reasonably possible to calculate the minimum possible difference in the sums of any two combinations, given a finite "n" and finite range on the size of integers?