Given a set of positive integers $\{q_i\}_{i=1}^n$, describe the set $s_t \in S$ of positive integers such that there exists only *one* linear combination of $\sum_{i=1}^n a_i q_i = s_t$.

In the comic above, it’s pretty obvious with the amount of money given, that Calvin was hoping to get four “D”s. In fact, all integers from 1 to 9 can only be expressed in one permutation.

A satisfying answer to all sets of integers might be less trivial.