For a set of numbers we say that has distinct subset sums if all distinct subsets of have distinct sums. How many subsets of have distinct subset sums?
Details and assumptions
The empty set (the set of no elements) has a sum of 0 by convention.
As an explicit example, the subset satisfies the conditions, since it has subsets, whose sums are 0, 1, 2, and 3, which are distinct.