Equal sum subsets hybrid

Question

The problem is the following:

You are given a set of positive integers { a1 , a2 , a3 , ... , an } in which there are no same numbers ( a1 exists only once ,a2 exist

Answer 1

If the answer is no, then the sum of all n numbers is at least 2^n-1. So if n is large, and the numbers are 32-bit integers, for instance, then the answer is almost always yes. If n is small, you can probably brute-force.

The hardest case is probably when n is around 30.