Given n distinct positive numbers a1,a2,...,an.
We construct all the possible sums (from 1 to n terms).
Prove that among those 2^n-1 sums there are at least n(n+1)/2 different ones.
Source: a problem from Soviet Union 1963 contest
(In reply to Solution
by John Dounis)
Nicely presented full-proof solution.
However - there is a minor typo: please edit:
"....Having costructing that then we can continue with the next set with size n-1: