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 re: Solution
You started nicely with the set 1,2,3,4...etc
All you needed was to show a mapping from your set and the sums to set a1,a2,a3 etc and its sums.