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:
                            s/b n-2.

Posted by Ady TZIDON on 2011-12-07 22:57:20