ASU 245 All Soviet Union MO 1977 sums of subsets of set of positive integers
Source:
July 6, 2019
combinatoricsSum
Problem Statement
Given a set of positive numbers. For each its nonempty subset consider the sum of all the subset's numbers. Prove that you can divide those sums onto groups in such a way, that the least sum in every group is not less than a half of the greatest sum in the same group.