MathDB

245

Part of 1977 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 245 All Soviet Union MO 1977 sums of subsets of set of positive integers

Source:

7/6/2019
Given a set of nn positive numbers. For each its nonempty subset consider the sum of all the subset's numbers. Prove that you can divide those sums onto nn 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.
combinatoricsSum