MathDB

12

Part of 1997 Moldova Team Selection Test

Problems(1)

Let $A$ be a set of $n$ positive integers.

Source: Moldova TST 1997

8/8/2023
For every nonempty set of real numbers SS{} denote σ(S)\sigma(S) the sum of its elements. Let AA{} be a set of nn{} positive integers. Show that the set of all sums σ\sigma{} of all nonempty sets of AA{} can be partitioned in nn{} groups such that the ratio between the greatest number and the smallest number from each group is less than 22.