Polish 2nd stage 2010, 6th problem (arithmetic means)
Source:
November 11, 2010
ceiling functiongraph theorycombinatorics proposedcombinatorics
Problem Statement
The -element set of real numbers is given, where . Prove that there exist at least two-element subsets of this set, in which the arithmetic mean of elements is not less than the arithmetic mean of elements in the whole set.