MathDB
Partition set with equal sum and differnt cardinality

Source: IMO Shortlist 2018 C1

July 17, 2019
combinatoricsIMO Shortlistnumber theoryalgebrageometryprojective geometry

Problem Statement

Let n⩾3n\geqslant 3 be an integer. Prove that there exists a set SS of 2n2n positive integers satisfying the following property: For every m=2,3,...,nm=2,3,...,n the set SS can be partitioned into two subsets with equal sums of elements, with one of subsets of cardinality mm.
Back to ProblemsView on AoPS