MathDB
Find a big sum-free subset

Source: 2022 Bulgarian Spring Math Competition, Problem 11.4

March 27, 2022
Combinatorial Number TheorySubsetsnumber theorycombinatoricsProbabilistic MethodBulgaria

Problem Statement

Let n≥2n \geq 2 be a positive integer. The set MM consists of 2n2−3n+22n^2-3n+2 positive rational numbers. Prove that there exists a subset AA of MM with nn elements with the following property: ∀\forall 2≤k≤n2 \leq k \leq n the sum of any kk (not necessarily distinct) numbers from AA is not in AA.
Back to ProblemsView on AoPS