2021 IMO Problems/Problem 6


Let $m\ge 2$ be an integer, $A$ be a finite set of (not necessarily positive) integers, and $B_1,B_2,B_3,...,B_m$ be subsets of $A$. Assume that for each $k = 1, 2,...,m$ the sum of the elements of $B_k$ is $m^k$. Prove that $A$ contains at least $m/2$ elements.

Video solution

https://youtu.be/vUftJHRaNx8 [Video contains solutions to all day 2 problems]