2021 IMO Problems/Problem 6

Revision as of 23:03, 30 July 2021 by Renrenthehamster (talk | contribs) (Problem)

Problem

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://www.youtube.com/watch?v=vUftJHRaNx8 [Video contains solutions to all day 2 problems]

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