2021 IMO Problems/Problem 6

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Let $m \ge 2$ be an integer, $A$ be a finite set of (not necessarily positive) integers, and $B_1, B_2, B_3 , \ldots, B_m$ 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]

See also

2021 IMO (Problems) • Resources
Preceded by
Problem 5
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Last Problem
All IMO Problems and Solutions