IMO 2021, Problem 6

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IMO 2021, Problem 6

Unread post by tanmoy » Wed Jul 21, 2021 8:21 pm

Let $m \ge 2$ be an integer, $A$ be a finite set of (not necessarily positive) integers, and $B_1,B_2, B_3, \ldots, B_m$ 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.
"Questions we can't answer are far better than answers we can't question"

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