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2021 IMO Problems/Problem 6

Revision as of 00:02, 31 July 2021 by Renrenthehamster (talk | contribs) (Created page with "==Problem== Let <math>m>2</math> be an integer, <math>A</math> be a finite set of (not necessarily positive) integers, and <math>B_1,B_2,B_3,...,B_m</math> be subsets of <math...")
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Problem

Let $m>2$ 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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