# Difference between revisions of "2021 IMO Problems/Problem 6"

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==Problem== | ==Problem== | ||

− | Let <math>m | + | Let <math>m\ge 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>A</math>. Assume that for each <math>k = 1, 2,...,m</math> the sum of the elements of <math>B_k</math> is <math>m^k</math>. Prove that <math>A</math> contains at least <math>m/2</math> elements. |

==Video solution== | ==Video solution== | ||

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

## Revision as of 23:03, 30 July 2021

## Problem

Let be an integer, be a finite set of (not necessarily positive) integers, and be subsets of . Assume that for each the sum of the elements of is . Prove that contains at least elements.

## Video solution

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