Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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]

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2021_IMO_Problems/Problem_6&oldid=159305"