Difference between revisions of "2021 IMO Problems/Problem 6"
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| − | ==Problem== | + | == Problem == |
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. | 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://youtu.be/vUftJHRaNx8 [Video contains solutions to all day 2 problems] | https://youtu.be/vUftJHRaNx8 [Video contains solutions to all day 2 problems] | ||
| + | |||
| + | == See also == | ||
| + | |||
| + | [[Category:Olympiad Combinatorics Problems]] | ||
Revision as of 10:35, 18 June 2023
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://youtu.be/vUftJHRaNx8 [Video contains solutions to all day 2 problems]
