Problem

Source: Iran TST 2023 ; Exam 2 Problem 6

Tags: Subsets, combinatorics



Suppose that we have $2n$ non-empty subset of $ \big\{0,1,2,...,2n-1\big\} $ that sum of the elements of these subsets is $ \binom{2n+1}{2}$ . Prove that we can choose one element from every subset that some of them is $ \binom{2n}{2}$ Proposed by Morteza Saghafian and Afrouz Jabalameli