MathDB

5

Part of 2016 Serbia National Math Olympiad

Problems(1)

Combinatorics with subsets,SMO 2016P5

Source: Serbia Math Olympiad 2016 Day 2 P5

4/2/2016
There are 2n−12n-1 twoelement subsets of set 1,2,...,n1,2,...,n. Prove that one can choose nn out of these such that their union contains no more than 23n+1\frac{2}{3}n+1 elements.
combinatoricsProbabilistic Method