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Problem 4 of Third round

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

September 9, 2022
combinatoricsset theory

Problem Statement

Let x1,…,xnx_1,\dots ,x_n be real numbers. We look at all the 2n−12^{n-1} possible sums between some of the numbers. If the number of different sums is at least 1.8n1.8^n, prove that the number of sums equal to 20222022 is no more than 1.67n1.67^n.
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