MathDB

Let

x_1,\ldots,x_n

be real numbers. For any set

I\subset\{1,2,…,n\}

let

s(I)=\sum_{i\in I}x_i

. Assume that the function

I\to s(I)

takes on at least

1.8^n

values where

I

runs over all

2^n

subsets of

\{1,2,…,n\}

. Prove that the number of sets

I\subset \{1,2,…,n\}

for which

s(I)=2019

does not exceed

1.7^n

.
Proposed by Fedor Part and Fedor Petrov, St. Petersburg State University

Problem Statement