MathDB

You are given

n

not necessarily distinct real numbers

a_1, a_2, \ldots, a_n

. Let's consider all

2^n-1

ways to select some nonempty subset of these numbers, and for each such subset calculate the sum of the selected numbers. What largest possible number of them could have been equal to

1

?
For example, if

a = [-1, 2, 2]

, then we got

3

once,

4

once,

2

twice,

-1

once,

1

twice, so the total number of ones here is

2

.
(Proposed by Anton Trygub)

Problem Statement