MathDB

Three elements of a set

Source: BdMO 2023 Higher Secondary National P2

February 12, 2023

algebra

Problem Statement

Let {

a_1, a_2,\cdots,a_n

} be a set of

n

real numbers whos sym equals S. It is known that each number in the set is less than

\frac{S}{n-1}

. Prove that for any three numbers

a_i

a_j

and

a_k

in the set,

a_i+a_j>a_k