MathDB

A collection of

n > 2

numbers is called crowded if each of them is less than their sum divided by

n - 1

. Let

\{a, b, c, ,...\}

be a crowded collection of

n

numbers whose sum equals

S

. Prove that:
(a) each of the numbers is positive,
(b) we always have

a + b > c

,
(c) we always have

a + b \ge \frac{S}{n-1}

. (Regina Schleifer)

Problem Statement