MathDB

Smallest possible value of m

Source: Dutch Mathematical Olympiad

September 19, 2005

Problem Statement

Let

a_1,a_2,a_3,a_4,a_5

be distinct real numbers. Consider all sums of the form

a_i + a_j

where

i,j \in \{1,2,3,4,5\}

and

i \neq j

. Let

m

be the number of distinct numbers among these sums. What is the smallest possible value of

m