MathDB

We call a set

X

of real numbers three-averaging if for every two distinct elements

a

and

b

X

, there exists an element

c

X

(different from both

a

and

b

) such that the number

(a + b + c)/3

also belongs to

X

. For instance, the set

\{ 0, 1008, 2016 \}

is three-averaging. What is the least possible number of elements in a three-averaging set with more than 3 elements?

Problem Statement