MathDB

We say a triple of real numbers

(a_1,a_2,a_3)

is better than another triple

(b_1,b_2,b_3)

when exactly two out of the three following inequalities hold:

a_1 > b_1

a_2 > b_2

a_3 > b_3

. We call a triple of real numbers special when they are nonnegative and their sum is

1

. For which natural numbers

n

does there exist a collection

S

of special triples, with |S| \equal{} n, such that any special triple is bettered by at least one element of

S

Problem Statement