MathDB

Let N \equal{} \{1,2 \ldots, n\}, n \geq 2. A collection F \equal{} \{A_1, \ldots, A_t\} of subsets

A_i \subseteq N,

i \equal{} 1, \ldots, t, is said to be separating, if for every pair

\{x,y\} \subseteq N,

there is a set

A_i \in F

so that

A_i \cap \{x,y\}

contains just one element.

F

is said to be covering, if every element of

N

is contained in at least one set

A_i \in F.

What is the smallest value

f(n)

t,

so there is a set F \equal{} \{A_1, \ldots, A_t\} which is simultaneously separating and covering?

Problem Statement