ILL 1988 Problem 18

Let $N = \{1,2 \ldots, n\}, n \geq 2.$ A collection $F = \{A_1, \ldots, A_t\}$ of subsets $A_i \subseteq N,$ $i = 1, \ldots, t,$ 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 $f(n)$ of $t,$ so there is a set $F = \{A_1, \ldots, A_t\}$ which is simultaneously separating and covering?