IMO Shortlist 1988 problem 10

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Dodao/la: arhiva
2. travnja 2012.
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?
Izvor: Međunarodna matematička olimpijada, shortlist 1988