IMO Shortlist 1989 problem 29


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2. travnja 2012.
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155 birds P_1, \ldots, P_{155} are sitting down on the boundary of a circle C. Two birds P_i, P_j are mutually visible if the angle at centre m(\cdot) of their positions m(P_iP_j) \leq 10^{\circ}. Find the smallest number of mutually visible pairs of birds, i.e. minimal set of pairs \{x,y\} of mutually visible pairs of birds with x,y \in \{P_1, \ldots, P_{155}\}. One assumes that a position (point) on C can be occupied simultaneously by several birds, e.g. all possible birds.
Izvor: Međunarodna matematička olimpijada, shortlist 1989