ILL 1989 Problem 89

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.