Let n be an odd positive integer. On
some field, n gunmen are placed such
that all pairwise distances between
them are different. At a signal, every
gunman takes out his gun and shoots
the closest gunman. Prove that:
(a) at least one gunman survives;
(b) no gunman is shot more than 5
times;
(c) the trajectories of the bullets do
not intersect.
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