Let n≥4, and consider a (not necessarily convex) polygon P_1P_2\hdots P_n in the plane. Suppose that, for each Pk, there is a unique vertex Qk=Pk among P_1,\hdots, P_n that lies closest to it. The polygon is then said to be hostile if Qk=Pk±1 for all k (where P0=Pn, Pn+1=P1).(a) Prove that no hostile polygon is convex.
(b) Find all n≥4 for which there exists a hostile n-gon. geometrycombinatorial geometry