RU-ALLRUSSIAN 1980 Problem 7

There are several settlements around Big Lake. Some pairs of settlements are directly connected by a regular shipping service. For all $\mathrm{A} \neq \mathrm{B}$ , settlement A is directly connected to X iff B is not directly connected to Y, where B is the next settlement to A counterclockwise and Y is the next settlement to X counterclockwise. Show that you can move between any two settlements with at most 3 trips.