Question 24
There are several settlements around Big Lake. Some pairs of settlements are directly connected by a regular shipping service. For all $A \neq B$, 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.