Question 133
Suppose a country has a system of roads such that the roads intersect in towns only and do not intersect in between the towns. Furthermore, from any town one can reach any other town if one can go in either of the two directions on each road. For no pair of towns is there more than one direct road connecting them. The government decided to make each road one-way, i.e. if towns $A$ and $B$ are connected by a road, then one can use it to get from $A$ to $B$, or from $B$ to $A$. Moreover, for each town there must be at least one road coming into that town and at least one road leaving it. Will it always be the case that in this country there exists a town from which one can get to any other town (possibly passing through some other towns on the way), or to which one can get from any other town (possibly passing through some other towns on the way)?