Question 6
In countries of the Silk Road there are finite number of cities and some of them are connected by directed roads (one pair of cities can have several roads, moreover they can have an opposite direction). It is known that every two paths by these roads form the city $A$ to the city $B$ use at least one same road. Prove that some of the roads is common part for all the paths from $A$ to $B$ ($A$ and $B$ are two given cities).