Question 111
In a country between each pair of cities there is at most one direct road. There is a connection (using one or more roads) between any two cities even after the elimination of any given road. We say that the city $A$ can be $k$-directionally connected to the city $B$, if: we can orient at most $k$ roads such that after arbitrary orientation of remaining roads for any fixed road $L$ (directly connecting two cities) there is a path passing through roads in the direction of their orientation starting at $A$, passing through $L$ and ending at $B$. Suppose that in a country with $n$ cities, any two cities can be $k$-directionally connected. What is the minimal value of $k$? (Azer Kerimov).