Question

In Wonderland, there are `n` cities, and every two of them are connected by a road. The roads meet only in the cities (there are no junctions outside the cities). A wicked magician wants to turn all the roads into one-way streets in such a way that if you leave any city, you can't return to it anymore.

a. Prove that the wicked magician can do this.

b. Prove that there exists a city from which one can reach any other city, and that there exists a city from which it is impossible to leave at all.

c. Prove that there exists a path that passes through all the cities and there is only one such path.