In some state, there are 101 cities.
a) Each city is connected to each of the other cities by one-way roads, and 50 roads lead into each city and 50 roads lead out of each city. Prove that you can get from each city to any other, having travelled on no more than on two roads.
b) Some cities are connected by one-way roads, and 40 roads lead into each city and 40 roads lead out of each. Prove that you can get form each city to any other, having travelled on no more than on three roads.