Question 5
On a distant planet, there are $2014$ cities, some pairs of which are connected by two-way roads. It turns out that the population of each city is the average of the populations of the cities to which it is connected by a single road, and moreover that it is possible to travel from every city to every other city by a sequence of roads.
Prove that all cities have the same population.
Prove that all cities have the same population.