Yay for 2014! #3

Discrete Mathematics Level 4

On a certain island nation, there exists a capital, a village, and several cities. There are \(2015\) roads that exit the capital and \(2014\) roads that exit each city. What number of roads can possibly exit the village such that it is always possible to travel from the village to the capital by traveling on roads only without leaving the island?


Since the nation is an island, no roads can leave the island or lead to any location that is not the capital, the village, or one of the cities.

This problem is inspired from another problem.

This problem is part of the set Yay for 2014!.


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