Question 59
There are a few cities in a country; one of them is the capital. There is a direct flight between any two of the cities, and any flight connecting two given cities has the same price. Suppose that all trips that begin and end in the same city and go exactly once through every other city have the same total cost. Prove that all trips that begin and end in the same city, miss the capital and go exactly once through every remaining city have the same total cost.