Round trips that miss the capital cost the same
Source: Baltic Way 2010
November 19, 2010
combinatorics proposedcombinatorics
Problem Statement
There are some cities in a country; one of them is the capital. For any two cities and there is a direct flight from to and a direct flight from to , both having the same price. Suppose that all round trips with exactly one landing in every city have the same total cost. Prove that all round trips that miss the capital and with exactly one landing in every remaining city cost the same.