MathDB
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 AA and BB there is a direct flight from AA to BB and a direct flight from BB to AA, 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.