Country with cities and flights
Source: Romania 2017 IMO TST 1, problem 5
March 18, 2018
combinatorics
Problem Statement
A planar country has an odd number of cities separated by pairwise distinct distances. Some of these cities are connected by direct two-way flights. Each city is directly connected to exactly two ther cities, and the latter are located farthest from it. Prove that, using these flights, one may go from any city to any other city