4. How can the minimum number of air routes be used to connect 50 cities so that travel from one city to another requires at most two flights (one transfer)?
(31st Moscow Mathematical Olympiad Problem)
4. Fix one city, and connect it to each of the other 49 cities with an air route, so as to meet the requirements of the problem. On the other hand, to connect 50 cities with air routes, at least 49 air routes are needed. In summary, the minimum number of air routes required is 49.