Planes and cities
Source: All Russian Olympiad 2017,Day1,grade 9,P1
May 3, 2017
combinatorics
Problem Statement
In country some cities are connected by oneway flights( There are no more then one flight between two cities). City called "available" for city , if there is flight from to , maybe with some transfers. It is known, that for every 2 cities and exist city , such that and are available from . Prove, that exist city , such that every city is available for .