MathDB

The country Dreamland consists of

2016

cities. The airline Starways wants to establish some one-way flights between pairs of cities in such a way that each city has exactly one flight out of it. Find the smallest positive integer

k

such that no matter how Starways establishes its flights, the cities can always be partitioned into

k

groups so that from any city it is not possible to reach another city in the same group by using at most

28

flights.
Warut Suksompong, Thailand

Problem Statement