MathDB
Roads and cities

Source: St Petersburg Olympiad 2010, Grade 9, P5

September 14, 2017
combinatorics

Problem Statement

There are 20102010 cities in country, and every two are connected by road. Businessman and Road Ministry play next game. Every morning Businessman buys one road and every evening Ministry destroys 10 free roads. Can Business create cyclic route without self-intersections through exactly 1111 different cities?