MathDB
Problem 8 of Third round

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

September 22, 2018
graph theorycombinatorics

Problem Statement

Some of the towns in a country are connected with bidirectional paths, where each town can be reached by any other by going through these paths. From each town there are at least n3n \geq 3 paths. In the country there is no such route that includes all towns exactly once. Find the least possible number of towns in this country (Answer depends from nn).