MathDB
Travel companies, true from 11 up

Source: Romanian TST 5 2007, Problem 3

June 7, 2007
inequalitiesquadraticscombinatorics proposedcombinatorics

Problem Statement

Three travel companies provide transportation between nn cities, such that each connection between a pair of cities is covered by one company only. Prove that, for n11n \geq 11, there must exist a round-trip through some four cities, using the services of a same company, while for n<11n < 11 this is not anymore necessarily true.
Dan Schwarz