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 cities, such that each connection between a pair of cities is covered by one company only. Prove that, for , there must exist a round-trip through some four cities, using the services of a same company, while for this is not anymore necessarily true.Dan Schwarz