5 airway companies operate in a country consisting of 36 cities. Between any pair of cities exactly one company operates two way flights. If some air company operates between cities A,B and B,C we say that the triple A,B,C is properly-connected. Determine the largest possible value of k such that no matter how these flights are arranged there are at least k properly-connected triples. inequalitiescombinatorics proposedcombinatorics