a) Four merchants want to travel from Athens to Rome by cart. On the same day, but different times they leave Athens and arrive on another day to Rome, but in reverse order. Every day, when the evening comes, each merchant enters the next inn on the way. When some merchants sleep in the same inn at night, then on the following day at dawn they leave in reverse order of arrival, because they can only park this way on the narrow streets next to the inns. They cannot overtake each other, their order only changes after a night spent together in the same inn. Eventually each merchant arrives in Rome while they sleep with every other merchant in the same inn exactly once. Is it possible, that the number of the inns they sleep in is even every night? b) Is it possible if there are $8$ merchants instead of $4$ and every other condition is the same?