The participants in a race consisted of 3 teams with 3 runners on each team. A team was awarded 6-n points if one of its runners finished in nth place, where 1≦n≦5. If all of runners finished the race and if there were no ties, was each team awarded at least one point?
(1)No team was awarded more than a total of 6 points.
(2) No pair of teammates finished in consecutive places among the top five places.