KöMaL 2008 K189

In a mathematics lesson, the teacher gave the students five kinds of problems to practise. There were three problems of each kind. Students got 1 mark for solving a single problem of a kind, 4 marks per problem if they solved two of the same kind, and 9 marks per problem if they solved all three of a kind. The students worked on the problems and received marks in teams. At the end of the lesson, every team had a different number of marks, but all their numbers of marks were found to be divisible by 3. What was the maximum possible number of teams?