Hello guys, I don't know if this is the right subreddit to ask this in, but I have a problem trying to organize a tournament that consists of 16 teams. The idea was to do 5 or 6 rounds, with groups of 4 teams each, where no team faces an other team for two times, but I noticed that it's impossible to do more than 3 rounds. What is the mathematical explanation for this? Are there any other real solutions ?

It's for a waterpolo tournament for kids! Thank you very much!