Consider the following tournament:
There are 12 teams, 6 disciplines and 6 rounds, each round and each event happens simultaneously. Is it possible to create a tournament such that no team does the same discipline twice nor meets a team they have already played. There is no reward for winning teams meeting winning teams.
This is a real live problem which bothers me quite a bit. It seems impossible (mostly due to trial and error and some trying to apply math) but I cannot prove it. Given it can not be solved I would of course like to see the argument. I do not know if such math exists, but some kind of formalised best tournament would also be interesting.
Edit: An example could be (assuming teams 1 to 12 are just numerated)
Round 1: Soccer 1 vs 2, Baseball 3 vs 4, Basketball 5 vs 6, Hockey 7 vs 8, Ultimate 9 vs 10, Football 11 vs 12
Round 2: Soccer 3 vs 6, Baseball 5 vs 8, Basketball 7 vs 10, Hockey 9 vs 12, Ultimate 11 vs 2, Football 1 vs 4 and so forth.
So the disciplines should preferably be simultaneous. Sorry for not writing that explicitly the first time.