My friend and I are hosting a game of "Beer Olympics". We have 8 events (Beer Pong, Darts, Frisbee, etc.). Lets call these Event1, Event2, Event3, etc.
We also have 16 teams of two people. Lets call them TeamA TeamB TeamC, etc.
Our dream is that every team will play against every other team, and each team will compete in each event. Cause that sounds the most fun right?
So we tried to come up with a solution, or prove that no solution existed.
We quickly found that it's impossible for an even grid of 2x2.. Try it! (Yet it is always possible, AND trivial, to solve for an odd numbered grid) And we were content with it being unsolvable.
Then a friend of ours (With a masters in mathmatics) came along and suggested that 2x2 may be a special case. Our hunch is that it is generally impossible, but we can't seem to prove it. Any ideas?