Thought I would necro this thread rather then start an identical one, hope thats OK

I am also interested in the solution(if it exists) to this problem.

I have an identical problem to the OP, 12 teams with 4 teams per match (all players play the game at the same time, its a boardgame). Each ROUND consists of 3 match's, with each team participating in a single match of 4 unique teams. Or put another way, all 12 teams participate each round, spread across 3 matchs, and only ever participate in a single match per round.

I would like to know the MINIMUM number of rounds (I assume it will be quite large) that will result in each team participating in a match, with each other team, an EQUAL number of times.

If this number is not ridiculously high, then a schedule to go along with it would also be appreciated. I am hoping that someone has some stat software they can plug this into ?

Games are short in duration, and the schedule will be played over a year or more, so a high number is not too much of a problem.

Thankyou for your time, I do appreciate it.

BTW After reading some of the response s above, it would seem to indicate that a solution is not possible, regardless of how many rounds you play. Is this correct or am I reading it wrong.