Frankly i think that it is safe to assume they are all facing the same puzzles, we all saw them in that big room with windows looking at their alternates, seems logical to me that all the rooms connecting to that room would be the same and so on.

It could be a bracket-type competition. two teams face off in the same situation, one survives, faces another team that survived the same situation, one of those two teams survives and faces a new challenge with yet another team to have survived the same situation, and so on and so forth until only one team is left standing. then the whole thing resets.

Think mortal combat, only instead of fighting, each player needs to beat the other at a puzzle in order to pass on.