Assume you have 8 teams playing in a round robin tournament. Obviously in order for each team to play each other team there must be 7 rounds (N-1). Now let us say that there are 7 different games that each team must play. (ex: 1 Hole washers, 3 hole washer, Bocce Ball, Horse Shoes, etc.) The questions are the following: (for purposes of this brain teaser we will define ?a round? as an instance of every team playing a single game against a single opposing team)Is it possible for each team to play each other team exactly once, AND each game exactly once?What is the minimum number of rounds of round robin play in which each team could play each other team, AND each team plays each game?(allowing for duplicate matchups and multiple tries at a single game)What is the maximum number different games such that N teams can play each game in the process of playing each other team in N-1 Rounds.

JJH41924, not sure if i misunderstand your problem, but here is a schedule, with each round all teams playing the same game:game A: (12) (34) (56) (78)game B: (13) (25) (48) (67)game C: (14) (27) (35) (68)game D: (15) (28) (37) (46)game E: (16) (23) (58) (47)game F: (17) (26) (38) (45)game G: (18) (24) (36) (57)seems to me the general case is the trivial (2N,2,1)-block design with N-1 rounds and N-1 games

wileysw, Thank you for answering my question. I apologize for being unclear. I left out an important detail that you have made me aware of. Each team must play each game and each other team in the span of N-1 rounds. However, there exists only one instance of each game, and thus each game can only be played once in each round. So, each team, and each game can only be used once in each round.I meant the first question "Is it possible for each team to play each other team exactly once, AND each game exactly once?" as a quick no, because I am fairly certain that it is impossible, although I cannot prove it. I am primarily interested in the last 2 questions.Let me know if this makes more sense.

yes it makes sense - it also makes the question considerably harder.i fiddled around with the simplest case of N=4. seems you need at least 5 rounds for each team to get to play all 3 gamesat this point, i do not have a good approach in mind for larger N except brute force search by computer