Round Robin Conundrum

[Klcook89]

Hello!! I’m new here! I have been trying to figure out how to create a round robin tournament for 8-10 teams... we have 9 events but can make it only 8 if needed. We thought it would be around 9 rounds but have come to find that won’t work perfectly. Basically we want to make sure everyone plays each game once but we don’t mind if teams play the same team twice. We do want them to play all teams but can repeat if needed. Is there anyone that can help with this?? Thank you!!!

[Ian Wakeling]

There is a 'Room square' for 10 teams and 9 events in this old posting which is probably the perfect solution you were looking for.  If you follow the Wikipedia link beneath the old thread there is the 8 team and 7 event schedule that might also be useful.  Anything else in the range given is going to be less than perfect.  For example with 8 teams and 8 events, some of the pairings must be repeated (the first and last rounds are the same):

(A B) (C D) (E F) (G H) (---) (---) (---) (---)
(F H) (---) (B D) (A C) (---) (E G) (---) (---)
(---) (F G) (---) (---) (B C) (---) (E H) (A D)
(---) (---) (C G) (B E) (A F) (D H) (---) (---)
(D G) (A E) (---) (---) (---) (---) (B F) (C H)
(C E) (B H) (---) (D F) (---) (---) (A G) (---)
(---) (---) (A H) (---) (D E) (C F) (---) (B G)
(---) (---) (---) (---) (G H) (A B) (C D) (E F)

For 9 teams and 9 events delete all the games involving team J from the first Room square, but of course there will be one event that each team does not play.

[Arank13]

What about 9 teams with 8 events?!

[Ian Wakeling]

It will still not be possible to balance teams across events.  The best that can be done is as follows (9 rounds in rows, 8 events in columns):

(---) (D F) (---) (I G) (A E) (---) (---) (B C)
(E H) (---) (B F) (---) (I D) (C G) (---) (---)
(---) (A G) (---) (H F) (---) (E D) (B I) (---)
(---) (---) (E G) (---) (C F) (---) (H D) (A I)
(A C) (---) (---) (E I) (---) (B H) (---) (D G)
(B D) (C I) (---) (---) (H G) (---) (A F) (---)
(---) (B E) (A D) (---) (---) (I F) (---) (C H)
(F G) (---) (H I) (A B) (---) (---) (E C) (---)
(---) (A H) (---) (C D) (B G) (---) (---) (E F)

where teams A,C,G & I all play one of the events twice, and another event not at all.  Each team has exactly one bye round.