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Title: Beer Olympics - brain exploding!!
Post by: Ashleesaran@gmail. on June 11, 2017, 07:04:39 PM

I'm hosting a beer Olympics and have 9 teams . I currently have 7 games and have been wracking my brain trying to figure it out. I want everyone to play every game once (it doesn't matter if they play the same team more than once). Is this impossible?

Would it be better with 8 games?

Please help!!

Title: Re: Beer Olympics - brain exploding!!
Post by: Ian Wakeling on June 12, 2017, 05:50:07 AM

I think what you want is impossible.  It is definitely impossible if you require everyone to play every game exactly once.

The fundamental problem is the odd number of teams.  It would be better to have 8 or 10 teams, then there would be options.

With an odd number of teams, you also have to balance the byes, as it is important that everyone gets the same number of games.

Title: Re: Beer Olympics - brain exploding!!
Post by: Ian Wakeling on June 12, 2017, 12:27:37 PM

I thought about this problem some more - and I think the best compromise would be to use this all-play-all schedule :

 G1    G2    G3    G4    G5    G6    G7     Bye
(---) (A D) (---) (---) (B G) (C E) (H I)    F
(A G) (---) (E I) (---) (---) (D F) (B C)    H
(B E) (C I) (---) (F H) (---) (---) (D G)    A
(C H) (F G) (A B) (---) (D I) (---) (---)    E
(---) (E H) (A F) (B D) (---) (G I) (---)    C
(---) (---) (C D) (A I) (B H) (---) (E F)    G
(D H) (---) (---) (C G) (A E) (B F) (---)    I
(---) (B I) (---) (---) (C F) (A H) (E G)    D
(F I) (---) (G H) (D E) (---) (---) (A C)    B

Everyone has one of the 7 games they play twice.   Teams C, G and E all play game 7 twice (note the last column has 6 pairings, while the other columns only have 5).