Beer Olympics Schedule

[swanny1981]

My brain has been spinning trying to figure this out, but I found this site and hopefully you can lend a hand.

Here is the situation:

We are having a bachelor party this weekend and are planning on having a beer olympics type event.

There will be 10 teams.  There are currently 9 events.

What we want to happen is for each team to compete in every event, and to face off against each other team once.  The matches will be going on simultaneously.  Is there any way to make this work?  We are willing to adjust the number of events if necessary.  Or a team can have a bye during one of the time slots if necessary.  Whatever needs to be done to make this work.

Thanks in advance for any help!

[Ian Wakeling]

10 teams and 9 events can be made to work.  If you take the rows in the schedule below to be 9 rounds, and the columns to be 9 events, then all 10 teams (A to J) appear exactly once in every row and column, and all 45 possible face offs between teams occur exactly once.

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

This type of schedule is called a Room square.

[swanny1981]

Thanks so much for the help Ian.  Looks great.  In my head, I thought it was possible, I just couldn't figure out how.  Helps make the drinking event even better.