Round Robin Tournament Scheduling

Schedules - You must register to Post and Download => Requests => Topic started by: Lisa on January 05, 2008, 09:51:32 AM

Title: Middle school multi sport fun tournament
Post by: Lisa on January 05, 2008, 09:51:32 AM

Hello,
I am a PE teacher preparing a sports day with 12 teams, six different sports, six different locations (gym, field #1, field #2, pitch #3, etc...) with nine time slots of half an hour each, and 10 minutes allowed for rotation.  The scope of the day if fun, every team will play each sport, but will not be able to play each sport against each team...  Team 12 is made up of teachers and must play each team...
I am not a arithmetician, I have worked something out manually.  I would like to check it for mistakes against something more mathematically  computed.  Can you help?

Title: Re: Middle school multi sport fun tournament
Post by: Ian Wakeling on January 06, 2008, 03:52:50 AM

The best you can do here is to get each team to play against nine different opponents and to play each sport either once or twice.

The first nine rounds of the following schedule should be suitable:

     s1     s2     s3     s4     s5     s6
 r1 (F D)  (J K)  (A G)  (E L)  (C H)  (I B)
 r2 (E J)  (H F)  (B K)  (I C)  (L G)  (A D)
 r3 (L I)  (G B)  (J H)  (K D)  (E A)  (C F)
 r4 (G C)  (L A)  (I D)  (J B)  (F K)  (E H)
 r5 (H K)  (I E)  (L C)  (F A)  (D B)  (G J)
 r6 (A B)  (C D)  (E F)  (G H)  (I J)  (K L)
 r7 (D H)  (B L)  (C J)  (A I)  (K E)  (F G)
 r8 (K G)  (F J)  (D L)  (B E)  (A C)  (H I)
 r9 (C E)  (K I)  (H B)  (L F)  (G D)  (J A)
r10 (I F)  (E G)  (K A)  (D J)  (H L)  (B C)
r11 (J L)  (A H)  (G I)  (C K)  (B F)  (D E)

Notice that after 6 rounds every team will have played every sport exactly once.