Round Robin Tournament Scheduling

16 team beer olympics

Aduse · 2 · 146

Aduse

  • Newbie
  • *
    • Posts: 0
on: June 19, 2021, 12:53:57 PM
I have a 16 team 2 groups (A,B) which has 8 teams per group. We have 7 games for both groups to play being ( Game A,B,C,D,E,F,G ). I need each team to play each game and each team once! In both groups, and does not matter if teams have to play the same game in the same round.


Ian Wakeling

  • Forum Moderator
  • God Member
  • *****
    • Posts: 1135
Reply #1 on: June 20, 2021, 04:24:53 AM
There is good news as a schedule for this scenario exists, and it can be made to work with the additional constraint that all 7 games are played exactly once in each round.  Let group A be the teams numbered 1 to 8, and group B the teams 9 to 16, then the schedule below should work.  Columns correspond to rounds and are labelled R1 to R8.

          R1      R2      R3      R4      R5      R6      R7      R8
Game A: ( 9 10) ( 5  6) ( 1  2) (11 12) ( 7  8) ( 3  4) (13 14) (15 16)
Game B: (11 14) ( 2  7) ( 3  6) ( 1  8) ( 4  5) ( 9 16) (10 15) (12 13)
Game C: ( 1  5) ( 3  8) ( 9 13) (10 14) (12 15) ( 2  6) (11 16) ( 4  7)
Game D: (13 15) ( 9 11) ( 5  7) ( 2  4) (14 16) (10 12) ( 1  3) ( 6  8)
Game E: (12 16) (10 13) ( 4  8) ( 3  7) ( 1  6) (11 15) ( 2  5) ( 9 14)
Game F: ( 2  8) (12 14) (10 16) ( 9 15) (11 13) ( 1  7) ( 4  6) ( 3  5)
Game G: ( 6  7) ( 1  4) (14 15) (13 16) ( 2  3) ( 5  8) ( 9 12) (10 11)

   Bye: [ 3  4] [15 16] [11 12] [ 5  6] [ 9 10] [13 14] [ 7  8] [ 1  2]

Note that in each round one pair of teams (both from the same group) have a bye.