Pinball League Scheduling Help Needed

[hlaj78]

We have a pinball league with 24 members who will play against each other in 4-player games on 6 pinball machines simultaneously.  I am trying to come up with a schedule that will allow each player to play a different game during six rounds while not having any member play against another member more than once.  Please help.

Last year we had 20 members playing 5 4-player games in 5 rounds and I was able to come up with a solution without any problem.  

[Ian Wakeling]

I am not able to find an ideal solution to this problem, and think the only option is to compromise on the pairwise balance.  I have not checked in detail, but in the schedule below I think each player gets about 15 or 16 different opponents rather than the 18 different opponents that you were hoping for.

    Machine  1   Machine  2    Machine  3    Machine  4    Machine 5     Machine 6
R1 ( 3 17 9 15) (23 19  1 14) (13 12 24  8) ( 5 18 11 22) (20  7 16  4) ( 6 2 21 10)
R2 ( 1 18 7 13) (24 20  2 15) (14 10 22  9) ( 6 16 12 23) (21  8 17  5) ( 4 3 19 11)
R3 ( 2 16 8 14) (22 21  3 13) (15 11 23  7) ( 4 17 10 24) (19  9 18  6) ( 5 1 20 12)
R4 (21 11 6 24) ( 4  8 18 10) (19  2  5 17) (20  9  1 13) ( 3 23 12 14) (16 7 22 15)
R5 (19 12 4 22) ( 5  9 16 11) (20  3  6 18) (21  7  2 14) ( 1 24 10 15) (17 8 23 13)
R6 (20 10 5 23) ( 6  7 17 12) (21  1  4 16) (19  8  3 15) ( 2 22 11 13) (18 9 24 14)

Hope that helps.

[hlaj78]

This schedule may have to work.  It won't be totally fair because some players are world class and some other players may have to play the best person more than once.  However, since there are six rounds and six is not a prime number, it doesn't seem like it is mathematically possible to create four different cycles (players one through four on each game) without overlapping some players.  It's been a while since I've dealt with this type of theory, so perhaps someone can confirm or refute my conclusion.
Howard