I'm running a tournament and I need help evenly distributing the players. I have 9 players, 3 courts, and 5 time periods. There will be 3 players per court per time period. So, the data should/can look something like this:
A number can only be listed once per time period. No one can play in the same group of three more than once (ie group 1,2,3 can only play together in this threesome once during the tourney).
You would think that randomizing programs would make this an easy task, but it's not. Well, it's not to me at least.
The question is this: How can I evenly distribute these 9 players between three courts for each of the 5 time periods listed?
All 9 players must be listed for each time period.
Each threesome can only play together once during the tournament ( ie. if group 1,2,3 plays, then group 3,1,2 cannot be listed since they've already played together).
Each player must play in a group with each of the other players at least once (ex: group 1,2,3, group 1,4,5, group 1,6,7, and group 1,8,9 satisfies this criteria for player 1)
I'm not sure if the last criteria can be met with only 5 time periods available. If not, then I'll be happy with getting the closest to satifying the criteria.
I used SAS to create a dataset listing all possible 3 player combinations for the 9 players (84 different combinations total), and then I tried randomly assigning these groups to the time period/courts grid, but I could never quite satisfy the last part of my criteria.