Round Robin Tournament Scheduling

Schedules - You must register to Post and Download => Requests => Topic started by: BG on February 12, 2010, 01:43:45 PM

Title: Unique Permutations
Post by: BG on February 12, 2010, 01:43:45 PM

I have been searching the web and this site, but can't seem to find the info.  I have previously had this problem:

I want to divide 16 players into teams of 4 so that no two players are on the same team more than once.  Although there are many permutations of this data, I was able to find 5 unique permutations.

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

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

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

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

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

Now I would like to do the same thing except I have 21 items I'd like to divide into groups of three.  Can anyone find the unique permutations of this data?

Title: Re: Unique Permutations
Post by: BG on February 12, 2010, 01:49:58 PM

Actually, I may have just found the answer listed under golf threesome thread "9 golfers - 4 games"

Is this 21 player schedule correct?  Noone is paired with the same player more than once and yet they play all other players?

So this means that it will only take 10 rounds to complete?

Title: Re: Unique Permutations
Post by: Ian Wakeling on February 13, 2010, 12:10:17 PM

Hi,

I think the schedule that you have linked to is correct, and is exactly what you want.

Ian.