Unique Permutations

[BG]

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?

[BG]

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?

[Ian Wakeling]

Hi,

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

Ian.