4 player group games round robin many players

[mtickal]

I need a program to give groupings for a round robin for 4 player games. so everyone plays someone different each round

Say I have 16 players

it would look like this

round 1     (1      2      3      4)      (5      6      7      8)      (9      10      11      12)      (13      14      15      16)
round 2     (1      5      9      13)      (2      6      10      14)      (3      7      11      15)      (4      8      12      16)
round 3     (1      6      11      16)      (2      5      12      15)      (3      8      9      14)      (4      7      10      13)
round 4     (1      7      12      14)      (2      8      11      13)      (3      5      10      16)      (4      6      9      15)
round 5     (1      8      10      15)      (2      7      9      16)      (3      6      12      13)      (4      5      11      14)

If there is some kind of matrix that will do this, that would be great.
If this only works in multiples of 4, that's okay. I'm looking to do it for 12,16,20,24,28,32,36,40,44+ players.
any help would be great!

[Ian Wakeling]

If there is a series of schedules, it is for n=(12i+4) players where I is a positive integer, so 16, 28, 40 etc..  Then the number of opponents (n-1) is divisible by 3 and it is possible to have a perfect schedule as you have shown above. Mathematically this is a hard problem and there is no universal method of constructing the series.   I have included some links below that may help.

no schedule for 12 players
my 35 round schedule for 16 layers that avoids having the same three players together
20, 24, 28, 32 players  at Ed Pegg's web page.
36 players - 11 rounds
40 players

[mtickal]

thanks