16-player game tournament, 4-player games

[diginova]

I am hosting a 16-player tournament with 4-player games over 10 rounds.
I have a 5-round solution:

Rd.1 ABCD EFGH IJKL MNOP
Rd.2 AEIM BFJN CGKO DHLP
Rd.3 AFKP BELO CHIN DGJM
Rd.4 AGLN BHKM CEJP DFIO
Rd.5 AHJO BGIP CFLM DEKN

However, I want to extend it to 10 rounds, but not just copy the groups of 4 twice so there is some variance as to the groups of four (so when AD play, BC are not also playing)

How would I do this?

[Ian Wakeling]

You can use the first ten rounds of this schedule

[diginova]

Thanks! Is there a formula or pseudocode that I could utilize to extend it for any 4n number of players?

[Ian Wakeling]

What I did to make the 10 round schedule was to take a copy of the first 5 rounds, but permute the letters A to P.  Essentially I used trial and error to find a permutation of the letters that did not put the same three people together in a match.

But for other values of 4n there are greater problems.  Take 20 players for example - there are 19 opponents who will be seen 3 at a time.  As 3 doesn't divide into 19, you would have to play 19 rounds before you could arrange it so that everyone plays each other the same number of times (3 times).  So 28 players and 9 rounds, is the next value of 4n after 16 where a similar solution is possible.

Hope that helps,

Ian.