Not sure this is a math problem or just a problem but thought I would seek your help. 1st thing it helps if you play golf and understand the term 4BBB or 4 Ball Better Ball. Basically I am organising a 4 day 4 round golf competition, there are 12 players and I want to establish the most fair, random draw for the 4 day event that I can such that no two players play together as a pair more than once and the most variety possible is introduced in each round as is possible i.e. if possible each player plays with a differnt 3 people in each game or if the math doesnt add up in that way the number of time 2 people play in the same game is minimised and they certainly dont appear on the same side.
Day1 Event 1 would concivably start like this;
Player 1 & Player 2 v Player 3 & Player 4 - Game 1
Player 5 & Player 6 v Player 7 & Player 8 - Game 2
Player 9 & Player 10 v Player 11 & Player 12 - Game 3
Applying your mathematical genius what shoud Day2 Event 2 look like, day 3 Event 3 and Day4 Event 4 draws look like given the desire expressed above I.e. no 2 players play together more than once as a pairing and as far as possible each game comprises a set of four people who have not played together or with each other previously.
Hopefully it makes sense maybe more so if your a golfer, look forward to your responses.