I have been trying to solve this for quite a while without success. I have not found (I searched though) theory that could help me on wikipedia.
Here is the problem.
I have a group of n players (more than 7) I have a game (diplomacy for those who know !) that requires 7 players, one for these roles : E,F,G,I,A,R and T (countries in fact)
I want to set up a tournament (many games).
There will be n games.
(*) Every player gets into 7 different games, with different role each time
(**) Every game gets 7 different players
=> That is very easy to do.
However, when things get tough, is when you want to limit interactions between players. What I want is any player to interact (interact = play in same game) at most with one other player. (In other words, I want to prevent players from making such deals : "I help you in game A, you help me in game B")
So:
Question 1 : For which n is this possible ? (obviously at least 50)
Question 2 : When it is possible, how do you do it ?
Question 3 : What is the algo to minimize these interactions when it is not possible ?
For the record, I did implement a try-and-error program in python (using recursion), working quite well, but I never can get maximum intearctions between players limited to 1 (endless calculations)
thanks for any help !
PS This is no homework, it is for actually designing game tournaments
Here is the problem.
I have a group of n players (more than 7) I have a game (diplomacy for those who know !) that requires 7 players, one for these roles : E,F,G,I,A,R and T (countries in fact)
I want to set up a tournament (many games).
There will be n games.
(*) Every player gets into 7 different games, with different role each time
(**) Every game gets 7 different players
=> That is very easy to do.
However, when things get tough, is when you want to limit interactions between players. What I want is any player to interact (interact = play in same game) at most with one other player. (In other words, I want to prevent players from making such deals : "I help you in game A, you help me in game B")
So:
Question 1 : For which n is this possible ? (obviously at least 50)
Question 2 : When it is possible, how do you do it ?
Question 3 : What is the algo to minimize these interactions when it is not possible ?
For the record, I did implement a try-and-error program in python (using recursion), working quite well, but I never can get maximum intearctions between players limited to 1 (endless calculations)
thanks for any help !
PS This is no homework, it is for actually designing game tournaments