I need to solve the following problem for actual use.
- 10 people will be playing a game.
- They play the game 4 people at a time.
- Each time they play they garner points within the game.
- Each person needs to play against each other person at some time.
- Each person needs to play the same number of times.
- The winner is the person who has accumulated the most points at the end.
10 choose 4 is 210, so one solution is to have 210 rounds where every combination of 4 players plays the game. But this is an impractical number of rounds!
Is there a solution to this problem in less than 20 rounds? I suppose it would be okay if some rounds were played with only 3 people. How would I figure this out in the fairest way?
EDIT: An additional useful constraint would be that no player plays twice in a row, if that's possible.