We are with 6 players and we play matches 2 against 2. We play 3 matches on 1 day and we have 7 days to play. So we have 21 matches and i want that everyone plays equal times (as much as possible) with everyone and against everyone.
Attempt: Everyone is playing $~14~$ matches so everyone plays $~4x~$ times together with everyone except one person just $~3x~$. But then it stops for me...
You can assign three teams of 2 for a day and then let these three teams play each other on this day. There are 10 ways to assign 6 players to 3 teams of 2, so if you want to play through all these combinations you would need 10 days not just 7. You can pick 5 of these 10 ways to assign teams so that every player was teamed up with every other player once. If you want to play exactly 21 games in 7 days you can use the last two days for some finals or just playing in teams that are roughly equal strength.
