Math Is Fun Forum

Hi, I don't know what the right category for my problem should be, so sorry in advance if this is not the right one.
I'd like some help with te following.
There is a sports match between team A and team B.
Each team consists of 6 players. All matches are doubles matches.
Every team member will play with each of its other team members. So the match consists of 5 rounds of 3 doubles matches = 15 matches.
A possible line up for team A could be:
Round 1
1/6
2/5
3/4
Round 2
1/5
2/4
3/6
Round 3
1/4
2/3
5/6
Round 4
1/3
2/6
4/5
Round 5
1/2
3/5
4/6
Now each player of team A has played 1 exactly match with each of its team members.
My question: what should the line up of team B look like to make sure:
-each team member of team B plays a match with every team member (like team A does).
-the number of different opponents from the other team for each player is maximised
Since each player plays 5 matches and there a 6 opponents in the other team and all matches are doubles matches (making it 10 opponents) you might think there is a schedule whereby each player plays 2 of the players of the
opposing team once and 4 players twice, making it 10. But I don't know if that's possible.

Kind regards, Carlos
p.s. Chat GPT does not come with good solutions for this problem, I've tried it.