Thread: Combinatronics, fair matching

I am new here, I don't know if this is the right place for this post, but...feel free to delete or move this post as necessary.

Here is the problem:

n players
k players per team
Each player must play “with” and “against” every other player at least
once and an equal number of times using a minimal number of matches.
An easy example:
—
Players = 1, 2, 3, 4 (n = 4)
2 players per team (k = 2)
Matches:
1, 2 vs. 3, 4
1, 3 vs. 2, 4
1, 4 vs. 2, 3
After those 3 matches, all players played “with” and “against” each
other once.
As simple as it gets.
—
The challenge that is causing me trouble:
Find an efficient method to generate the minimal number of matches for
any n and k.
It sounded trivial at first…at first.

Obviously, I meant:

"After those 3 matches, all players played “with” each other once and “against” each
other twice.

Thanks for moving this thread to a more suitable location.