The Tennis Tournament

Four people, named "A", "B", "C" and "D", play one game of doubles tennis at lunch each day at an indoor court at work. At first they break up into pairs at random, but decide that a more orderly system is needed to guarantee that the players are mixed up as much as possible.

They figure out that they can play three rounds of games before they have to repeat a grouping. Here is the schedule they came up with:

        ==================
        4 Players, 1 Court

          Court   1    
        Day     -----
         1      AB CD
         2      AC DB
         3      AD BC
        ==================
      

One day while they are playing, they hear the sounds of another tennis game, and discover that there is another tennis court next door, where players "E", "F", "G" and "H" are playing. They decide that life would be even more fun if all 8 of them joined together in one rotation. They work on a new schedule, so that:

• On every day, there is a single game scheduled on each of the courts;
• Four people play a game on court 1; the other four play on court 2;
• The four people on a court are divided into two teams of two.

The players figure out a schedule of games that ensures that every player pairs exactly once with a given player, and opposes that player twice.

• How many days does this schedule of games last?
• What does such a schedule look like?
• Can the problem be solved for 12 players?
• Can the problem be solved for 16 players?

I give up, show me the solution.