All 12 play but never the same person twice?

[Len]

I have 2 Teams with 6 players on each Team for a total of 12 players. Call them Team A and Team B. We are playing Doubles Paddle Tennis (more fun for seniors than “real” Tennis), so 4 players (2 from each Team) are on the court at any one time.

I'm trying to find our if it is possible to arrange Round Robin Tennis Sets where no player ever plays twice with a player on their Team AND never plays a player on the other Team more than once.

The first Round is straight forward :>) but I cannot seem to meet the requirements in Round 2. And a Round 3 would be great.

All HELP! is appreciated, and I'm now going to look over the “Court Balanced Round Robin” discussion.
Thanks,
    Len

[Ian Wakeling]

Len,

If I understand correctly, that you only have one court, then what you want is possible.  For example:

(A1 A4 B1 B4)
(A2 A6 B2 B4)
(A3 A5 B3 B4)
(A3 A6 B1 B5)
(A1 A5 B2 B5)
(A2 A4 B3 B5)
(A2 A5 B1 B6)
(A3 A4 B2 B6)
(A1 A6 B3 B6)

However it is not possible to have a similar schedule where the 9 matches are arranged into 3 rounds, where all players play exactly once per round.  In other words, no such tournament is possible if there are 3 courts available and everyone must play simultaneously.

In the schedule above you need to randomise the order of play for the 9 matches, otherwise B4, B5 & B6 will complain about their byes coming together in large blocks.

[Len]

Ian -
THANK YOU so much for your system and ideas.

However, it appears that A1 does not play with A2 or A3. And B1 does not play with B2 or B3. If you have the system that takes these combinations into account, It would be great. I also think it gets pretty big (but maybe we could create multiple Tournaments to cover every possibility?).

FYI, we have 2 Paddle Tennis courts. Our little tournament has two levels of play, both with 12 players. By having Sets be 5 games (rather than our standard 6), we can get in 8 sets in an hour (4 per court). Our 55+ senior retirement community can have a very nice and fun morning. With a little effort, we should be able to randomize and integrate the two levels (although the three 90+ players and the five 80+ players like to play early).

By the way, if you would like to see Paddle Tennis in action, try http://www.venicebeachlivecam.tv/ where you can control the camera for 2 minutes at a time. Best early on Saturday and Sunday mornings.

Sincerely,
   Len

[Ian Wakeling]

Len,

For any one player there are 5 possible partners from their own team, and 6 possible opponents from the opposing team; unfortunately this makes the problem unbalanced and there can be no possibility of a fully balanced schedule unless you play 5 times as many games as above. That is 45 games in total, each player has 15 games, all partners 3 times, all opponents 5 times.  I say possibility as I don't have a way of constructing this 45 game schedule!

Note that you can make use of the fact that it is always 1/2/3 paired with 4/5/6.  If you make the former the stronger players and the latter the weaker players then you always have mixed ability partnerships within a team.

Ian.

[Len]

Thanks, Ian, for the great advice. This is our first attempt at setting up a tournament and it has been an interesting experience. There is a lot more "customizing" then we hoped for, but you gave us a good starting point. The next time should be easier.
Good luck and Enjoy,
   Len