Team based round robin

[rowanklein]

Firstly, what a great site and so many questions answered. Well done.

I've looked through a number of posts and not able to find a solution to the problem I'm trying to solve. Basically
- 2 teams of 10 players (2 male and 5 female). Let's say team A (M1-M5 & F1-F5) team B (G1-G5 & L1-L5)
- all players of similar standard so ranking adjustment / seeding not important.
- Total of 20 matches (so looking at 5 rounds with each player having a bye round)
- Mixed doubles draw. Looking for 4 matches for each player
- Each gender plays 4 matches with opposite gender of same team.
- Additional constraint that do not play against same player in any 4 matches.

The solution appears to be a 2 parts.
- 1st is a combination table construction (625 possible combinations).
- 2nd is picking out individual combinations that satisfy the no 2 people (same or opposite team) play in more than 1 game for/against each other. Eg M1F1vsG1L1 means that M1F4vsG3L1 is not an acceptable subsequent pairing. I've attached a spreadsheet with all combinations that don't include duplicate "1"players.

Working manually I got to 19 matches matching the criteria but couldnt get it up to 20. I forgot to save that partial solution. Wondering if their is a formula or so other method that removes the pure luck factor of manually trying to find a solution. 

The reason for this structure is to maximise the amount of different players people play with and against and make it a truly team event rather than a team of double pairing event. 

Thanks

[Ian Wakeling]

There is a way of solving this, and you could have all 20 players compete in each round if you wanted.  Start by looking at this ancient thread, where the message I wrote contains a downloadable file accessible from the paper-clip link (you need to be logged in to the forum to see the paper-clip).  Look at the 1st worksheet of this file - you can assign "Foursome 5" to be the byes, then make the following changes to the player names:
A1 to A5 -> M1 to M5
A6 to A10 -> F1 to F5
B1 to B5 -> G1 to G5
B6 to B10 -> L1 to L5

The transformed schedule should meet all your requirements - it was constructed using 4 mutually orthogonal Latin squares where each square represent one of the  groups of players above.  To see an example look for a set of MOLS(5) on this Wikipedia page. The other tabs in the spreadsheet gives similar schedule for multiples of 4 players from 20 to 72.  Hope that helps.