Help!

[Jingx]

Please help us to figure out the name chart for the following game.

1. 20 Females and 20 Males are invited to the game, in this game; there are total 10 runs for 10 games.
2. 1 F and 1 M are going to be selected to filing a team to against another pair of F+M.
3. Nobody can repeat any one of the games; also nobody will meet his/her partner or counter part again in the rest of process of the game. Each person has a chance to play 10 games in 10 runs with different partners and counter parts, which means 4 persons in 1st game can not meet any one of them again in the rest of games.
4. There is no elimination in this game; everyone can play from 1st game to 10th game.

We have sent out our invitations, but now we stuck in figuring out the name chart.

Is anyone can help us out?

Thank you so much

[Darryl]

With the parameters given, it's mathematically impossible.

at best you can only guarantee 9 games with unique partners/opponents

1 game will have to duplicate 1 oppenents

and that's assuming that a person that was your opponent can also in another game be your partner. Though you seemed to imply you would not see that person again at all. If that is the case, then you can only get 5 unique games.

[Darryl]

ahh i read wrong, you have a total of 40 players, not 20, so I think it can be done, let me think about it some more

...EDIT...

Oh, I got it. Imagine the first round pairings are just in sequential order and male are even and female is odd so:
Table 1 = 1,2,3,4
Table 2 = 5,6,7,8
Table 3= 9,10,11,12
Etc.
At the end of the round
The person in position one stays at current table
Person in position 2 moves to next table
Person in position 3 moves 2 tables
Person in position 4 moves 3 tables

of course people at table 40 wrap around to table 1

So Second round the first few tables will be:
Table 1 = 1, 38, 35, 32
Table 2 = 5, 2, 39, 36
Table 3 = 9, 6, 3, 40
etc.