I need to organise a mixed doubles badminton tournament where partners swap round from one game to the next.
There are 10 men and 10 ladies. Every man and lady should play one game with every possible partner of the opposite sex, 100 pairings, thus 50 games.
Is it possible to organise the games between pairs such that the following conditions apply?
a) every man plays against every man at least once
b) every lady plays against every lady at least once
c) everybody plays against as many opponents of the opposite sex as is possible

Can this be extended to any number of players?