Problem: A dating service has as clients six recently divorced heterosexual couples. Each client wants the opportunity to socialize with the other clients of the opposite sex, but refuses to be in the same room as his or her ex-spouse. The service wants to throw a sequence of parties to bring the clients together. They want each male and female client to attend one or more party, but of course no formerly married couple should attend the same party.
a) What is one way to do this? (Include the guest lists for the parties)
b) What is the fewest number of parties that can be held?
c) What are all the possible combinations of clients that have the fewest number of parties? (The guest lists for the parties in part b)