An old chestnut
goes like this:
N married couples (and no other people) are at a party, including the host and hostess (a married couple). Various pairs of people shake hands, though nobody shakes his/her spouse's hand.
At the end of the party, the host asks each other person, including his wife, how many other people he/she shook hands with. He gets a different answer from each person.
How many people's hands did the host shake?
How many people's hands did the hostess shake?