[Pamela Zave shared this problem with me.]
Hilary and Jocelyn are throwing a dinner party at their house and have invited four other couples. After the guests arrive, people greet each other by shaking hands. As you would expect, a couple do not shake hands with each other and no two people shake each other’s hands more than once. At some point during the handshaking process, Jocelyn gets up on a table and tells everyone to stop shaking hands. She also asks each person how many hands they have shaken and learns that no two people on the floor have shaken the same number of hands. How many hands has Hilary shaken?