[Taken from Halmos p. 8 with modifications by Stephanie Wilcox.]
My friend and I went to a party that had four other pairs of friends, making a total of ten people. As people arrived, a certain amount of handshaking took place in an unpredictable way, subject only to two obvious conditions: no one shook his or her own hand and no pair of friends shook each other's hands. When it was all over, I became curious and I went around the party asking each person: "How many hands did you shake?" I asked nine people (everybody, including my own friend), and I was interest to note, and I hereby report, that I got nine different answers. How many hands did my friend shake?