Problem of the Week-2: Let's Shake Hands

With an odd number of people in the room, ask everyone to shake hands an odd number of times. No person need shake everyone's hand. In fact, each person could just shake hands with the same small selection of people multiple times. All that is required is that every person be involved in an odd number of handshakes. Noting that it is impolite to refuse a handshake when offered and that shaking hands with yourself is considered invalid, what curious predicament do folks find themselves in when they attempt this experiment?

Posted: 2/2/04

Submit your answers (by e-mail or hard copy) before 4 pm on 2/13/04 to Noah Aydin.

Mathematics Dept.