Shaking Hands - Sept. 19-23, 1994 It's Bonita's birthday this Wednesday, and Braulio is throwing a party for her. There will be prizes for various games and contests. The coolest prize will be given to those who answer the following two-part problem: a) If each person shakes hands with everyone else at the party, how many handshakes will there be? b) What if everyone is seated at a table and shakes hands with everyone except the two people sitting on either side of them? Braulio hasn't said how many people are coming and probably doesn't know for sure, but several people are trying to figure out the answers to the contests before the party anyway. Can they do this? What could they bring to the party in order to come up with the answers quickly? Hints: Start with a few examples: What if two people were going to be at the party? How about three? Four? Try drawing a picture with each person as the vertex of a polygon. Correct solutions to the problem were submitted by: Jon Star's Class at Albuquerque Academy in Albuquerque, New Mexico Andrew Liu, College Park High School Anna Ustazewska, College Park High School Michele Gibney, College Park High School Cecilia Merediz, Fairfield High School Karen Lannutti, Mount St. Joseph Academy Sarah McLaughlin, Mount St. Joseph Academy Meg Tenny's Group at Dover-Sherborn High School Eric Ostrowski at Shaler Area High School Annie Chan, Burnaby South Secondary School Al Trezza and Matt Walker, Shaler Area High School Louise, Ryan, and Ben, Colorado Creative Education's Learning Center Lauren Mariani, Moira McCarthy, Hannah Guhm, Katherine Stroup, and Eric Wahl, Masterman High School Next problem || Previous problem || Table of Contents || Forum Home Page