Project 1
We have considered the problem of determining the number of handshakes
which occur if there are nineteen people in a room and each person
shakes hands with every other person exactly one time. For this
project I want you to do two things. First, describe, clearly and
logically, how your group solved this problem for nineteen
people. Once you have done this solve the problem for an arbitrary
number of people. That is, if there are n people in the room and
everyone shakes hands with every other person exactly once, how many
handshakes occur? Give a clear and concise explanation of the method
you used to reach this conclusion. Do you think this method has any
utility in helping to solve other, more difficult, problems? (This is
the ``looking back'' part of Pólya's problem solving technique.)