jmc

Question

23 people attend a party. Each person shakes hands with at most 22 other people. What is the maximum possible number of handshakes, assuming that any two people can shake hands at most once?

Accepted Answer

Note that if each person shakes hands with every other person, then the number of handshakes is maximized. There are 232 = (23)(22)2 = (23)(11) = 230+23 = 253 ways to choose two people to form a handshake.