Shaking Hands at a Gathering Situation:at a gathering of n people,everyone shook hands with at least one person,and no one shook hands more than once with the same person. Problem:show that there must have been at least two of them who had the same number of handshaking. ●Solution: Pigeon:the n participants Pigeonhole:different number between 1 and n-1. Shaking Hands at a Gathering  Situation: at a gathering of n people, everyone shook hands with at least one person, and no one shook hands more than once with the same person.  Problem: show that there must have been at least two of them who had the same number of handshaking.  Solution:  Pigeon: the n participants  Pigeonhole: different number between 1 and n-1