This will be difficult to count, especially if you have a large class. Try the problem in small groups and then compare different methods for finding the answers, or try it with a few learners at the front of the class and the remainder of the class counting the handshakes. How many handshakes are there for 2 people, how many for 3 people, how many for 4 people and so on?
When the handshaking is finished discuss how many handshakes took place. Can you see a pattern? Can you explain it? Can you find a method for getting the answer whatever the size of the group? Can you find different methods of finding the number of handshakes?
This problem is adapted from the NRICH task Handshakes with permission of the University of Cambridge. All rights reserved.