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?
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This problem is adapted from the NRICH task Handshakes with permission of the University of Cambridge. All rights reserved.