If all the students in this room shook hands with each other, how many handshakes would there be altogether?
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Can you find a formula for the number of handshakes given the number of students?
Edward and Lucy invite four couples to dinner. Each person shakes hands only with the people that he or she has not met before. Edward then asks his wife and eight guests how many hands they shook, and he receives nine different answers. How many people did Lucy shake hands with?
Bellos, Alex. Can You Solve My Problems?: a Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles. Guardian Books, 2017.
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Teacher, do your students have access to computers such as tablets, iPads or Laptops? This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:
However it would be better to assign one of the student interactive activities below.
Here is the URL which will take them to a related student activity.
See the National Curriculum page for links to related online activities and resources.