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The Pigeonhole Principle

Discover a simple idea that guarantees surprising facts, such as two people in a class sharing a birthday month.

Grade 7Math OlympiadMathLogicNumber SenseIntermediate40 to 60 min3 materials

What you'll learn

  • State the pigeonhole principle in your own words
  • Identify the pigeons and the holes in a problem
  • Write a short, clear proof

Objective

Learn the pigeonhole principle and use it to prove that certain situations must happen.

STEM concepts

ProofWorst case reasoningLogical argument
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Step-by-step instructions
Prediction, test sheet and results
Why does it work, challenge and project report

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