Practice problems and test your proof technique knowledge
Use the playground to experiment with the Pigeonhole Principle, then test your understanding with our comprehensive quiz. The quiz covers basic concepts, identifying pigeons and holes, the generalized principle, and challenging applications.
Experiment freely with different numbers of pigeons and holes. Build intuition before taking the quiz!
Drag the pigeons into the holes. When you have more pigeons than holes, at least one hole must contain 2+ pigeons!
If n+1 objects are placed into n containers, at least one container must hold more than one object. This simple fact is surprisingly powerful in mathematics!
Answer 30 questions across three difficulty levels. Filter by difficulty or take the full quiz!
Topic: Basic Principle
If you have 5 pigeons and 4 pigeonholes, what does the Pigeonhole Principle guarantee?
Congratulations on exploring the Proof Techniques module! You've covered:
Stay tuned for more proof techniques coming soon, including the extremal principle and double counting!