Practice - Pigeon-Hole Principle
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Practice Questions
Test your understanding with targeted questions
If you place 10 apples into 9 boxes, how many boxes will contain at least 2 apples?
💡 Hint: Consider how many more apples there are than boxes.
What happens if there are 7 pairs of gloves and only 5 pairs of gloves can be stored?
💡 Hint: How many gloves do you have vs. storage space?
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Interactive Quizzes
Quick quizzes to reinforce your learning
If you have 20 items and only 15 containers, will at least one container have more than one item?
💡 Hint: Think about the basic logic behind resource allocation.
What is the minimum number of people needed to guarantee either 3 mutual friends or 3 mutual enemies?
💡 Hint: Review the principle's application in social dynamics.
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Challenge Problems
Push your limits with advanced challenges
Prove that if you have 100 socks and you’re putting them into 80 drawers, at least one drawer must contain at least 2 socks.
💡 Hint: Think about how drawers can be filled.
If you collect rebounds from 15 basketball games and there are only 10 hoops to shoot at, show using a pigeon-hole approach that at least one hoop must have 2 rebounds.
💡 Hint: Relate rebounds to the principle’s logic.
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Reference links
Supplementary resources to enhance your learning experience.