Practice Pigeon-hole Principle (10.5) - Basic Rules of Counting - Discrete Mathematics - Vol 2
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Pigeon-Hole Principle

Practice - Pigeon-Hole Principle

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

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.

Question 2 Easy

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?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

If you have 20 items and only 15 containers, will at least one container have more than one item?

True
False

💡 Hint: Think about the basic logic behind resource allocation.

Question 2

What is the minimum number of people needed to guarantee either 3 mutual friends or 3 mutual enemies?

4
5
6

💡 Hint: Review the principle's application in social dynamics.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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