Practice Pigeon-Hole Principle - 10.5 | 10. Basic Rules of Counting | Discrete Mathematics - Vol 2
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10.5 - Pigeon-Hole Principle

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

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?

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

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.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation