Practice Application of Pigeonhole Principle - 17.5.2 | 17. Module No#08 | Discrete Mathematics - Vol 2
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17.5.2 - Application of Pigeonhole Principle

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Provide an example illustrating the Pigeonhole Principle using fruits and containers.

💡 Hint: Think of how many items you have versus containers.

Question 2

Easy

What is the midpoint of points (2, 6) and (8, 10)?

💡 Hint: Use the midpoint formula.

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

What is the fundamental idea behind the Pigeonhole Principle?

  • Every item must go in a different container
  • If there are more items than containers
  • at least one container must hold multiple items
  • Items must be distributed evenly

💡 Hint: Consider a simple example of baskets and fruits.

Question 2

True or False: The midpoint of two points with non-integer coordinates is always non-integer.

  • True
  • False

💡 Hint: Think about coordinate combinations.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Identify 3 different sets of integers from 1 to 20 that, if choosing 8 at random, must yield pairs summing to 12. Show your reasoning.

💡 Hint: Count the pairs available and what happens with extra selections.

Question 2

Using the Pigeonhole Principle, prove that for any selected set of 100 integers chosen from 1 to 200, at least two numbers will yield the same modulo 100.

💡 Hint: Think about the range of results possible and total selections.

Challenge and get performance evaluation