Practice Proof using Pigeonhole Principle - 17.7.2 | 17. Module No#08 | Discrete Mathematics - Vol 2
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17.7.2 - Proof using Pigeonhole Principle

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define the Pigeonhole Principle in your own words.

💡 Hint: Think about distributing items in boxes.

Question 2

Easy

What is the midpoint formula?

💡 Hint: It involves averaging the corresponding coordinates.

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 does the Pigeonhole Principle state?

  • If ten items are put into nine boxes
  • at least one box has two items.
  • All items will fit into the boxes available.
  • Every box will contain one item.
  • If objects are grouped into boxes
  • each box must hold the same amount.

💡 Hint: Remember the connection between items and containers.

Question 2

True or False: The midpoint of two points can be a non-integer.

  • True
  • False

💡 Hint: Think about averaging even and odd coordinates.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Consider a group of ten friends, each picking from five distinct fruits. Show how the Pigeonhole Principle guarantees fruit overlaps among their selections.

💡 Hint: Group the choices into the types of fruits available.

Question 2

Using the Pigeonhole Principle, prove that among any ten consecutive integers, at least two of them will produce the same remainder when divided by five.

💡 Hint: Count the number of integers and the possible remainders.

Challenge and get performance evaluation