Practice - Proof using Pigeonhole Principle
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Practice Questions
Test your understanding with targeted questions
Define the Pigeonhole Principle in your own words.
💡 Hint: Think about distributing items in boxes.
What is the midpoint formula?
💡 Hint: It involves averaging the corresponding coordinates.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Pigeonhole Principle state?
💡 Hint: Remember the connection between items and containers.
True or False: The midpoint of two points can be a non-integer.
💡 Hint: Think about averaging even and odd coordinates.
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Challenge Problems
Push your limits with advanced challenges
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.
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.
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Reference links
Supplementary resources to enhance your learning experience.