Practice - Application of Pigeonhole Principle
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Practice Questions
Test your understanding with targeted questions
Provide an example illustrating the Pigeonhole Principle using fruits and containers.
💡 Hint: Think of how many items you have versus containers.
What is the midpoint of points (2, 6) and (8, 10)?
💡 Hint: Use the midpoint formula.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the fundamental idea behind the Pigeonhole Principle?
💡 Hint: Consider a simple example of baskets and fruits.
True or False: The midpoint of two points with non-integer coordinates is always non-integer.
💡 Hint: Think about coordinate combinations.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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