Practice - Age Group and Pigeonhole Principle Application
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Practice Questions
Test your understanding with targeted questions
Define a strictly increasing subsequence.
💡 Hint: Think about an example where numbers go up.
What does the pigeonhole principle state?
💡 Hint: Consider how this might apply to people and birthdays.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is a strictly increasing subsequence?
💡 Hint: Think of a climbing path.
Does the pigeonhole principle allow for items to fit without overlap?
💡 Hint: Consider how many people can fit into a car.
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Challenge Problems
Push your limits with advanced challenges
Provide a proof using the pigeonhole principle to show that among any 10 individuals selected randomly, there must be at least two who share the same birthday month.
💡 Hint: Think of how many months the year has versus the number of persons.
Given a sequence of 10 distinct integers, demonstrate using theorems related to subsequences that there must be increasing subsequences of at least 4 numbers.
💡 Hint: Think about how they can be grouped and compared in ranges.
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Reference links
Supplementary resources to enhance your learning experience.