Practice Age Group And Pigeonhole Principle Application (18.2.1) - Subsequence Existence
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Age Group and Pigeonhole Principle Application

Practice - Age Group and Pigeonhole Principle Application

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a strictly increasing subsequence.

💡 Hint: Think about an example where numbers go up.

Question 2 Easy

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

Question 1

What is a strictly increasing subsequence?

A sequence where elements decrease
A sequence where each element is equal
A sequence where each element is larger than the previous

💡 Hint: Think of a climbing path.

Question 2

Does the pigeonhole principle allow for items to fit without overlap?

True
False

💡 Hint: Consider how many people can fit into a car.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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