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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
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 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.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation