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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a strictly increasing sequence. Give an example.
💡 Hint: Think about numbers that follow one another and keep getting larger.
Question 2
Easy
What is a subsequence?
💡 Hint: Remember, the order should remain the same.
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 defines a strictly increasing sequence?
- Each number is greater than the last
- Each number is less than the last
- Numbers can repeat
💡 Hint: Think about how numbers compare to each other.
Question 2
True or False: In every set of n + 1 distinct real numbers, there must be a strictly increasing subsequence of length n + 1.
- True
- False
💡 Hint: Reflect on the properties of increasing subsequences.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using 9 distinct integers from 1 to 20, demonstrate through a sequence how the pigeonhole principle ensures either an increasing or decreasing subsequence of length 5.
💡 Hint: Look for how many distinct lengths can be achieved and overlap them.
Question 2
Given the sequence of prime numbers up to 30, find a subsequence of at least 4 numbers that is strictly increasing and explain your reasoning.
💡 Hint: Remember that primes inherently don't repeat, aiding your subsequence choice.
Challenge and get performance evaluation