Practice - Divisibility in Arbitrary Subsets
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Practice Questions
Test your understanding with targeted questions
Define a strictly increasing sequence.
💡 Hint: Think of numbers placed from smallest to largest.
What is a subsequence?
💡 Hint: Consider how you can pick elements but skip some.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What defines a strictly decreasing sequence?
💡 Hint: Visualize a staircase going down.
True or False: A subsequence must consist of consecutive elements.
💡 Hint: Think about how you might skip numbers in a list.
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Challenge Problems
Push your limits with advanced challenges
Prove that in any sequence of 10 distinct positive integers, there exists a subsequence of length 4 that is either strictly increasing or strictly decreasing.
💡 Hint: Look for the lengths you can compare among backs and see how they lead to pairs.
Given a set of 15 random numbers, verify if the assertion that you can find a subsequence of length 5 that’s either increasing or decreasing holds true.
💡 Hint: Divide the numbers into groups based on parity and analyze their compositions.
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Reference links
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