Practice Pigeonhole Principle Application (18.1.4) - Subsequence Existence
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Pigeonhole Principle Application

Practice - Pigeonhole Principle Application

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does the Pigeonhole Principle state?

💡 Hint: Think about how items can be grouped.

Question 2 Easy

Give an example of a strictly increasing sequence.

💡 Hint: Each term should be larger than the previous term.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Pigeonhole Principle guarantee?

It guarantees a unique solution.
It guarantees duplicates in containers.
It guarantees an increasing subsequence.

💡 Hint: Think about how items can be distributed.

Question 2

True or False: Every sequence of 4 distinct numbers must have an increasing subsequence of length 3.

True
False

💡 Hint: Try arranging 4 numbers differently.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a set of numbers {6, 2, 4, 8, 7}, find all increasing subsequences of at least length 3.

💡 Hint: Use combination of mappings to construct new subsequences.

Challenge 2 Hard

Show that for any set of 10 distinct integers, there must exist an increasing subsequence of length 4.

💡 Hint: Consider the distribution of integers in ranges.

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