Practice Pigeonhole Principle Application (18.1.4)

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6 sample questions

Question 1.
What does the Pigeonhole Principle state?
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Think about how items can be grouped.
Question 2.
Give an example of a strictly increasing sequence.
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Each term should be larger than the previous term.
3Question 3.
What does the Pigeonhole Principle guarantee?
- It guarantees a unique solution.
- It guarantees duplicates in containers.
- It guarantees an increasing subsequence.
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Think about how items can be distributed.
4Question 4.
True or False: Every sequence of 4 distinct numbers must have an increasing subsequence of length 3.
- True
- False
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Try arranging 4 numbers differently.
Question 5.
Given a set of numbers {6, 2, 4, 8, 7}, find all increasing subsequences of at least length 3.
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Use combination of mappings to construct new subsequences.
Question 6.
Show that for any set of 10 distinct integers, there must exist an increasing subsequence of length 4.
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Consider the distribution of integers in ranges.

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