Practice Pigeonhole Principle Argument (18.3.2)

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6 sample questions

Question 1.
Define a strictly increasing sequence.
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Think about how numbers can be arranged.
Question 2.
What does the Pigeonhole Principle state?
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Consider how this applies to simple grouping.
3Question 3.
What is a strictly increasing sequence?
- A sequence where all elements are the same
- A sequence where each element is larger than the previous
- A sequence in descending order
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Think about how numbers grow.
4Question 4.
True or False: The Pigeonhole Principle can always be applied to find a repeated value in sets.
- True
- False
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Reflect on grouping elements.
Question 5.
Given the set of integers {1, 2, ..., 10}, prove that in any selection of 6 values, either there will be a strictly increasing or a strictly decreasing subsequence of length 4.
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Think about maximum sequences you can get.
Question 6.
For the sequence (3, 5, 2, 4, 1), identify the increasing and decreasing subsequences of maximum length.
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Look for sequences that can skip numbers.

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