Practice Application Of Pigeonhole Principle (17.5.2) - Module No#08 - Discrete Mathematics - Vol 2

Practice: Application of Pigeonhole Principle

Lesson 17.5.2Module No#08

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9 questions

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6 sample questions

Question 1.
Provide an example illustrating the Pigeonhole Principle using fruits and containers.
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Think of how many items you have versus containers.
Question 2.
What is the midpoint of points (2, 6) and (8, 10)?
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Use the midpoint formula.
3Question 3.
What is the fundamental idea behind the Pigeonhole Principle?
- Every item must go in a different container
- If there are more items than containers
- at least one container must hold multiple items
- Items must be distributed evenly
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Consider a simple example of baskets and fruits.
4Question 4.
True or False: The midpoint of two points with non-integer coordinates is always non-integer.
- True
- False
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Think about coordinate combinations.
Question 5.
Identify 3 different sets of integers from 1 to 20 that, if choosing 8 at random, must yield pairs summing to 12. Show your reasoning.
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Count the pairs available and what happens with extra selections.
Question 6.
Using the Pigeonhole Principle, prove that for any selected set of 100 integers chosen from 1 to 200, at least two numbers will yield the same modulo 100.
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Think about the range of results possible and total selections.

5 more questions in this section. Enroll free to practise them all.