Practice Proof Using Pigeonhole Principle (17.7.2) - Module No#08 - Discrete Mathematics - Vol 2

Practice: Proof using Pigeonhole Principle

Lesson 17.7.2Module No#08

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8 questions

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6 sample questions

Question 1.
Define the Pigeonhole Principle in your own words.
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Think about distributing items in boxes.
Question 2.
What is the midpoint formula?
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It involves averaging the corresponding coordinates.
3Question 3.
What does the Pigeonhole Principle state?
- If ten items are put into nine boxes
- at least one box has two items.
- All items will fit into the boxes available.
- Every box will contain one item.
- If objects are grouped into boxes
- each box must hold the same amount.
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Remember the connection between items and containers.
4Question 4.
True or False: The midpoint of two points can be a non-integer.
- True
- False
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Think about averaging even and odd coordinates.
Question 5.
Consider a group of ten friends, each picking from five distinct fruits. Show how the Pigeonhole Principle guarantees fruit overlaps among their selections.
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Group the choices into the types of fruits available.
Question 6.
Using the Pigeonhole Principle, prove that among any ten consecutive integers, at least two of them will produce the same remainder when divided by five.
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Count the number of integers and the possible remainders.

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