Practice Identifying Pigeons And Holes (17.6.1) - Module No#08 - Discrete Mathematics

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6 sample questions

Question 1.
Explain the pigeonhole principle in your own words.
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Think about socks in drawers.
Question 2.
What is the midpoint of (3,5) and (7,9)?
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Add x-coordinates and y-coordinates separately, then divide by 2.
3Question 3.
What does the pigeonhole principle state?
- If items equal holes
- all containers are full.
- More items than containers results in at least one full container.
- There are empty containers.
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Think about sock drawers!
4Question 4.
True or False: Two distinct integers selected from 1 to 8 cannot sum to 9.
- True
- False
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Check the pairs methodically.
Question 5.
Demonstrate that selecting 5 coordinates (x,y) within a certain range guarantees common parity.
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Remember your mapping from earlier!
Question 6.
Given any integer k, what is the least number of 1's you can arrange to find a multiple of k consisting only of 0s and 1s?
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Consider the remainders calculated.

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