Practice - Identifying Pigeons and Holes
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Practice Questions
Test your understanding with targeted questions
Explain the pigeonhole principle in your own words.
💡 Hint: Think about socks in drawers.
What is the midpoint of (3,5) and (7,9)?
💡 Hint: Add x-coordinates and y-coordinates separately, then divide by 2.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the pigeonhole principle state?
💡 Hint: Think about sock drawers!
True or False: Two distinct integers selected from 1 to 8 cannot sum to 9.
💡 Hint: Check the pairs methodically.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Demonstrate that selecting 5 coordinates (x,y) within a certain range guarantees common parity.
💡 Hint: Remember your mapping from earlier!
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?
💡 Hint: Consider the remainders calculated.
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Reference links
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