Practice - Lecture No#38
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Practice Questions
Test your understanding with targeted questions
List the possible pairs of integers from 1 to 8 that sum to 9.
💡 Hint: Look for pairs where one number increases and the other decreases.
What is the midpoint formula for two points (x1, y1) and (x2, y2)?
💡 Hint: Think about averaging the coordinates.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the pigeonhole principle guarantee in the context of distinct points?
💡 Hint: Think about how points can be categorized.
Choosing 5 integers from 1 to 8 always results in what?
💡 Hint: Consider the defined pairs available.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Consider the integers from 1 to 15. Prove that choosing any 8 integers guarantees a pair that sums to 16.
💡 Hint: How many pairs can you make from the given integers?
Construct a proof showing that for any integer n, a number constructed with n 1s is divisible by n.
💡 Hint: Explore numbers like 1, 11, 111, and analyze their remainders.
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Reference links
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