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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
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.
Question 2
Easy
What is the midpoint formula for two points (x1, y1) and (x2, y2)?
💡 Hint: Think about averaging the coordinates.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the pigeonhole principle guarantee in the context of distinct points?
- A. At least one point will be repeated
- B. At least one pair of points will have integer midpoints
- C. All points will have integer coordinates
💡 Hint: Think about how points can be categorized.
Question 2
Choosing 5 integers from 1 to 8 always results in what?
- True
- False
💡 Hint: Consider the defined pairs available.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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?
Question 2
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.
Challenge and get performance evaluation