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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the pigeonhole principle?
💡 Hint: Think about distributing items.
Question 2
Easy
Provide an example of a number composed only of the digit 1 and is divisible by 2.
💡 Hint: Think of how you can represent 2 with 1s.
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?
- At least one item must be duplicated
- No items will be duplicated
- All items will be distinct
💡 Hint: Think about how to distribute items among limited spaces.
Question 2
What is the outcome of x_i - x_j if both yield the same remainder?
- True
- False
💡 Hint: Think about the structure formed by subtracting two similar numbers.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using the pigeonhole principle, prove that among any 10 integers chosen between 1 and 10, at least two must share a common divisor greater than 1.
💡 Hint: Consider how many integers share divisors.
Question 2
Develop a short proof that for any integer k, a number with k digits can be formed using just 0s and 1s to showcase some multiples.
💡 Hint: Consider the number of digits and how they fit remainders.
Challenge and get performance evaluation