Practice - Question 10
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Practice Questions
Test your understanding with targeted questions
What is the pigeonhole principle?
💡 Hint: Think about distributing items.
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.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the pigeonhole principle guarantee?
💡 Hint: Think about how to distribute items among limited spaces.
What is the outcome of x_i - x_j if both yield the same remainder?
💡 Hint: Think about the structure formed by subtracting two similar numbers.
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Challenge Problems
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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.
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.
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