Practice - Introduction to Counting Problems
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Practice Questions
Test your understanding with targeted questions
What is the base condition for counting strings of length 1 and 2?
💡 Hint: Think of the possible strings.
Write the recurrence relation for counting bit strings with no consecutive zeros.
💡 Hint: Think about where a string can start.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a recurrence equation?
💡 Hint: Consider how terms can be calculated based on earlier values.
True or False: The Fibonacci sequence is an example of a recurrence relation.
💡 Hint: Think of how Fibonacci is traditionally defined.
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Challenge Problems
Push your limits with advanced challenges
Given C(1) = 2, C(2) = 3. Using the derived relation, calculate C(8) and provide the reasoning for each step.
💡 Hint: Draw out or visualize a tree for each sequence.
Construct a different counting function that also uses a recurrence relation and compare its properties with our strings without consecutive zeros.
💡 Hint: Identify how many strings might be invalid and adjust the relations accordingly.
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