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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does C(0) equal?
💡 Hint: How many valid sequences are possible with no pairs?
Question 2
Easy
What is the value of C(1)?
💡 Hint: Think of the simplest case of one pair of parentheses.
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 is the value of C(3)?
- 3
- 5
- 7
💡 Hint: Recall the example we discussed regarding valid arrangements.
Question 2
Is C(n) always equal to a positive integer?
- True
- False
💡 Hint: Think about what Catalan numbers represent in combinatorics.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Calculate C(4) using the recurrence relation and list all valid sequences.
💡 Hint: List combinations for n = 3 and apply them step-wise.
Question 2
Explore another combinatorial problem that shares a bijection with Catalan numbers. Describe it.
💡 Hint: Draw the connection based on how parentheses reflect balance in sequences.
Challenge and get performance evaluation