20.6 - Conclusion and Summary
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Practice Questions
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What does C(0) equal?
💡 Hint: How many valid sequences are possible with no pairs?
What is the value of C(1)?
💡 Hint: Think of the simplest case of one pair of parentheses.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the value of C(3)?
💡 Hint: Recall the example we discussed regarding valid arrangements.
Is C(n) always equal to a positive integer?
💡 Hint: Think about what Catalan numbers represent in combinatorics.
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Challenge Problems
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Calculate C(4) using the recurrence relation and list all valid sequences.
💡 Hint: List combinations for n = 3 and apply them step-wise.
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.
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