Practice Second Problem: Sequences Of 1s And -1s (21.1.3) - Catalan Numbers - Derivation of Closed Form Formula
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Second Problem: Sequences of 1s and -1s

Practice - Second Problem: Sequences of 1s and -1s

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

How many sequences are formed with 2 1s and 2 -1s?

💡 Hint: Think about choosing positions for 1s.

Question 2 Easy

If a sequence has more -1s than 1s, is it valid?

💡 Hint: Recall the definition of valid sequences.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for the number of valid sequences with n 1s and n -1s?

C(2n
n)
C(2n
n + 1)
Both A and B

💡 Hint: Think of how we derive valid counts.

Question 2

True or False: If a sequence has an initial position with a negative sum, it is invalid.

True
False

💡 Hint: Refer back to the definition of valid sequences.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Find the number of valid sequences for n=4 and explain your approach.

💡 Hint: Make sure to outline both sets clearly.

Challenge 2 Hard

Create a sequence of n=5 and justify its validity.

💡 Hint: Visualize how the sum changes as you construct the sequence step-by-step.

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