Practice Counting 1s And -1s In S' (21.1.12) - Catalan Numbers - Derivation of Closed Form Formula
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Counting 1s and -1s in S'

Practice - Counting 1s and -1s in S'

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does a valid sequence of 1s and -1s imply?

💡 Hint: Think about summation and how it behaves.

Question 2 Easy

Calculate C(4, 2).

💡 Hint: This is a simple combinatorial count.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

C(2n
n)
C(2n
n+1)
C(2n
0)

💡 Hint: This is basic combinatorics — think pairs!

Question 2

True or False: Bad sequences maintain non-negative sums.

True
False

💡 Hint: Reflect on our definition of bad sequences.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider the sequence S = {1, -1, 1, -1, -1, 1}. Show it's a bad sequence and demonstrate what its reflection would look like.

💡 Hint: Trace through the negative point.

Challenge 2 Hard

Find the number of valid sequences for n=4 and explain why they are equivalent to C(8, 4) - C(8, 5).

💡 Hint: Break it down into visual paths.

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Reference links

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