Practice Second Problem: Sequences Of 1s And -1s (21.1.3) - Catalan Numbers

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
How many sequences are formed with 2 1s and 2 -1s?
Show hintHide hint
Think about choosing positions for 1s.
Question 2.
If a sequence has more -1s than 1s, is it valid?
Show hintHide hint
Recall the definition of valid sequences.
3Question 3.
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
Show hintHide hint
Think of how we derive valid counts.
4Question 4.
True or False: If a sequence has an initial position with a negative sum, it is invalid.
- True
- False
Show hintHide hint
Refer back to the definition of valid sequences.
Question 5.
Find the number of valid sequences for n=4 and explain your approach.
Show hintHide hint
Make sure to outline both sets clearly.
Question 6.
Create a sequence of n=5 and justify its validity.
Show hintHide hint
Visualize how the sum changes as you construct the sequence step-by-step.

4 more questions in this section. Enroll free to practise them all.