2024 AMC 8 Problems/Problem 13

Revision as of 17:34, 26 January 2024 by Alwaysright11 (talk | contribs) (Solution 1)

Buzz Bunny is hopping up and down a set of stairs, one step at a time. In how many ways can Buzz start on the ground, make a sequence of $6$ hops, and end up back on the ground? (For example, one sequence of hops is up-up-down-down-up-down.)

$\textbf{(A)}\ 8 \qquad \textbf{(B)}\ 9 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 11 \qquad \textbf{(E)}\ 12$

Solution 1

Looking at the answer choices, you see that you can list them out. Doing this gets you:

UUDDUD


UDUDUD UUUDDD UDUUDD UUDUDD

Counting all the paths listed above gets you 5 or B.

-ALWAYSRIGHT11

Video Solution 1 (easy to digest) by Power Solve

https://youtu.be/X5Xk0wYXypk

Video Solution 2 by Math-X (First fully understand the problem!!!)

https://www.youtube.com/watch?v=Td6Z68YCuQw

~Math-X

Video Solution 3 by OmegaLearn.org

https://youtu.be/dM1wvr7mPQs

Video Solution by CosineMethod [🔥Fast and Easy🔥]

https://www.youtube.com/watch?v=-kCN6R9U944