Question

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.)

$4$

$5$

$6$

$8$

$12$

Video solution:

Click to load, then click again to play

Written solution:

We can deduce from the choices that it is possible to exhaust all possible cases for this problem. Note that all sequences must start with up $(U)$ and end with down $(D)$ , and that it should not be possible to go down more times than Buzz has gone up so far. Keeping this in mind, we can arrive at the following possible cases: $UUUDDD$ $UUDUDD$ $UUDDUD$ $UDUDUD$ $UDUUDD$ which is a total of five possible sequences.

Thus, B is the correct answer.

2024 AMC 8 Problem 13

Video solution:

Written solution:

Problem 13 in Other Years