2024 AMC 8

Complete problem set with solutions and individual problem pages

Problem 13 Medium

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

Answer:B

Solution 1

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

Counting all the paths listed above gets you .

Solution 2

Any combination can be written as some re-arrangement of . Clearly we must end going down, and start going up, so we need the number of ways to insert 2 's and 2 's into . There are ways, but we have to remove the case , giving us .