Problem:
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 hops, and end up back on the ground? (For example, one sequence of hops is up-up-down-down-up-down.)
Answer Choices:
A.
B.
C.
D.
E.
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 and end with down , 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:
which is a total of five possible sequences.
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions