Problem:
Every day at school, Jo climbs a flight of stairs. Jo can take stairs , or at a time. For example, Jo could climb , then , then stairs. In how many ways can Jo climb the stairs?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Jo can climb stair in way, stairs in ways: or , and stairs in ways: or . Jo can start a flight of stairs with stair, leaving stairs to go and ways to climb them, or with stairs, leaving stairs to go and ways to climb them or with stairs, leaving to go and way to climb it. This means there are ways to climb stairs. By the same argument, there must be ways to climb stairs and ways to climb stairs.
Making a systematic list is another approach.
The number of ways Jo can climb the stairs is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions