Problem

Beth lives in a house with thirteen stairs. She can go down the stairs one at a time or two at a time.

Cat going down the stairs.

For example, she could go down 1 step, then 1 step, then 2 steps, then 2, 2, 1, 2, 1, 1.

In how many different ways can she go downstairs?


Susie lives in the same house as Beth. Her legs are longer, so she can go down the stairs one at a time, or two at a time, or three at a time.

In how many different ways can she go downstairs?


What would happen if Beth and Susie move to another house with a different number of stairs?