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?

We could start by considering a mini house with fewer stairs.

It might be helpful to introduce some notation. For example, we could let \(B_n\) denote the number of ways in which Beth can go down \(n\) stairs.