Bhadra’s house has a staircase with 12 steps. She can go down the steps one at a time or two at a time. For example, she could go down 1 step, then 1 step, then 2 steps, then 2, 2, 1, 1, 1, 1. In how many different ways can Bhadra go down the 12 steps, taking one or two steps at a time? How can you ensure that you have found all possible ways?

Apinhole camera is made out of a light-tight box with a piece of film attached to one side and pinhole on the opposite side. the optimum diameter d(in millimeters) of the pinhole can be modeled by d=1.9[ (5.5 x 10^-4) l) ] ^1/2, where l is the length of the camera box (in millimeters). what is the optimum diameter for a pinhole camera if the camera box has a length of 10 centimeters