A stairway has 100 steps. You can climb it by one step at a time, or by two steps. How many different ways to ascend this stairway exist?

I can't think of any easy equation or algorithm for solving this quickly, but it obviously has a definite and finite answer.

My first step is to rephrase the question, focusing in on the steps that are skipped when you take two together, and then converting the problem into pure number theory:

How many subsets of (1, 2, 3, ..., 100} are there that satisfy the follwing condition: if n is a member of subset (A sub m), then neither n + 1 nor n - 1 can be members.

Posted by TomM on 2002-09-05 19:02:27