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?

(In reply to re: A new approach with no proof by levik)

A nit here. The Fibonacci sequence goes 1, 1, 2, 3, 5... In this particular case, though, the first number is skipped, so n is off by one. That's why the answer is the 101st Fibonacci number instead of the 100th.

Posted by friedlinguini on 2002-09-05 21:56:09