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
A new approach with no proof by TomM)
I think I can justify this trend...
Generalize the stairway to n steps.
Think about the last step you will take on the stairs. It is either onestep or twostep. Which means you are either standing at n1 or at n2.
So the number of ways to ascend n steps is equal to the number of ways to get to step n1 plus the number of ways to get to step n2. This is exactly the Fibonacci sequence.

Posted by levik
on 20020905 20:44:08 