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(2): A new approach with no proof
If you consider a flat hallway to be a "stairwell" with zero steps (as I did in my listing, then you do have the first "1" as well, but it still results in the 101st Fibonacci number being associated with 100 steps.
I did a search for Fibonacci and found the following page: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpuzzles.html
It has a number of puzzles which are clearly variant "word problem" clothing for two or three Number Theory problems invoving Fibonacci numbers. The generic version of this starwell problem is included, and the following are the same problem in other clothing: Bee-Line; Chairs, No Neighboring Teachers; Stepping stones; Leonardo's Lane.
Anyway, this confirms that we have found the correct answer.
Posted by TomM
on 2002-09-06 06:28:58