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(3): A new approach with no proof by TomM)

Yes, the 101st Fibonacci number is the correct solution. I got the same answer using a different (more complicated lol) method of adding up the numbers of combinations:
SUM (n+0)!/n!0!, (n-1)!/(n-2)!1!, (n-2)!/(n-4)!2!, ... , (0+n/2)!/0!(n/2)!
I wasn't actually calculating all these expressions individually, but I created a couple of formulas in Excel and copied them a few times till i got to (0,50) and then summped up the results.

Posted by lucky on 2002-09-06 09:25:52