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 Limit by TomM)

I decided to generalize the problem, solve it for some smaller numbers of steps and see if there was a pattern.

This is what I found:

0 steps -> 1 set
1 step -> 1 set
2 steps -> 2 sets
3 steps -> 3 sets
4 steps -> 5 sets
5 steps -> 8 sets

This sequence is awfully familiar: it is the Fibonacci sequence (It does turn up in the strangest places.) If this holds up, then the number of ways to climb the stair, given the restrains is the 101st Fibonacci number (573147844013817084101)

Posted by TomM on 2002-09-05 19:37:34