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 Lawrence)

You may have guessed, but Fibonacci was a maths guy who came up with the following sequence used in all manner of maths inc. expanding brackets.
Basically, forms a triangle with numbers by adding one asbove and adding extra line ie:

Line 1: 1
Line 2: 1 1
Line 3: 1 2 1
Line 4: 1 3 3 1
Line 5: 1 4 6 4 1
Line 6 1 5 10 10 5 1
etc.

You get the idea. It's used in so much stuff it's not true.

Posted by Dacre on 2003-09-01 06:33:49