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): who's Fibonacci? Simple answer by Dacre)

Actually, the triangle you mention is usually associated with Blaise Pascal (Pascal's Triangle), not Fibonacci, though the triangle was known in China much before the time of either one. Fibonacci popularized arabic numerals in the west, but mostly his name is attached to the sequence

1,1,2,3,5,8,13,21, ...

where each term is the sum of the two preceding terms.

Posted by Charlie on 2003-09-01 10:56:56