math
You have 2 floors, and there are 14 steps inbetween the two floors. you have a cat that can get to the top by either taking one step at a time or two steps. ( at one time going up the cat can take both one or two steps). How many possible combinations are there for the cat to get to the top?

Let f (n)  the number of options that a cat can pass through n steps. On the n  th step can proceed or (n  1)  th, or (n  2)  th. Number of options to pass n is the number of steps to pass the options n  1 steps plus the number of options to pass n  2 steps, that is f (n) = f (n  1) + f (n  2). It is obvious that f (1) = 1 and f (2) = 2. Thus f (n) is (n + 1)  th Fibonacci number.
1,1,2,3,5,8,13,21,34,55,89,144,233,377,
610< 15th Fibonacci number
posted by Mgraph
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