Discussion
Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:
1. At any stage, Ankita can move either one or two stairs up.
2. At any stage, Ankita cannot move to a lower step.
Let F(N) denote the number of possible ways in which Ankita can reach the Nth stair. For example, F(1) = 1, F(2) = 2, F(3) = 3.
The value of F(5) is ___.
Answer: A
F(5) is 8.
The last move onto stair N is either a single step from stair N - 1 or a double step from stair N - 2, so:
\[ F(N) = F(N-1) + F(N-2) \]
With F(1) = 1, F(2) = 2 and F(3) = 3, this gives F(4) = 3 + 2 = 5 and F(5) = 5 + 3 = 8, the Fibonacci numbers.
Listing by the number of double steps confirms it: no double step (1 way), one double step among four moves (4 ways), two double steps among three moves (3 ways), total 8. 5 is F(4), one stair short.
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