# I want to ask how do you figure this relation out. Can anyone explain it literally?

• Hi,
After thinking your code, I found the relation between the ways like a Fibonacci number.

But how do you guys figure this relation out?

Does it have logical literally explanation?

Hope anyone can help me.

Thanks a lot.

• Hi,

I didn't recognise that it was a Fibonacci number the first minute so I followed the lead of a recursive solution:

Can I figure out the number of solutions for a N steps stair (which I'll name S[N]) if I already know the number of solutions for a N-1 steps stair?

From any N-1 solution I can just climb another step to get a N steps solution.

Therefore the answer S[N] is at least equal to S[N-1].

Now we have forgotten all the solutions which end by a 2 steps climb. This set of solutions is equal to S[N-2] (because there is room for a 2 steps climb).

We conclude that S[N] = S[N-1] + S[N-2].

And suddenly you find yourself thinking about the reproduction rate of rabbits.

Hope it helps

• Thank you very much!
You explain it clearly!
I suddenly understand the solution's meaning.