Question 1133157: There are 10 steps from ground level to the top. The 6th step is under repair and only can be crossed but not step on.
Mike walks up the steps with one or two steps at a time. How many different ways can he walk up to the top?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
In the classic problem like this, none of the steps is under repair.
If Mike can walk up the steps either one or two steps at a time, then he can get to step n from either step (n-1) or step (n-2). Using that reasoning....
He can only get to step 1 from "step 0": 1 way
He can get to step 2 from either step 0 or step 1: 1+1 = 2 ways
He can get to step 3 from either step 1 or step 2: 1+2 = 3 ways
He can get to step 4 from either step 2 or step 3: 2+3 = 5 ways
... and so on. The pattern you get is the Fibonacci sequence.
You can solve your problem using the same logic; but now you can't land on the 6th step. That will change the numbers in two ways:
(1) You can only get to the 7th step from the 5th step; and
(2) You can only get to the 8th step from the 7th step.
If you understand the process, it should be easy to determine the total number of ways he can reach the top.
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