Question 1133157
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In the classic problem like this, none of the steps is under repair.<br>
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....<br>
He can only get to step 1 from "step 0": 1 way<br>
He can get to step 2 from either step 0 or step 1: 1+1 = 2 ways<br>
He can get to step 3 from either step 1 or step 2: 1+2 = 3 ways<br>
He can get to step 4 from either step 2 or step 3: 2+3 = 5 ways<br>
... and so on.  The pattern you get is the Fibonacci sequence.<br>
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:<br>
(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.<br>
If you understand the process, it should be easy to determine the total number of ways he can reach the top.