Stairy Situation
Probability
Level
2
There is a staircase with 10 steps. You can move one or two steps at a time. How many ways can you reach the top?
45
55
89
77
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1 solution
S ( n ) means how many ways can you reach the top if there are n steps.
There are two cases for each n > 1 :
Case 1: At the last step we moved one step. This is n − 1 ways.
Case 2: At the last step we moved two steps. This is n − 2 ways.
From that: S ( n ) = S ( n − 1 ) + S ( n − 2 ) .
S ( 1 ) = 1
S ( 2 ) = 2
…
S ( 1 0 ) = 8 9
Note: S ( k ) is the k + 1 . item of the Fibonacci series .