math
posted by J
You have 2 floors, and there are 14 steps inbetween the two floors. you have a cat that can get to the top by either taking one step at a time or two steps. ( at one time going up the cat can take both one or two steps). How many possible combinations are there for the cat to get to the top?

Mgraph
Let f (n)  the number of options that a cat can pass through n steps. On the n  th step can proceed or (n  1)  th, or (n  2)  th. Number of options to pass n is the number of steps to pass the options n  1 steps plus the number of options to pass n  2 steps, that is f (n) = f (n  1) + f (n  2). It is obvious that f (1) = 1 and f (2) = 2. Thus f (n) is (n + 1)  th Fibonacci number.
1,1,2,3,5,8,13,21,34,55,89,144,233,377,
610< 15th Fibonacci number
Respond to this Question
Similar Questions

math
Ben ran up threefourths of the steps three at a time, onesixth of the steps two at a time, and the final 10 steps one at a time. How many steps did Ben run up in all? 
elementary
Two buildings have 60 floors altogether. Building A has 3 floors for every 2 floors of Building B. How many floors does each building have? 
Math
2 buildings have 60 floors altogether. Building A has 3 floors for every 2 floors of building B. How many floors does each building have? 
Microeconomics
As part of their chores on Saturday mornings, they have to clean the bathrooms and wash the floors of the house while their parents go grocery shopping. In one hourâ€™s time, Mike can clean two bathrooms or wash six floors. Linda, … 
Math
I am really have a tough time trying to solve this problem. I think my first three steps are correct but I am not sure. Could someone please help me? 
Math
Alice, Beth, and Charlene start climbing a staircase, each with her left foot on step 1 and then her right foot on the next consecutive step. Alice climbs one step at a time, Beth two steps at a time, and Charlene three steps at a … 
Algebra Grade 7
A cat likes to play on stairs. Starting at the bottom landing, the cat jumped up 4 steps, then down 2 steps. Then the cat jumped up 5 steps and fell down 3. In two more jumps of 4 steps and then 2 steps, the cat reached the top of … 
math
An elevator went up 8 floors, then down 6 floors, down 5floors, up to 10 floors down 2floors and up 9 floors. If it stopped on the 15th floors. On what floors did it starts? 
math
Jammed is building a two story house in which the top floor is 12feet above the bottom floor the local building code specifies that the hight of a step cannot be above 7.5 inches what is the maximum height of a step in a staircase … 
math
An elevator starts out at the 1st floor. It goes up 4 floors, down 2 floors, up 5 floors, down 3 floors, up 2 floors and stops. What floor is it now on?