How many ways can I go up some steps?

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Homework Help Overview

The problem involves determining the number of ways a person can ascend a staircase with specific movement rules: one step at a time, skipping one step, or skipping two steps, with a restriction on the final step. The tasks include calculating the ways to ascend a staircase of 7 steps and finding the number of steps in a staircase that allows for 987 ways of ascent.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • One participant suggests a case-wise solution for the 7-step problem. Another participant references Fibonacci numbers as a potential method for solving the problem but expresses uncertainty about their application. There is also a discussion about the validity of using Fibonacci numbers in relation to the problem's conditions.

Discussion Status

The discussion is ongoing, with participants exploring different approaches and questioning the assumptions behind the problem's setup. Some guidance regarding Fibonacci numbers has been mentioned, but there is no consensus on their relevance to the problem.

Contextual Notes

One participant notes that the problem may be based on a test from a physics/engineering program, which could influence the interpretation of the solution methods. There is also a concern that the problem's author may have incorrect assumptions about the relationship to Fibonacci numbers.

Paulo Serrano
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Homework Statement


A person can go up one step at a time, skip a step at a time, or skip two steps at a time, with the exception of the final step, which obviously you can only go one step up.

a) Calculate the different ways someone can up up a staircase with 7 steps.
b) Calculate the number of steps in the staircase if the total number of ways I can go up it is N=987



Homework Equations



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The Attempt at a Solution

 
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With only 7 steps, I think a case-wise solution may be quicker.
 
This was from the test to major in physics/engineering from Rio De Janeiro Federal University last year. The answer sheet says you have to use Fibonacci numbers. I have no idea what those are or how they work, so I'm going to read about them on wikipedia.

if someone can give me a summary of how it works, though, I'd appreciate it.
 
Fibonacci numbers are numbers form a sequence of numbers, the first 2 are
f(0) = 0 and f(1) = 1 and the rest is computed by f(n) = f(n-1) + f(n-2).
This is called a recurrence relation
The numbers you'll get are related with a similar relation.

If you want to go up a staircase of n steps with n at least 3, the first step could move up 1, 2 or 3 steps. The number of ways is the sum of the number of ways to climb the smaller steps that are left.

Unfortunately, question b makes me think that the author of this problem DOES think that the numbers are from the fibonacci sequence, which is wrong. It would be right if you could move only 1 or 2 steps up at a time.
 

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