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Homework Help: 7 steps to climb in how many ways?

  1. Feb 5, 2005 #1
    You have 7 steps to climb. You can go up 1 step or 2 steps at a time. In how many different ways can you climb the steps? Use the chart below to help organize your work.

    number of steps: 1 2 3 4 5 6 7
    number of ways:

    I dont understand what am I supposed to write in the chart?
     
  2. jcsd
  3. Feb 5, 2005 #2

    dextercioby

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    This is a problem in which VISUALIZATION and a pen & a paper would help considerably.

    So how about leaving side questions aside (sic) and tell us how would u go about solving it...??

    Daniel.
     
  4. Feb 5, 2005 #3
    Ok Um Im not sure if this is what the question is asking but I think

    Number of steps: 1 2 3 4 5
    Number of ways: 1 2 3 5 9

    Ok this is what I did i sketched the number of steps and then using the fact that u can only take 1 or 2 steps I saw how many combinations I can get for example for 4 steps I got you could take (1 1 1 1) (121) (112) (211) (22) These are all steps. There are 5 possible ways of goin up the stairs?
     
    Last edited: Feb 5, 2005
  5. Feb 5, 2005 #4

    dextercioby

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    In that way you won't cover all possibilities... :wink: You have to find all possible sequences of integers between 1 & 7 (heads/ends included) in which consecutive terms (different) would differ by maximum 2 units...

    Daniel.
     
  6. Feb 5, 2005 #5
    What you're being asked to fill out in the chart is how many ways can the numbers 1 and 2 be added together to make various numbers.

    for example the first few are

    1: 1
    2: 2
    3: 3
    4: 5
     
  7. Feb 5, 2005 #6
    I think I might have got it lol I was editting my last post when u posted this and I got the same for 1-4 steps
     
  8. Feb 5, 2005 #7
    steps 1 2 3 4 5 6 7

    ways 1 2 3 5 9 11 18

    This is what I got how do I know if I have missed any combinations? What was the point of this?
     
  9. Feb 6, 2005 #8
    I've just been doing some more and it looks like you've made a mistake, i got

    1, 2, 3, 5, 8, 13, 21

    Just looking at it makes me think its the fibbonachi sequence
     
    Last edited: Feb 6, 2005
  10. Feb 6, 2005 #9
    You have been doing alot with fibonacci lately, havent you aisha? This is another example.
     
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