7 steps to climb in how many ways?

[aisha]

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 don't understand what am I supposed to write in the chart?

 

[dextercioby]

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.

 

[aisha]

Ok Um I am 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?

 

[dextercioby]

In that way you won't cover all possibilities... 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.

 

[Erienion]

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

 

[aisha]

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

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

 

[aisha]

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?

 

[Erienion]

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

 

[Parth Dave]

You have been doing a lot with fibonacci lately, haven't you aisha? This is another example.