Permutation and combination question (pretty tough) (1 Viewer)

[Haz_taz]

Jessica is about to walk a flight 10 stairs. She can take either one or two stairs at a time. How many different ways can she walk up the flight of stairs?

The answer is 89, just not sure how

 

[idkkdi]

Jessica is about to walk a flight 10 stairs. She can take either one or two stairs at a time. How many different ways can she walk up the flight of stairs

55

 

[Haz_taz]

55

Hi, thanks for replying. How did you get 55?

 

[idkkdi]

Hi, thanks for replying. How did you get 55?

10th fibonacci number

 

[Haz_taz]

10th fibonacci number

Could this be done combinatorically (not using fibonacci)

 

[idkkdi]

jokes, that mighrt be wrong lol



meant 89 fibonacci 11

 

[Haz_taz]

jokes, that mighrt be wrong lol



meant 89

BRUH

 

[idkkdi]

BRUH

fibonacci seems like the best way,
combs is kinda a trek and its just fibonacci made complicated.

 

[idkkdi]

@Qeru comb this?

 

[Qeru]

Jessica is about to walk a flight 10 stairs. She can take either one or two stairs at a time. How many different ways can she walk up the flight of stairs?

The answer is 89, just not sure how

This question is very similar to a pervious perms and combs q on this website (I think involving coins?)

The question can be rewritten as:

where x is the number of times she takes 1 stair and y is the number of times she takes 2 stairs.

Now simply list all integers x and y that satisfy this equation:
(0,5) we can arrange these in ways
(2,4) we can arrange these in ways
(4,3) we can arrange these in ways
(6,2) we can arrange these in ways
(8,1) we can arrange these in ways
(10,0) we can arrange these in ways

So: i.e. the 11th fibonacci number.

This result can be generalised for 2n steps to yield the cool identity:


Ill leave an odd number of steps i.e. 2n+1 steps as an exercise for the reader.

 

[Haz_taz]

Thankyou very much Qeru, How about if it was in 2 dimensions, so like if a person could go 1 or 2 steps, and they had to go forward 10 steps, then right 10 steps

 

[Haz_taz]

@Qeru pls help, I have one more question above

 

[Qeru]

Thankyou very much Qeru, How about if it was in 2 dimensions, so like if a person could go 1 or 2 steps, and they had to go forward 10 steps, then right 10 steps

The person has to make a net movement of 10 steps to the left and 10 steps to the right. So this is basically just 20 steps in total with 1 or 2 steps so the answer is the I think.

 

[Haz_taz]

The person has to make a make movement of 10 steps to the left and 10 steps to the right. So this is basically just 20 steps in total with 1 or 2 steps so the answer is the I think.

like fibonacci sequence number 21?

 

[Qeru]

like fibonacci sequence number 21?

Yes I think so

 

[CM_Tutor]

The question being discussed here was on the Bored of Studies MX1 Trial paper in 2020, q14(c). The paper is available at https://community.boredofstudies.org/attachments/2020-bos-trials-mathematics-extension-1-pdf.29352/

 

[Paradoxica]

The question being discussed here was on the Bored of Studies MX1 Trial paper in 2020, q14(c). The paper is available at https://community.boredofstudies.org/attachments/2020-bos-trials-mathematics-extension-1-pdf.29352/

yeah and we didn't sugar coat it by splitting into odd and even cases in the main steps of the proof