Counting Question (1 Viewer)

[braintic]

This is for HSCers - veterans please don't answer, at least until it's been open for a while.

You are permitted to climb an n-step staircase by climbing one or two stairs with each step.
For example, you might climb a 12-step staircase as follows:
2-2-1-2-1-1-1-2
Explain why the number of ways of climbing the n-step staircase is given by the (n+1)th Fibonacci number.
(where I am taking the first two Fibonacci numbers to be 1 and 1)

 

[Qeru]

This is for HSCers - veterans please don't answer, at least until it's been open for a while.

You are permitted to climb an n-step staircase by climbing one or two stairs with each step.
For example, you might climb a 12-step staircase as follows:
2-2-1-2-1-1-1-2
Explain why the number of ways of climbing the n-step staircase is given by the (n+1)th Fibonacci number.
(where I am taking the first two Fibonacci numbers to be 1 and 1)

This has been posted before and has also been in a BOS trial.

 

[idkkdi]

This has been posted before and has also been in a BOS trial.

who asked it first?

 

[Qeru]

who asked it first?

I dont remember but it involved 12 steps instead of n steps.

 

[braintic]

This has been posted before and has also been in a BOS trial.

I guess this is why this site has died - too many people jumping in to discourage.
I asked it here 6 years ago. Has everyone here scoured all old posts?

 

[Qeru]

I guess this is why this site has died - too many people jumping in to discourage.
I asked it here 6 years ago. Has everyone here scoured all old posts?

Well another guy asked it a few weeks ago. If you really want we can copy paste the answer here

 

[braintic]

Well another guy asked it a few weeks ago. If you really want we can copy paste the answer here

Alternatively, we could wait for someone who hasn't seen the question before to contemplate it.

 

[CM_Tutor]

I mentioned that it came up in question 14(c) of the 2020 BoS MX1 trial from October last year. Qeru is correct that it was discussed in March in this thread: https://boredofstudies.org/threads/permutation-and-combination-question-pretty-tough.394319/

I also posted a bunch of Fibonacci related questions in January, in this thread: https://boredofstudies.org/threads/2nd-order-recursion.393592/

 

[braintic]

I'm not saying he was not correct, only that there was no point in mentioning it other than to discourage contributors.
So I will now take my cue and contribute my part to the sorry desertification of this site by leaving and never again trying to contribute much-needed stimulus material here.

 

[Where's the Funny?]

bruh this is sad

 

[CM_Tutor]

I'm not saying he was not correct, only that there was no point in mentioning it other than to discourage contributors.
So I will now take my cue and contribute my part to the sorry desertification of this site by leaving and never again trying to contribute much-needed stimulus material here.

The point in mentioning it was that a contributor seeking help is provided with direction to where to fund help, and a contributor (such as yourself) offering stimulus material is advised that the question was recently discussed. Your stimulus material is welcome, it was just unfortunate that you choose a problem that was discussed very recently and that was also on the 2020 BoS MX1 trial. I don't think it is fair to say that Qeru was seeking to discourage contributors - in fact, he is one who seems to enjoy challenging questions.

I, for one, welcome you and anyone else contributing questions, answers, discussions, resources, ...