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        riddles >> microsoft >> ladder problem
        
(Message started by: BenVitale on Jan 26th, 2008, 6:40pm)
Title: ladder problem
Post by BenVitale on Jan 26th, 2008, 6:40pm
You are presented with a ladder. At each stage, you may choose to advance either one rung or two rungs. How many different paths are there to climb to any particular rung; i.e. how many unique ways can you climb to rung "n"?

After you've solved that, generalize. At each stage, you can advance any number of rungs from 1 to K. How many ways are there to climb to rung "n"?
Title: Re: ladder problem
Post by Bojan_Basic on Jan 26th, 2008, 10:07pm
This one already exists here (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_microsoft;action=display;num=1198687412).
Title: Re: ladder problem
Post by towr on Jan 27th, 2008, 7:11am
The generalization to taking up to K steps is fairly straightforward from where the older thread leaves off:
[hide]You get the recursion fn=fn-1+fn-2+ .. + fn-k[/hide]


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