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Topic: ladder problem (Read 2267 times) |
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Benny
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ladder problem
« on: Jan 26th, 2008, 6:40pm » |
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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"?
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If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
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Bojan_Basic
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Re: ladder problem
« Reply #1 on: Jan 26th, 2008, 10:07pm » |
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This one already exists here.
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towr
wu::riddles Moderator
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Re: ladder problem
« Reply #2 on: Jan 27th, 2008, 7:11am » |
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The generalization to taking up to K steps is fairly straightforward from where the older thread leaves off:
You get the recursion fn=fn-1+fn-2+ .. + fn-k
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| « Last Edit: Jan 27th, 2008, 7:11am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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