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Proof of recursive formula for “fusible numbers”

There are N ropes given and

it is given that each ropes burn in 1 hour

You have to calculate 40 minutes using these. How can I do that?? I made 45 minutes, but 40 is not made by me. Help me please.

Thanks in advance.

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    Is there any other information about the lengths of the ropes, the type of rope, anything? How did you get 45 minutes?2012-09-15
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    first burn first rope from both end and burn second rope from one end, when the first rope burns completely means 30 minutes passes. At this time, burn second rope from another end , it will burn completely in 15 minutes. Means 30 + 15 minutes = 45 minutes2012-09-16
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    Lighting ends of ropes and lighting other ends when some ropes have burnt down can time periods that are multiples of $\frac{1}{2^N}$ hours but some kind of cheat a finite number of ropes don't seem able to time $\frac{2}{3}$ of an hour.2012-09-16
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    exactly, I also thought the same thing, but this is asked in interview to me, I don't know why interviewer ask wrong question in an interview2012-09-16
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    @jhamb: Often the interviewer will be interested in seeing how the candidate reacts to problems he _cannot_ solve. In many situations this can be more relevant for predicting fit than just knowing which riddles the candidate has memoized well enough to solve on the spot. (For example, if the job involves figuring out not only how to do things but also whether they can be done profitably at all, it wouldn't do to hire someone who is not comfortable with declaring that he doesn't see a good way to do something).2012-09-16
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    Voting to close as subproblem of [Proof of recursive formula for "fusible numbers"](http://math.stackexchange.com/questions/40404/proof-of-recursive-formula-for-fusible-numbers)2012-09-17
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    Every fusible number is a rational number with denominator of the form $2^n$. So $\frac23$ is not a fusible number.2016-01-26

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