Today I was at a job interview and the last question was, "How can I measure 5 minutes by lighting two ropes that each take an hour to burn but do not burn uniformly?" (classical).
I know how to measure 15 minutes and 45 minutes, but 5 minutes....?
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can you cut or burn the ropes? – cats Nov 17 '16 at 22:07
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you can cut and burn them if you want, but burning is not uniform as usual. – user32000 Nov 17 '16 at 22:08
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Does one rope burn for 15min and the other 45min? This isn't clear in the question... – dhuang Nov 17 '16 at 22:10
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2This answer seems to imply that it is impossible. It states that you can only measure time intervals that can be expressed as $\frac{m}{2^n}$ hours for integers $m$ and $n$. 5 minutes is $\frac1{12}$ of an hour, an dyou can't express $\frac1{12}$ as $\frac{m}{2^n}$, so it seems that your task is impossible. – GentlePurpleRain Nov 17 '16 at 22:13
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Both ropes burn for 1 hour. – user32000 Nov 17 '16 at 22:13
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What are m and n? – user32000 Nov 17 '16 at 22:14
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@user32000 $m$ and $n$ can be any integers. But there is no way to express $\frac1{12}$ no matter what integers you use for $m$ and $n$. – GentlePurpleRain Nov 17 '16 at 22:17
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1You light one of the ropes, and use the light from it to look at your watch. – Sconibulus Nov 17 '16 at 22:28
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You're MacGyver, so you use the ropes and pieces of your clothes to build a working clock. – Alenanno Nov 17 '16 at 22:31
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Cut the first rope into 12 pieces and light one end of each. Throw the second rope in the trash. If at any time one of the twelve segments is about to be completely consumed, cut some of the extra off of any of the other longer pieces and attach to the nearly-consumed segment, so that all twelve segments finish burning at the exact same time. Then 60 minutes of rope is consumed in 5 minutes.
Avarkx
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@Rubio the other comments on the question point out that a 5 minute interval isn't possible using the standard method - the only way around it is to cheese the non-homogeneous nature of the ropes out of the problem. – Avarkx Nov 17 '16 at 22:35
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@user32000 What they probably should have said is "Oh, I copied the question I was meant to ask you down wrong." Sounds like you might have dodged a bullet in terms of your future employment, imo – Avarkx Nov 17 '16 at 22:39
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Please don't curse. Curse free communities are nice communities. – greenturtle3141 Nov 17 '16 at 22:39
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@user32000 Maybe, but unless you're applying for "rope incinerator," the value of the question is pretty suspect. Brain-teasers, as silly as I think they are for interview questions, are supposed to at least have some plausible answer. – Avarkx Nov 17 '16 at 22:46