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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$\begingroup$ can you cut or burn the ropes? $\endgroup$– catsNov 17, 2016 at 22:07
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$\begingroup$ you can cut and burn them if you want, but burning is not uniform as usual. $\endgroup$– user32000Nov 17, 2016 at 22:08
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$\begingroup$ Does one rope burn for 15min and the other 45min? This isn't clear in the question... $\endgroup$– dhuangNov 17, 2016 at 22:10
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2$\begingroup$ This 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. $\endgroup$– GentlePurpleRainNov 17, 2016 at 22:13
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1$\begingroup$ You light one of the ropes, and use the light from it to look at your watch. $\endgroup$– SconibulusNov 17, 2016 at 22:28
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1 Answer
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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.
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2$\begingroup$ Come on. Seriously, you're accepting this? $\endgroup$– Rubio ♦Nov 17, 2016 at 22:30
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$\begingroup$ Well the cuttingextra part part is a little bit too much but... $\endgroup$ Nov 17, 2016 at 22:33
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$\begingroup$ @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. $\endgroup$– AvarkxNov 17, 2016 at 22:35
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$\begingroup$ @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 $\endgroup$– AvarkxNov 17, 2016 at 22:39
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$\begingroup$ Please don't curse. Curse free communities are nice communities. $\endgroup$ Nov 17, 2016 at 22:39