Rope Burning Interview Question

Posted in Quantitative, Science by Elliott Back on November 22nd, 2006.

Kottke just posted the infamous rope-burning interview problem, which is actually quite easy:

You are given two ropes and a lighter. This is the only equipment you can use. You are told that each of the two ropes has the following property: if you light one end of the rope, it will take exactly one hour to burn all the way to the other end. But it doesn’t have to burn at a uniform rate. In other words, half the rope may burn in the first five minutes, and then the other half would take 55 minutes. The rate at which the two ropes burn is not necessarily the same, so the second rope will also take an hour to burn from one end to the other, but may do it at some varying rate, which is not necessarily the same as the one for the first rope. Now you are asked to measure a period of 45 minutes. How will you do it?

The solution is the following:

Light rope #1 at one end
Light rope #2 at both ends
When rope #2’s ends meet, light rope #1 at the other end. 30 minutes have been measured so far, leaving 30 minutes left on rope #1.
When rope #1’s ends meet, fifteen minutes have been measured, for a total of 45 minutes.

This entry was posted on Wednesday, November 22nd, 2006 at 10:56 pm and is tagged with rope 1, light rope, rope 2, first five minutes, uniform rate, interview question, end of the rope, fifteen minutes, ropes, 30 minutes. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback.

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mr nice ash 2 years ago 1 point
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that's pretty good but i think the most appropriate question is how will you burn those ropes at exactly 45 minutes.

if i will just be asked by 'how will i measure 45 minutes', i'll probably just say, 'i'll take a look at my watch' ;)

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http://dhost.info/mrniceash

. . 1 year ago 1 point
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That question is so old. was published in 2002. everyone who has interviewed with wall street firms knows it.

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Tang 1 year ago 1 point
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This is the popular answer, but I itself violates the assumption of non uniform burning rate as you are assuming that 1/2 of the rope will burn in 30 mins,
which is not necessarily true.

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Tang 1 year ago 1 point
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Sorry what I meant was not expressed properly above
and could be misleading.
What I meant was : since burning rate is not uniform across all cross sections of the rope it is not certain
whether the rope when lighted from both ends will burn out in 30 mins. Remember what the question says "non uniform burning rate" - which means a fire on one rope end could take e.g 59.99 mins to burn 1/1000 th of its length, and 0.01 secs to burn the rest.

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Elliott Back 1 year ago 1 point
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Yes--which is fine. But you've lit the rope at both ends, so when they meet, at 999 ft and 1ft, half the time is up. They don't have to meet in the middle to measure half of the time interval. Go back, Tang, and think about it some more ;)

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http://elliottback.com

Rob T 1 year ago 1 point
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Elliott Back,

that's fine, but it still took 59.999 minutes to burn one side and .001 minutes to burn the other -leaving you no certain way to measure 30 minutes. You need a uniform rate or at least the avg rate of time to be the same. I beleive the question is flawed from the start

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Anna 11 months ago 1 point
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Elliott is right, its a matter of common sense, when you start burning from both the ends at the same time say 10:00 AM, by the time the rope is completely burnt, at whatever rate the rope burns on either sides, it will take 30 minutes to burn the entire rope. The left hand side might burn 10% in half hour and the right hand side might burn 90% in the same time doesn't matter.

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feriDruri 9 months ago 1 point
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Recently a good friend of mine told me to go to the local pharmacy and buy myself Rabeprazole. I am very curious to know what kind of medicine is this? Anyone can help?
I will be very grateful indeed.

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http://buyusapills.com

Sean 4 months ago 1 point
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Yes, Elliot and Anna are correct. The way Rob T and Tang are thinking about it involves lighting from both ends and the each half burns independently of the other half. This would not be true however. If it takes 59 minutes to burn the first half and 1 minute to burn the second half, the rope would still be burned in 30 min. After 1 min, there would be 58 min left to burn the first half and 0 min left to burn the second half--but the flame that burned the second half will begin burning the first half from the other side. Therefore it would take 29 minutes for the second half to burn, and adding that extra one minute from the beginning gives you 30 overall.

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