Comments on: Rope Burning Interview Question http://elliottback.com/wp/rope-burning-interview-question/ Internet & Technology Wed, 08 Feb 2012 10:01:08 +0000 http://wordpress.org/?v=2.9.2 hourly 1 By: beth http://elliottback.com/wp/rope-burning-interview-question/#comment-2193196 beth Wed, 07 Jul 2010 18:26:12 +0000 http://elliottback.com/wp/archives/2006/11/22/rope-burning-interview-question/#comment-2193196 how would u do 52.5 minutes? how would u do 52.5 minutes?

]]> By: Nick http://elliottback.com/wp/rope-burning-interview-question/#comment-2190505 Nick Mon, 11 Jan 2010 18:01:36 +0000 http://elliottback.com/wp/archives/2006/11/22/rope-burning-interview-question/#comment-2190505 This is a pretty unusual rope, Vimal, which might take 59.99 minutes to burn 1/1000th of its length, and 0.01 minutes to burn the rest. Still so sure it will always burn at the same rate in either direction? ;) Anyway, it's easy enough to design a rope that will burn slowly for the first half and faster for the second half *AND* do so in both directions. Simply take two ropes that burn faster in one direction than the other. Let's say they take 32 minutes to burn in one direction and 28 minutes in the other. Now join the "fast" ends. Voila: the rope will burn end to end in one hour but when lit from both ends will take 32 minutes! This is a pretty unusual rope, Vimal, which might take 59.99 minutes to burn 1/1000th of its length, and 0.01 minutes to burn the rest. Still so sure it will always burn at the same rate in either direction? ;)

Anyway, it’s easy enough to design a rope that will burn slowly for the first half and faster for the second half *AND* do so in both directions. Simply take two ropes that burn faster in one direction than the other. Let’s say they take 32 minutes to burn in one direction and 28 minutes in the other. Now join the “fast” ends. Voila: the rope will burn end to end in one hour but when lit from both ends will take 32 minutes!

]]> By: Vimal http://elliottback.com/wp/rope-burning-interview-question/#comment-2190463 Vimal Fri, 08 Jan 2010 06:18:00 +0000 http://elliottback.com/wp/archives/2006/11/22/rope-burning-interview-question/#comment-2190463 Nick, The analogy of the cyclists, though appearing to be similar, isn't similar. Suppose, like you say, the course of the cyclists is like a hill, halfway uphill and half way downhill. In this case, there exists a symmetry. No matter which end you start from, the first half is always uphill (and so takes more time). There's no such summetry for the rope. You can't design a rope that'll burn slowly for the first half and faster for the second half *AND* do so in both directions! If you burn both ends of the rope, it will burn in half the time! Nick,

The analogy of the cyclists, though appearing to be similar, isn’t similar.

Suppose, like you say, the course of the cyclists is like a hill, halfway uphill and half way downhill. In this case, there exists a symmetry. No matter which end you start from, the first half is always uphill (and so takes more time).

There’s no such summetry for the rope. You can’t design a rope that’ll burn slowly for the first half and faster for the second half *AND* do so in both directions!

If you burn both ends of the rope, it will burn in half the time!

]]> By: Nick http://elliottback.com/wp/rope-burning-interview-question/#comment-2190301 Nick Sat, 26 Dec 2009 17:51:42 +0000 http://elliottback.com/wp/archives/2006/11/22/rope-burning-interview-question/#comment-2190301 Gene, We're told that the rope takes an hour to burn from one end to the other, and I think we can reasonably assume that's the case no matter which end is lit. But it doesn't immediately follow that if we light *both* ends it will take the rope 1/2 hour to burn out. To see why, you only have to imagine two cyclists who can both cycle from A to B (or B to A) in one hour. Yet when they both set off at the same time, one from A and one from B, it takes them not 30 but 45 minutes to meet. Why? Because they've both been cycling uphill! That's the flaw in the riddle. We have to assume something like: any given section of each rope takes the same time to burn in either direction. We're not told that, and I'm not convinced it's a reasonable or (given the uneven nature of the rope) a physically realistic assumption to make. Gene,

We’re told that the rope takes an hour to burn from one end to the other, and I think we can reasonably assume that’s the case no matter which end is lit. But it doesn’t immediately follow that if we light *both* ends it will take the rope 1/2 hour to burn out.

To see why, you only have to imagine two cyclists who can both cycle from A to B (or B to A) in one hour. Yet when they both set off at the same time, one from A and one from B, it takes them not 30 but 45 minutes to meet. Why? Because they’ve both been cycling uphill!

That’s the flaw in the riddle. We have to assume something like: any given section of each rope takes the same time to burn in either direction. We’re not told that, and I’m not convinced it’s a reasonable or (given the uneven nature of the rope) a physically realistic assumption to make.

]]> By: Gene http://elliottback.com/wp/rope-burning-interview-question/#comment-2190300 Gene Sat, 26 Dec 2009 15:22:44 +0000 http://elliottback.com/wp/archives/2006/11/22/rope-burning-interview-question/#comment-2190300 Nick, The way to think about it is that the rope burns for one hour no matter which side is lit. The composition of the rope doesn't matter. If you light it from one end it will burn to a certain point on the rope in 1/2 hour, leaving some length of rope that will burn in the remaining 1/2 hour. Therefore if you light both ends the fires will meet at that point in 1/2 hour. Nick,

The way to think about it is that the rope burns for one hour no matter which side is lit. The composition of the rope doesn’t matter. If you light it from one end it will burn to a certain point on the rope in 1/2 hour, leaving some length of rope that will burn in the remaining 1/2 hour. Therefore if you light both ends the fires will meet at that point in 1/2 hour.

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