Logic Puzzle: The Burning Rope

HMTKSteve

You are equipped with two lengths of rope and some matches.

Your goal is by burning the rope(s), to identify when exactly 45 minutes has passed. All you know about the ropes:

• The ropes are of different length and you don't know how long they are.
  
• Each rope burns in precisely 1 hour.
  
• Each rope has a non-uniform density, meaning it is thicker at some points than others. Consequently, burning half a rope cannot be guaranteed to take 30 minutes.
  

Without Googling for the answer can you figure out the solution?

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Without Googling for the answer can you figure out the solution?

Nope, 2AM is not a moment when I can successfully solve this logic puzzle. After googling the answer though I DOH'd.

Walker

Screw that, I'd just buy a watch.

HungryJoe

I was more interested in why you didn't want people to Google than in the actual problem. Unless you have a second identity as Kasper B. Graversen, I'd say you've been engaging in plagiarism.

HMTKSteve

I was more interested in why you didn't want people to Google than in the actual problem. Unless you have a second identity as Kasper B. Graversen, I'd say you've been engaging in plagiarism.

I did not claim to be the author of the puzzle. Stating not to Google the answer is SOP.

In fact, if you do a google search for burning rope riddle you will find many pages of results. The one you are thinking of is this page here The Burning Rope Problem which is dated 23/07/08. The google results go back much farther and many lack attribution.

The riddle was even placed in a digg comment on on 10/12/2007. Before you accuse someone of plagiarising I expect solid proof that the information is not public domain and that you know who owns the copyright.

HungryJoe

Come off it, Steve. You've never had an original thought in your life. You posted this problem without attribution and without saying that it is in the public domain because yhou wanted people to think you were the author.

lackofcheese

Come off it, Steve. You've never had an original thought in your life. You posted this problem without attribution and without saying that it is in the public domain because yhou wanted people to think you were the author.

Can I then say you were doing the same thing with those law problems in the Obama thread? You only showed their source after I looked it up.
I'd say Steve is placing emphasis on the fact that he wants to test people's intelligence rather than just their Googling skills.


Light one rope at both ends. When that one burns out, half an hour will have passed.

Now, cut the next rope in half, and light both ends of both halves. If both burn out at the same time, 45 minutes has passed. Otherwise, when the first of the halves of rope has burned out, split the next half in two, light the ends that are not yet burning, and continue to repeat this step ad infinitum.

Explanation:- You have one rope left, which has a value of 60, and here we'll say y = 60. Note that initially, the time remaining (15 mins = y/4) is a quarter of the time value of the remaining rope. Let's say when you cut the second rope in half (so you split it into time periods of x and y-x, where x<= y/2. Hence by burning both at both ends, the time required for each x/2 and (y-x)/2. If x = y/2, then they will both take y/4 mins to burn out (and 45 minutes has passed). Otherwise, after the first half has burned out (taking x/2 to do so), the second rope will now have a time value of (y-x)-x = y-2x. The time remaining until 45 mins is y/4-x/2. You can see that again, the remaining rope has a time value of 4 times the amount of time remaining until 45 mins. So, you can let y' = y-2x, and repeat the process ad infinitum.

Consequently, since at each step the remaining time is exactly a quarter of the time value of the remaining piece of rope (or half if it's burned at both ends), the process can be repeated until 45 minutes has indeed passed.


There is likely a better way, but I haven't come up with one yet.

HungryJoe

Come off it, Steve. You've never had an original thought in your life. You posted this problem without attribution and without saying that it is in the public domain because yhou wanted people to think you were the author.

Can I then say you were doing the same thing with those law problems in the Obama thread? You only showed their source after I looked it up.

You can if you want. However, if I remember correctly, you responded before I was finished editing my post. Sometimes if I post from my phone, I have to edit the post more than once to get it right. In fact, sometimes I have to edit more than once if I use a proper computer if I screw something up or forget something.

Even if I hadn't edited it though, that essay question was from the professor that I had for Torts at U.K. I submit that I earned the right to post an essay question from him even without attribution due to the trauma and emtional distress of attending his class.

In the alternative, I'd argue that the post, even if unedited, was fair use since we were talking about law school-type hypotheticals. The conversation was for a nonprofit educational purpose.

lackofcheese

Before you accuse someone of plagiarising I expect solid proof that the information is not public domain and that you know who owns the copyright.

Actually, even if it's public domain, that does not mean you are excused from making attribution.

What is the "public domain?"

Works that are no longer protected by copyright, or never have been, are considered "public domain." This means that you may freely borrow material from these works without fear of plagiarism, provided you make proper attributions.

I'd say you can be excused by an inability to find the true author. However, it would probably be best if you had initially posted to that effect.

lackofcheese

Aha, I've got it! I knew I was onto something with the first one, though a solution that requires an infinite number of actions is not very nice.

Initially, light one rope on both ends while you light the other on only one end.
After 30 mins, the rope lit on both ends will have burned out, while the other rope will have 30 mins left.
If you now also light the remaining rope on the other, non-burning end, it will take another 15 mins to burn out.
30 + 15 = 45.

Banta

Who cares if it is his own idea or not, the important bit is that it's an interesting puzzle.

Walker

Yeah, I feel stupid now. In my defense, I become more and more apathetic and stupid from 12 AM onward.

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Now, cut the next rope in half,

You are equipped with two lengths of rope and some matches.

You cannot cut jack. You were going correctly until you started cutting ropes. You know the answer now, but remember that logical thinking != crazy math. And your infinite solution will always fail, seeing as 45 minutes does not take infinity to pass.

lackofcheese

Now, cut the next rope in half,

You are equipped with two lengths of rope and some matches.

You cannot cut jack.

I was misled by this:

Consequently, burning half a rope cannot be guaranteed to take 30 minutes.

However, there is still a way you can basically cut the rope - set fire to the middle of the rope. It should burn in both directions, and it would still make my infinite solution work.

You were going correctly until you started cutting ropes. You know the answer now, but remember that logical thinking != crazy math.

Though the latter is not required in this case, the two are not mutually exclusive.

And your infinite solution will always fail, seeing as 45 minutes does not take infinity to pass.

Wrong. That solution did not take an infinite amount of *time*, just an infinite number of *steps*. The steps get smaller and smaller; they make an infinite series that nonetheless adds to 45 minutes.

I continue to contend that my infinite solution is valid, though the amendment of burning from the middle instead of cutting is required. (i.e. burn one rope from both ends, after this is done, burn the second rope from the middle and both ends. When and if only one piece remains, burn that piece from the middle and both ends. Repeat this last step ad infinitum, until there is no rope left.).
However, I do not disagree that the usual solution is better.

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Wrong. That solution did not take an infinite amount of *time*, just an infinite number of *steps*. The steps get smaller and smaller; they make an infinite series that nonetheless adds to 45 minutes.

You try to set fire to anything in no time. n.~ The math was valid yes, but it would utterly fail because of human limitations.

lackofcheese

to identify when exactly 45 minutes has passed

Note the use of "exactly".

You try to set fire to anything in no time. n.~ The math was valid yes, but it would utterly fail because of human limitations.

If human limitations are included, the puzzle has no solution

Perhaps if it had been worded as "as close as possible to 45 minutes", with human limitations in mind, the "proper" solution would take priority. However, even then, both would probably be within seconds of 45 minutes.

GreyHuge

I have the solution, I solved this problem a while ago.

Here's what you do, (spoilers) You light two ends of one rope and one end of the other, when the first rope has burned completely you then light the unlit end of the second rope, when that rope has been reduced to ash 45 minutes have elapsed. (spoilers)

@myself: Even though lackofcheese has the wrong solution, Infinite Steps is not equal to Infinity, didn't you ever take Calculus? Sums/Integrals, gosh!

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@myself: Even though lackofcheese has the wrong solution, Infinite Steps is not equal to Infinity, didn't you ever take Calculus? Sums/Integrals, gosh!

You entirely missed my point. Please insult someone after having read and understood all they said. Hmmm-kay?

to identify when exactly 45 minutes has passed

Note the use of "exactly".

I noted it, did you look at your own solution? Your math is correct, you will however never be able to exactly determine when 45 minutes have passed with that method, you merely approach 45 minutes.

If human limitations are included, the puzzle has no solution

Yes it does, it's called practical thinking. What is easier, lighting a match and setting a very, VERY, small piece of rope on fire, which burns for about 0.0000003 of a second, and in the mean time light another match and prepare to set the next, smaller, piece of rope on fire? Against setting a second end of a rope on fire for which you have 30 minutes to prepare, light a match and time setting said end on fire when another rope has burned up. The real solution is actually feasible by a human, most logic puzzles you'll find can be done by a human being.

[L]ogical thinking != crazy math.

lackofcheese

Even though lackofcheese has the wrong solution

I got the "right" solution later on.

Yes it does, it's called practical thinking. What is easier, lighting a match and setting a very, VERY, small piece of rope on fire, which burns for about 0.0000003 of a second, and in the mean time light another match and prepare to set the next, smaller, piece of rope on fire? Against setting a second end of a rope on fire for which you have 30 minutes to prepare, light a match and time setting said end on fire when another rope has burned up. The real solution is actually feasible by a human, most logic puzzles you'll find can be done by a human being.

Let me put this succinctly.
To attain exactly 45 minutes with the "right" solution, it is required that you light the next bit of rope within zero time of the previous rope burning out. However, this is impossible given human limitations. It is irrelevant that you have 30 minutes to prepare - you still can't respond instantaneously. So, by your logic, both solutions are wrong.

Churba

How do you know each rope burns for exactly an hour?

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How do you know each rope burns for exactly an hour?

The Flying Spaghetti Monster made the ropes. His creations are flawless! With the exception of mankind, which is most likely a mere experiment in the breeding of stupidity and its antidote.