arael

you have two pieces of ropes. The given is that they both burn for 60 seconds each. The rate/length is not given and therefore should not be assumed.

the question is: if you need to time 30 seconds, how do you burn the ropes so that you know it's thirty seconds with the given information. and as i mentioned before, the rate/lenght is not to be assumed so don't answer "cut the rope in half" because you have no idea if it burns at a constant rate.

if you can answer the question above, try timing 15 seconds

KnifeMissile

I really do think that you're missing an important detail of your puzzle. As it is, I really don't think there's enough information to solve it.
However, here's a puzzle for you!

Show that, if the rope burns symmetrically (burns at the same rate in either direction), then lighting both ends of the rope at the same time (like tying the two ends together, for example) will result in the two burns meeting up with each other in 30 seconds, regardless of the rate in which the rope burns!

saltfish

Same deal as KnifeMissle, BUT, Take the two ropes and place them parrallel and where their ends meet. Light the bottom rope on the right side, and the top rope on the left side.

Then, when the two ends begin to burn toward one another, when the two buring parts meet, you have found the middle.

-SF

lordjeebus

30 seconds: light both ends of one rope simultaneously -- because it is lit twice and the burns don't meet until the rope is gone, the rope disappears twice as fast. I don't think any additional information is necessary for this answer to work.

are the ropes identical?

EDIT: if they are identical, you can use the saltfish method, and when the burns line up (ie. after 30 sec), you can light the non-burning end of one of the remaining pieces. It will burn up 15 sec. later.

KnifeMissile

Actually, they won't necessarily meet in the middle. Your solution only works if the ropes burn at a constant rate, and arael said they don't.

If you're having trouble understanding this then imagine a rope that burns really fast for most of the rope and then burns very slowly for the last little bit. Do you think your idea will work then?

KnifeMissile

Actually, you are assuming (as I have said, before) that the rope burns symmetrically.

Again, saltfish's method only works if the rope burns at a constant rate.

If we may assume that the ropes burn symmetrically then we can get 15 seconds from burning the first rope from both ends while burning the second rope from a single end. When the first rope finishes burning, 30 seconds will have passed. After 30 seconds, if we stop the second rope from burning and then re-burn what's left from both ends then we will have our 15 seconds!

The ropes needn't even be identical!

lordjeebus

You're right that I'm wrong about the saltfish method.

It is not necessary that the ropes burn symmetrically for my (EDIT: and your) 30 second solution. If you light the ends simultaneously, you will burn from each end for the same duration of time because the burns terminate at the same time, when they reach each other. Because one burn will burn a whole rope for 60 seconds, two burns working at the same time will require exactly half the time.

KnifeMissile

Thank you for the acknowledgement.

Yes, symmetry is necessary. Consider a rope that burns the first 99% of itself in only 2 seconds but takes a full 58 seconds to burn the last 1%. Now, the funny thing about this rope is that it burns the same way in the other direction. So, if you were to burn both ends at the same time, it would burn for about 1 second, which is a far cry from our intended 30!

lordjeebus

It would still burn for 30 seconds. The burn on the fast end would spend 2 seconds working on the first 99% and the other 28 seconds working on that last 1%. The burn on the other end would spend 30 seconds on that 1%. 28+30 = 58 burn-seconds required to get rid of that last piece.

EDIT: I now get what he's talking about. Disregard the above.

lordjeebus

EDIT: Ignore this post, I figured out what knifemissle was talking about

lordjeebus

OK, ignore everything I've said. I misunderstood your "symmetry" concept.

I reread your first post and now I get what you're saying. You're right -- the rope does have to burn at the same rate at each point regardless of which way the burn is traversing the rope.

Is there such a thing as a non-symmetrical rope, following your definition of symmetry?

KnifeMissile

I'm glad we got that cleared up. Was I not clear on that or was this a simple misunderstanding?

I was afraid you'd ask this question.
While most rope will burn symmetrically, most rope will also burn at a constant rate. The question is so peculiar that it's really abstract and it's best not to compare it too much to reality...

sprocket

Look at the riddle again. It simply says do not assume the ropes are a certain length or they burn at the same speed. It simply says you have 2 ropes that could be any length that will burn up completely in 60 seconds. In order for this riddle to really work you have to assume each rope burns at a constant speed the whole length of the rope, so lighting the ropes at both ends would result in a 30 second burnination. The longer of the ropes will obviously burninate more material than the shorter one but in the same amount of time.

__________________
Remember, wherever you go... there you are.

KnifeMissile

With all due respect, I suggest you look at the riddle again...

It doesn't "simply" say anything! The quote "as i mentioned before, the rate/lenght is not to be assumed so don't answer 'cut the rope in half' because you have no idea if it burns at a constant rate," is quite telling. It's clear that arael is not simply saying that the two ropes burn at different rates or he wouldn't have ruled out the "cut the rope in half" solution...

saltfish

The rate/length is not given and therefore should not be assumed.


DAMNIT, didn't see that.

-sf

saltfish

I'm assuming the following is true: (Feel free to correct)

Each rope has a different:
Length
Average Burn Rate

Both of the ropes do not have a constant burn rate, therefore, any segment of the rope may have a different burn rate.

-----

If in fact the burn rates for a single rope was not constant, I would then tend to think that this problem may have become too complex. If there are different lengths, and their overall burn rates (through the entire burn) were constant, then the puzzle would be easily solved, as I beleive someone has already said:

-------------------------*
+ Rope 1
-------------------------*

--------------------------------------------------- Rope 2

Light the *'s and at the same time light one end of the 2nd rope. when the two burning spot meet, supposedly at the +, stop the burning of the 2nd rope. Once again, assuming that burn rate is constant for each rope, and there is no speed-up/slow-down for an individual rope you'd be ok.


-SF

saltfish

Ok guys and gals, I have something to add to this:

http://www.astrohoroscopes.com/puzzl.../burnrope.html

Q:
There are two lengths of rope.
Each one can burn in exactly one hour.
They are not necessarily of the same length or width as each other.
They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.

By burning the ropes, how do you measure exactly 45 minutes worth of time?

A:
If you light both ends of one rope, it will burn in exactly a 1/2 hour. Thus, burn one rope from both ends and the other rope from only one end. Once the one rope (which is burning from both ends) finally burns out (and you know a 1/2 hour has elapsed), you also know that the other rope (which is burning from only one end) has exactly 1/2 hour left to burn. Since you only want 45 minutes, light the second end of the rope. This remaining piece will burn in 15 minutes. Thus, totaling 45 minutes.



--------------

Now, going by that was stated in the question:

"They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour."

Have they shot themselves in the foot? If the width is not consisent then using the "burn both ends and stop the 2nd rope method" would not be accurate. How can that be correct?


-SF

teflonian

After reading everyone's responses last night I was convinced that burning them from both ends would not work due to the possible change in burn rate of the rope. However, after waking up this morning I was convinced otherwise... I believe my mental block last night was assuming the burns would meet in the middle. That doesn't have to be the case obviously, but I think it was holding me back last night. I am sure there is a mathematical proof of this if you assume a few things like, i.e. the burning of a rope from both ends doesn't create more heat that would burn up the rope quicker than the smaller heat from one burn. In any case I do believe the rope should burn up completely in 30 seconds if you start the rope burning from each end at the same time. Every infinitesimal segment of the rope burns at a given rate. The total burn time using one flame for a length of rope is 60 seconds. Using two flames will use the entire available fuel (rope) in 30 seconds as every infinitesimal segment will burn at the same rate it burned at with one flame. The flames could meet up in the middle if the burn rate of each segment is roughly similar, but that is not necessary and is not assumed. If it takes 58 seconds to burn one finite segment as knifemissle suggested than one flame will eat through all the other segments in 2 seconds while the other flame knaws on the one segment. The two flames will then knaw together for the remaining 28 seconds on the remaining segment. Not quite a mathematical proof, but I am convinced this would work in theory. (But not in practice as I do believe the added heat would increase the burn rate of the infinitesimal segments.)

Finding a way to measure 15 seconds would involve both ropes as Saltfish discovered the answer too.

arael

ya.. guys.. the answer is as easy as burning both sides of one rope..... it's not that complicated. under the assumption it burns for 60 seconds, you can correctly assert that burning it on both sides will give you 30 seconds. doesn't matter if the rate changes as you move through the rope.. doesn't even matter if it ends up not in the middle. you burn both sides, it will burn for 30 seconds. i can actually write a proof for it.. but it's too much trouble because that would involve copy and pasting lots of mathmatical symbols. Anyways..did someoen tackle the 15 seconds one already??

arael

By the way, as soon as someone solves the 15 second problem, i will put another puzzle up.. i have tons of these enjoy

KnifeMissile

Well then, by all means, post the other puzzle.
The fact that you're asking this question reveals that you have not been reading the thread!

KnifeMissile

They have not shot themselves in the foot. It's absolutely correct, it doesn't matter (as they've stated) if the rate is not constant, it will still burn twice as fast.

Also, as they have worded it, the rope will burn symmetrically. arael didn't articulate this puzzle very well...

dimbulb

I think you are the one who is confused. The wordings of both arael and saltfish's puzzles describe the same puzzle.

in saltfish's puzzle the rope most certainly does NOT burn symmetrically or at a constant rate.

Don't think of the rope in terms of length. Think of it in terms of (burn time)/flame and all will be fine.

I think all this confusing wording about thickness/length/burn rate is an attempt to prevent people from coming up with trivial answers.


NEXT puzzle please!

lordjeebus

KnifeMissle: I think that the word "symmetry" is confusing people the way it confused me.

Everybody else: What he's saying is that, at a given point, a rope burning from the left may not burn at the same rate as one burning from the right. Yes, in total it takes 60 seconds each way, but that doesn't mean that for any given segment of the rope, it takes the same amount of time to burn it from one end as it does from another.

That having been said, I think you're thinking too hard if you demand this to be accounted for in the question, as it is counterintuitive for a rope to exist that burns at different rates at certain points based on the direction of burn.

Next puzzle please!!!

KnifeMissile

I assure you that none of this is confusing.
Both wordings attempt to describe the same puzzle but I contend that one is much more articulate than the other...

In saltfish's puzzle, the rope most certainly does burn symmetrically. You just haven't read what is meant by "symmetric," in this case.

Finally, the rope needn't burn at a constant rate in order for the solution to work. This is where I think you're confused. It was saltfish who thought that the solution would only work with a constant burn rate, not me. Read this thread again...

Who thinks of the rope in terms of length? What are you on about?

It's not just an attempt to prevent trivial answers, it's an attempt to keep the question interesting. Otherwise, you'd simply answer "cut the rope in half," and people would wonder why you'd even ask the question...

KnifeMissile

I agree that it is counterintuitive but, then again, so is a variably burning rope.

And, again, I agree that it's time for the next puzzle. In fact, let me offer one!

dimbulb

way too much discussion on a very simple puzzle.
Cutting the rope in half IS a trivial question. You don't have to 'prove' yourself 'correct' all the time you know......

looking forward to your puzzle...