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Igniter Cords

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Burning Fuses - Back to the Water and Weighing Puzzles

Your job is to measure 45 minutes, if you have only two cords and matches to light the cords.

1. The two cords are twisted from various materials and so their different segments can burn at different rates.

2. Each cord burns from end to end in exactly one hour.

Describe your way of measuring the 45 minutes.

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

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Igniter Cords - solution

Start fire on both ends of one igniter cord and on one end of the second igniter cord. The very moment the first cord (where both ends burn) stops burning (that is after 30 minutes), start fire on the other end of the second cord (otherwise it would burn another 30 minutes). Thus the second igniter cord burns just 15 minutes from then. And that is all together 45 minutes.

Your job is to measure 45 minutes, if you have only two igniter cords and matches to light the cords. The two igniter cords have the following features:

1. They are twisted from various materials and also different parts can burn at different speed (e. g. after ten minutes they will not burn at the same point).

2. Every cord burns from ignition to the end exactly one hour.

Describe your way of measuring the 45 minutes.

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Posted · Report post

well the above reply says start ignition on both ends of the first cord.

The question specifies that it is being built from different materials , so how do we know

that it is exactly symmetrical materials are used from both points such that it will take exactly

30 minutes to reach the end ????

I suppose that answer will not be satiable.

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Posted · Report post

well the above reply says start ignition on both ends of the first cord.

The question specifies that it is being built from different materials , so how do we know

that it is exactly symmetrical materials are used from both points such that it will take exactly

30 minutes to reach the end ????

I suppose that answer will not be satiable.

It seems quite clear to me. Second condition says:

2. Every cord burns from ignition to the end exactly one hour.

So if you ignite the same cord on both ends, it should stop burning after half an hour. And, of course, spot where the fire from both ends meets does not have to be in the middle at all.

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yes sir, i got your point, my mistake, i dint understand it, apologies for that.

Regards,

Sunil.

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Posted · Report post

that was the extra credit on one of my calc 3 exams. i loved the puzzle then, still a great puzzle now. incidentally, i got it right on the exam =D

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Posted · Report post

could you not just fold one cord in half then make note of the middle, then fold that half in the middle and make note of the quarter, then light and wait for that quarter to burn?

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could you not just fold one cord in half then make note of the middle, then fold that half in the middle and make note of the quarter, then light and wait for that quarter to burn?

i believe you are expecting for the quarter to burn for 15 minutes. however, due to the nature of the cords not burning at regular speeds in the middle of the cords, folding the cord into quarters won't necessarily give you a time of 15 minutes. the reason we can safely measure half an hour is because we know that the entire cords will burn for 1 hour, so if you light it from the ends, the cord will only last 30 minutes. however, if you start burning it from somewhere that isn't an end, you will get variable times.

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Posted · Report post

The first guy has the right idea. like me

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I believe this solution is also possible .. Please comment ...

1. Ignite the first cord at the two ends and somewhere approximately in the middle so that the fire from the middle propagates towards the two ends. It should take 15 minutes for this first cord to burn out completely (There would be two pieces of the first igniter cord since it was ignited at the middle as well - EVERY LAST BIT should burn out)

2. Ignite at the second cord at the two ends as soon as the first cord "completely" burns out. This would take another 30 minutes.

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All of this seems fine to me except one thing... Didn't the original question request timing 45 minutes, rather than the 30 everyone is talking about?

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I believe this solution is also possible .. Please comment ...

1. Ignite the first cord at the two ends and somewhere approximately in the middle so that the fire from the middle propagates towards the two ends. It should take 15 minutes for this first cord to burn out completely (There would be two pieces of the first igniter cord since it was ignited at the middle as well - EVERY LAST BIT should burn out)

2. Ignite at the second cord at the two ends as soon as the first cord "completely" burns out. This would take another 30 minutes.

This would not be an accurate measurement. If the cords burned at constant speed throughout the whole cord, and you started at exactly the center, this would be fine, but this is not the case in the rules.

Even though you're trying to start one at the approx. middle, you might get differing times. One might burn up in 12 and the other 18. Without thinking too hard on it, the average would probably be 15 minutes, but even then, we cannot measure something on averages.

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I do not see how this one can be solved. The given answer is incorrect; It assumes that there is 30 minutes left to burn on the second cord. There may be 50 or only 2. Please correct my logic if necessary.

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It assumes that there is 30 minutes left to burn on the second cord. There may be 50 or only 2. Please correct my logic if necessary.

There is only 30 minutes to burn on the second cord for the following reason:

If three ends of two cords are all lit at the same time, the one lit at both ends will be finished burning in 30 minutes. At this point the second cord will be finished burning in 30 minutes if left alone. However, if instead of leaving it alone, the other end of that cord is lit at the very moment the other cord finished burning, it will now finish burning in 15 minutes.

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easy

45=30+15=60/2+30/2;

first ignite both ends of first one cord, but only one end of second cord,

when the first one burn out, it is 30 mins,

ignite the other end of second one, left 30,

when all burn out, it is 30+15=45.

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I do not see how this one can be solved. The given answer is incorrect; It assumes that there is 30 minutes left to burn on the second cord. There may be 50 or only 2. Please correct my logic if necessary.

While I knew the answer was correct, I was still having trouble getting straight in my head the non-constant rate of burning. However, if a rope takes 1 full hour to burn, and you've been burning it for 30 minutes, no matter what the rate of burning, then the rest of the rope will have to take another 30 minutes to burn. Therefore, if you've set both ends of a 1-hour rope on fire, it will burn in 30 minutes meaning that the rest of the OTHER rope that hasn't burned yet is 30 minutes worth of rope... then, you light the other end of that making it 15 minutes worth of rope.

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How about this:

fold the first cord at the middle (you can make sure this is the case by making sure the opposite ends meet when folded), and light it up (such that both ends start burning at the same time)

While it is burning (and it should take 30 minutes) fold the other cord twice (so that you have it in quarters).. once the first cord finishes burning, light the other cord (such that all four bits start burning).. this should take 15 minutes, and you have a total of 45!

ok, so technically, you might argue that the parts might burn eachother, but you can always space them out such that they don't!

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Posted · Report post

don't u need 2 mention dat composition of both the cords is xactly same...?

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don't u need 2 mention dat composition of both the cords is xactly same...?

NO. the beauty of this problem is know you dont give a crap what they are made off. they could be even tapered so that one end is really skinny. The only thing you know is that the full length takes 1 hour. When you fold it in half and light both ends simultaneously the flames will not meet in the middle but they will definitely meet after exactly 30 mins. The other rope (which may be very different) has also been burning for exactly 30 mins. This leaves 30 mins left on the second rope. Not half the length of the rope but half the rope in terms of time. That rope is immediately folded and lit. The two flames meet 15 minutes later at an arbitrary location. The total elapsed time is exactly 30+15=45 minutes

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I believe this solution is also possible <!-- s:o --><!-- s:o --> .. Please comment ... <!-- s:roll: --><!-- s:roll: -->

1. Ignite the first cord at the two ends and somewhere approximately in the middle so that the fire from the middle propagates towards the two ends. It should take 15 minutes for this first cord to burn out completely (There would be two pieces of the first igniter cord since it was ignited at the middle as well - EVERY LAST BIT should burn out)

There's no telling the time it takes each piece to burn. One half lit at each end may burn up in 5 minutes, while the other half takes 25 (even though they are of equal length). All we know is 60 minutes in total.

In that case:

----------10 min----------|----------50 min----------

Or in another, 22 minutes and 8 minutes:

----------44 min----------|----------16 min----------

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A little off topic, but I just had an interview yesterday for a software engineering job, and one of the technical questions was this exact problem. The worst part about it was that I read this riddle before on this site, but I couldn't think of it for the life of me when it mattered! Ugh. I got it after a hint though, but still, would have been nice to nail it.

So it turns out reading riddles all day at work isn't a total waste of time afterall :P

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How about this:

fold the first cord at the middle (you can make sure this is the case by making sure the opposite ends meet when folded), and light it up (such that both ends start burning at the same time)

While it is burning (and it should take 30 minutes) fold the other cord twice (so that you have it in quarters).. once the first cord finishes burning, light the other cord (such that all four bits start burning).. this should take 15 minutes, and you have a total of 45!

ok, so technically, you might argue that the parts might burn eachother, but you can always space them out such that they don't!

I don't think this would work. All four bits would have to be burning the whole time for it to work. However, one of the four might burn almost instantly leaving a different piece to burn for a pretty long time. The value in burning both ends of the rope is that you know the rope is being consumed twice as fast for the entire period. If one of the four bits burns faster than the others, then the rope is only being consumed at the pace of three flames instead of four. Since we're not sure how fast each bit will burn, we can't do it this way.

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While it is burning (and it should take 30 minutes) fold the other cord twice (so that you have it in quarters).. once the first cord finishes burning, light the other cord (such that all four bits start burning).. this should take 15 minutes, and you have a total of 45!

Not quite - but this did give me an idea.

If you burn the first cord at both ends then it will be consumed in 30 minutes - we all get that.

However, if you take the second cord and burn it at both ends AND somewhere in the middle so there are four flames on the cord then it will be consumed four times as fast so in 15 minutes. The only caveat here is that there has to be four flames on the cord at ALL TIMES. So if you start burning the cord in the middle and after two minutes one of the pieces is consumed completely, you have to start burning the other piece in the middle again.

It would take a bit more effort than the original solution but I think it would still work.

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1. Start the process with three cords

2. Ignite cord "a" on both ends and cord "b" on one end.

3. When cord "a" has burned out there is 30 minutes left in cord "b"

4. Ignite the second side of cord "b" and one end of cord "c"

5. When cord "b" has burned out (15 minutes later) there will be 45 minutes left in cord "c"

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Whoops, jumped here from another thread....didn't catch the two cord limit...

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Posted (edited) · Report post

It seems quite clear to me. Second condition says:

2. Every cord burns from ignition to the end exactly one hour.

So if you ignite the same cord on both ends, it should stop burning after half an hour. And, of course, spot where the fire from both ends meets does not have to be in the middle at all.

I shall submit my question very soon as i feel some flaw in the solution

Edited by arun
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