How To Solve The Two Rope Puzzle

You have two ropes and a lighter. Each rope burns in 60 minutes, but the ropes do not burn at a constant rate. How can you measure 45 minutes by burning the ropes? Some of you might have heard this problem before. If so, try this variation: how can you measure 50 minutes? Watch the video for a solution to each problem.

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[sabriath]

You state that you have to make sure that 3 flames are constantly going at all times....if the single flame reaches the end while 2 are racing toward each other, you'll end up with 2 flames. You never stated what to do at this point, but you need to extinguish one of the flames and relight in the middle again in order to retain the 3 flames.

[danielgrace]

The first problem where 45 minutes is measured is correct. But in the second problem there is an issue with the second rope that is burned. You cannot keep exactly three flames going if the piece (with the one flame) burns up before the other piece (with the two flames). Because if you were to light the remaining rope (with the two flames) with another flame somewhere in the middle you would then have four flames. If you could immediately put out one of the four flames, or cut the rope before lighting it then this issue could be rectified. But the video does not mention whether such actions are available or allowed.

[msndrstdmstrmnd]

Q: How do you measure 50 minutes by burning the two ropes?
A: Measure 45 minutes using the first way. Then wait five minutes :D

[Leonideez]

The issue with the 50 minute solution: The rope burns at an indeterminable interval, so when you light the second rope at one end and in the middle their is a possibility that the two flames meeting may take up to just shy of 30 minutes while the single flame runs through its part of the rope in anywhere from 1 sec to 19 minutes.  At any time where the end of the rope with the single flame finishes first, this method fails.

[NetRolllerD]

For the 50 min variant: What if the rightmost part of the split "middle" flame reaches the non-burning end before the other 2 flames meet? In this case, you end up with 2 flames, and since both ends are already on fire, you can only add flames in pairs, and thus never get 2.

[sleepib]

For the 50 minute solution, you also need the ability to extinguish the rope, in the event one of the center flames reaches the end you did not light. in that case you have to extinguish one end and re-light the middle.

[PUM_Productions]

I'm still a little stuck at the "burns at different rates", how do you know 95% of the rope won't burn up in the first 3 minuets the the last 57 minuets it burns slow?

[GenGariczek]

Your solution is wrong because of your own definition of the problem.

[davidjames]

Each rope burns in 60 minutes so regardless of how many times you light it, as long as it is lit at least once, it will burn up in 60 minutes. That is what the rule states and implies. So for example, if we light the rope at both ends initially, it will STILL take 60 minutes to burn. I think what he really meant (but didn't say) is the rope burns in 60 flame minutes meaning that if we use 2 flames it will then burn in 30 minutes but since he did not state that clearly, we have to go with his exact words which state each rope burns in exactly 60 minutes (so that means regardless of how many times/places it is lit). This is yet another Presh Talwalker fail as can be seen by the number of downvotes for this puzzle.

[klickwitch]

This math doesn't make any sense. You said at the very start: "the rope takes 60 minutes to burn, but it doesn't burn at a constant rate" Meaning the first cm could burn for 59 minutes, and then the last bit of rope burns up in just a few seconds. They way you're describing it implies there is consistantsy or at lest some predictability

[farstar]

Not only do I not like your "solution" to the 50 minute problem because it's very possible that the middle flame can reach the far end before meeting the first flame, but the fact that thinking an infinite amount of steps counts as a valid solution. It's reminiscent of how the "squaring the circle" problem works, except in that problem, infinite steps are not allowed, which I feel should apply to this sort of problem.

[DK_Son]

Just get a watch. Anyone burning ropes for time is a psychopath and a pyro.

[aleksandarrusinov]

You can measure 52.5, 56.25 and so on by solving the infinite series. This is a generalised form of "bee between two trains" question.

[yanivshemtov]

your 50 minutes solution is actually wrong because the flame you light in the middle (that splits into two) can reach the end of the rope and then both ends will be on fire and youll have two fires at each ends which in that case if you ligh tthe rope in the middle youll have four fires (because of the you cant garrenty that there will be an option to have three flames all the way)

[DanVWeller]

Why am I watching this? I have exams tomorrow

[ThePeterDislikeShow]

Zeno's paradox comes to mind.  You could end up only approaching the 20 minutes while never guessing the right spot.

[dwinson]

The problem with the 50 minute solution is that you've taken a problem that could feasibly be solved to one that is only possible in theory. The 45 minute solution entails lighting 3 ends at the start (easily done by folding one rope in half) and then lighting the other rope end after 30 minutes. All of this is reasonable. The 50 minute solution, however, relies on an 'at the limit' calculation which would entail an infinite number of operations. OK in theory but very unsatisfactory as a puzzle.

[patrickwienhoft]

Q: For the 50 minutes: If I light it somewhere in the middle, it might happen that the middle flame spreads faster to the end without light than to the one with light. If that happens, you end up with a rope with is lighted at both ends. What do I do then? Extinguish one flame? Am I allowed to do that?

[tomburris]

Since you introduced the possible error of having 3 flames always lit in your 50 minute variation, I propose a solution just as impossible, (if not more so). Cut the rope into infinitely small slices, and randomly arrange them back into a rope. Now the rope will burn evenly, and X% of the rope will burn in X% of the minutes.

[BeaDSM]

For the 50 minute version you would have to relight the rope an infinite number of times to get exactly twenty minutes from the second half of the second rope; since the ropes burn at an uneven rate there's no way to know where along the remaining rope to relight it and so it should take an infinite number number of relights to ensure that there are always three flames. I think a better answer is 'no, you cannot measure 50 minutes'. Without proof, I'd conjecture that it may be the same mathematically as attempting to trisect a line.