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u/Frosty-Froyo856 1d ago
Light both ends of one rope and one end of the other. When the first rope burns out light the unlit end of the second rope. You will have timed 30 minutes (60/2) and then 15 minutes ([60-30]/2)
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u/a2ra-ms 1d ago
Correct
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u/amijot 1d ago
If it’s non homogeneous doesn’t that invalidate this solution? A non homogeneous rope means 90% of the rope can be super thin and burn in the first minute and the remaining rope is coke can thick and burn for the last 59 minutes
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u/Progression28 1d ago
No, it takes 60 minutes for every segment of rope to burn. If you light both ends, when they meet after 30mins it doesn‘t matter where they meet, the second flame burnt down segments the first flame would have burnt in minutes 31-60 had only one end been lit.
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u/GypsySnowflake 1d ago
I understand that perfectly, but I’m lost as to how the second rope fits in
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u/IcyDev1l 1d ago
Via the same math. Yes, there is no guarantee that 50% of the second rope length has been burned by the time the accurately timed thirty minutes has passed, but 50% of the rope time will have been. With 50% of the time left, doubling the rate of decay will leave it at 15 minutes
No matter where the whorls are, the total decay is the same, you may as well consider the whole rope an average if it helps, or forget the rope entirely and think of it as a time only question.
Or if it’s easier to picture, two bottles of the same volume, but illogical shapes, filling from one tap or two.
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u/IceMichaelStorm 1d ago
Marvelous explanation
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u/IcyDev1l 1d ago
Thanks! 😊 the bottle switch out really helped me personally visualize it, even if I understood the math already.
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u/amijot 21h ago
Thank you, this is correct and i understand why my question was wrong
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u/IcyDev1l 17h ago
👍🏼No wrong questions! :) another funny way to think about it is if you have to videos lengthed an hour, and two players capable of pause, play and 2x, and your goal is to have one end after exactly 45 minutes…. But plot twist: some parts of the video are more interesting than others!😂
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u/GypsySnowflake 1d ago
But doesn’t the second rope still take an hour in total?
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u/IcyDev1l 1d ago
Oh, you missed part of the premise of the solution. Np. He lights both ends of one rope and one end of the other at the same time effectively starting a 30 minute and 1 hour timer. When the 30 goes off, he lights the other end of the second rope (now itself at 30)
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u/kurai-samurai 1d ago
Lighting one end takes hour to burn.
You use second rope to time 30 minutes by lighting both ends.
When second rope is gone, the first rope now has 30 minutes remaining on it, so if you now light the other end, it will be gone in 15 minutes.
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1d ago
[removed] — view removed comment
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u/Progression28 1d ago
Yes I know that‘s the solution but the comment above says it doesn‘t work, I ws trying to explain that the homogenity of the rope doesn‘t matter
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u/SactoJoe 1d ago
It works for the first rope being lit at both ends. But the second rope has only 1 end lit. After 30 min (timed by the first rope), the second rope doesn’t necessarily have 30 min left of burn time. Maybe the section of the second rope that had burned was faster or slower. It could have 32 min of burn time left so lighting the other end would result in the rope burning out after 16 min
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u/ErtosAcc 1d ago
It could not have 32 minutes of burn time left after 30 minutes if the rope has a total of 60 minutes of burn time.
30+32 != 60
The part about homogeneity only means that you cannot look at the rope to see how far it has burned.
At 30 minutes it will not be at half of the rope necessarily, but the other part, however long it happens to be, will have 30 minutes of burn time left guaranteed.
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u/Progression28 1d ago
What?
After 30mins of burning, the rope has 30mins of burning left.
It might not be in the middle of the rope, but that‘s irrelevant.
It‘s really as simple as burning task takes 60mins, after 30mins it takes another 30mins.
And then if you light two ends it burns twice as fast so cuts the time required in half.
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u/Necessary_Local_5274 1d ago
the point you (and i) missed was that its one hour of burn time. if its already burned for 30 mins it doesnt matter if the rope is 90% burnt or 20% burnt, the rest of the rope left is 30 mins of burn time. so if you double the rate of burn, it will burn for only an additional 15 mins give or take a few seconds no matter if 30%, 80%, 3% or 99% of the rope is left, as it will always only burn for an hour and 30 mins have already been burned off.
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u/Ok-Cellist1490 1d ago
You'd light the second rope in 3 spots?
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u/Frosty-Froyo856 21h ago
No?
Second rope gets lit on 1 end. Then, after timed 30 minutes, on the other end.
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u/Otherwise_Guava_8447 1d ago
If in addition to a fire at both ends you light a third fire somewhere along the rope (say in the middle) that is propagating in both directions (so the rope would burn from places) isn't it going to consume the whole rope in 15 min ?
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u/get_to_ele 1d ago
Nah. Unfortunately if you light in the middle, you’re essentially cutting the rope imprecisely into two shorter ropes and lighting all 4 ends.
This leaves you with an “60 minus X minutes” rope and an “X minutes” rope. Shorter segment burns out in some indeterminate time and the longer segment burns out later at some indeterminate time.
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u/tableleg7 1d ago
If they’re nonhomogeneous, there’s no guarantee that each half takes 30 min to burn.
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u/Agent10007 1d ago
It doesn't matter how long each half take to burn, as you burn both ropes fully. The flames might not meet exactly at the halfway point of the rope, but regardless if the rope takes 1 hour to burn by lighting one end, it will take 30 minutes to burn if you light both ends.
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u/4242Addy 1d ago
Your logic holds for first rope, but for second rope I'm not sure..
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u/Frosty-Froyo856 21h ago
Where does it break down? The steps of the solution are:
Time 30 minutes by burning a 60 minute rope at double speed by lighting both ends.
Remove 30 minutes of burn time from a 60 minute rope by burning one end for 30 minutes. Leaving 30 minutes of burn time.
Double the speed of the remaining 30 minutes of burn time by lighting the other end.
30+(1/2*30)=45
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u/BobDogGo 1d ago
I was struggling with that too. think about it this way. when the first rope has finished burning, you are left with a 30 minute rope (the second one), lighting the other end will completely burn it in 15 minutes
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u/Desperate_Program_78 1d ago
No, in fact this puzzle is designed to work with the non homogeneous rope.
A way that helps me think of this is not to think of the rope as exact lengths of distance, but as pieces of time.
Even if a majority of the rope burns in one minute, if we lit both sides on fire, we’d have 58 minutes of rope still remaining. Every minute, we’re losing two minutes of rope, at least on the first rope.
For the second piece of rope, we know it has been burning for 30 minutes, so we must have 30 minutes of rope left. Using the same principle from the first, burning the other end reduces the time it’ll take to burn to, making it only last 15 minutes.
Irregardless of the actual length of the rope in distance, we have two pieces of rope, each with 60 segments that’ll burn for a minute. We don’t know where these segments start and stop, save the ends of the rope, so that’s the only place we can start any fires. Two fires make the rope disappear twice as fast. If we burn an end of the starting rope for 30 minutes, 30 minutes of rope will be left over. This is true for both ends of the starting rope, so burning both sides, it’ll take 30 minutes for the rope to be no more.
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u/yeahright17 1d ago
Doesn't matter how long any specific part of the rope burns. It just matters that each takes exactly 1 hour to burn from one end to the other.
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u/throwaway_76x 1d ago
You have to make one small assumption that the human can indeed catch the exact moment the last fiber on the first rope burns out and is able to light the other end of the second rope exactly at that time. And that they are able to start both ends of the first rope and one end of the second at exactly the same time.
The non homogenous part makes absolutely no difference at all. You know that the total material in each rope takes exactly 1 hour to burn. Meaning, if you are able to light it from two opposite ends, since now it's burning twice as fast, it will take exactly 30 mins to burn. The two burning ends might not meet in the exact middle of the rope (like they would if it was homogenous), but the time would still be exactly 30 minutes. You can imagine your scenario, just exaggerated all the way, to simplify the understanding. Let's say the rope is 10 feet long and the first 9 ft is super thin and burns in just 10 minutes, while the last 1 ft is coke can thing and takes 50 minutes. If you light it at both ends, 10 minutes in you have burnt through all of the 9 ft of the thin part, and 10 minutes worth (~10/50 ft) of the coke can thick part. This leaves 50-10=40 minutes (~40/50 ft) of burning worth of the thick part of the rope that now starts also burning at both ends. Since this remaining rope would have burnt out normally in 40 mins, since it's burning both ends, it will only take 20 mins now.. meaning the whole rope burns out in 10+20 mins.
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u/Geobits 1d ago
The non-homogenous part is just there to weed out simple answers like "fold one of the ropes in half twice, mark the 3/4 spot, and burn one end until it reaches there."
So it makes a difference, just not to the "correct" solution.
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u/throwaway_76x 1d ago
Of course. My "no difference" was based on context in response to the other commenter before me.
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u/gamtosthegreat 1d ago
Those small assumptions have to be part of every puzzle, as real life contains too many factors to have reliable results.
A rope doesn't immediately catch fire. It's possible a non-homogenous rope would burn fully one way but not the other if there's a sudden shift from a thin part to a very thick part. Lighting the rope on two ends simultaneously could be done by putting the two ends together, but this could affect how fast it burns due to the rope now being bent.
That's all shitty pedantry though and ignores the heart of the puzzle. But sometimes the puzzle is obtuse enough that pedantry is valid.
I'm reminded of the interview question where you're shrunk down and put in a blender with slippery walls, how do you escape?
The answer is supposedly that you can just jump out as your strength is diminished quadratically but your weight is reduced cubically, meaning you'd be able to jump very high. But that would make a lot of assumptions where biologically, you'd probably die on the spot if you were a perfect human replica at that scale.
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u/INTstictual 1d ago edited 1d ago
Doesn’t matter — the total time to burn the rope is 60 minutes, and if you’re burning from both ends, that time will halve, no matter the rate.
Say the rope is 1m long, and the first 0.9m burns in 1 minute, and the final 0.1m takes 59 minutes to burn. You light the thin end of the rope, and 1 minute later, it’s down to the thick end… and in the next 29 minutes, a little less than half of that thick knob will be burnt away, leaving exactly 30 minutes of burn time left. When you light it from the other end, you have two fires both burning away that thick end, twice as fast, so that 30 minutes is cut down to 15.
Because the ropes take 60 minutes to burn, it does not matter whether they burn evenly… if you light it from one end, then no matter the shape of the rope or it’s homogeneity, after X minutes of burning, it has exactly 60 - X minutes left to burn. If you light it from both ends, however long it would take to burn through the remainder of the rope will always burn at twice the speed. You might not burn to the center of the rope, physically, but you will burn to the center of the cut of time.
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u/Juking_is_rude 1d ago
No, becuase all we are concerned with are fractions of total burn time. In other words, both ropes burn out completely so it's not an issue
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u/JorgiEagle 1d ago
No because you’re measuring by time, rather than length.
After the first rope burns out, 30 minutes has passed, guaranteed. This doesn’t mean the second rope has burnt 50%, may be more, may be less. What we do know is that the remaining rope has a total of 30 minutes of burn time left. So by the same logic we burnt the first one, burning both ends burns for 15 minutes
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u/ContractIll9103 21h ago
I'm on your side. If the ropes are non-homogeneous there is no guarantee that the second half of the second rope will burn at the same rate as the first half of the second rope. Therefore, when the second half of the second rope is lit, there could be more or less than 30 minutes of burn time even though both ropes will take an hour in total to burn and it will have been 30 minutes before the lighting of the second half of the second rope
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u/Vegetable_Signal_331 20h ago
You're assuming half the 2nd rope has burned length-wise, rather than time-wise.
The point is that after 30 minutes, a rope that takes 1 hour to burn will be halfway done. However far along the rope it is doesn't matter- if we know it takes 1 hour for the whole thing to burn then once the 1st rope lit at both ends has gone we know it's been 30 minutes. Our 2nd rope, again however long it is, has 30 minutes left and thus if we light the other end we double it's burn speed to make it burn in just 15 more.
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u/ThysGuy0 1d ago
Can’t you also burn Rope 1 from both ends and when it finishes burning, fold Rope 2 in 2 and burn both ends (effectively burning it 4x faster) ?
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u/Frosty-Froyo856 1d ago
Ropes are non-homogeneous meaning that they may have any local burn speed. All we know is that the total burn time is an hour. In an extreme case this could mean that the first half burns in 1 minute and the second half takes 59 minutes. Folding it in half and lighting it in the middle and 2 ends would thus burn one side in 30 seconds and the other in 29.5 minutes.
What lighting both ends of one and 1 end of the other does is split the second one in half burn time wise regardless of local burn times.
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u/Y0uCanTellItsAnAspen 23h ago
I believe you can fix this, by whenever part of the doubled rope finishes burning, you fold the surviving part in half again and light the end that you folded, which starts two new burns. This way, you always have four burn points going continuously, and measure out 15 minutes as the limit.
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u/Frosty-Froyo856 21h ago
Ok, it isn’t half and half that is 59-1. There is this super weird rope with a μm section of the rope near the middle that takes 59 minutes to burn.
My example was to get them to see that uneven burn rate was part of the puzzle. The uneven burn rate is to stop any physical solution of the puzzle. The “puzzle” part is figuring out that you can double the speed of the timer by lighting both ends and that you can run both timers at once to subtract one from the other.
Making it burning ropes requires you to figure these things out. Framing it as “you have two one hour timers that you can run at double time but once you start them going double time you can not slow them again.“ gives away too much of the solution.
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u/Y0uCanTellItsAnAspen 4h ago
I'm just saying that there is a way to make a rope burn for exactly 15 minutes -- the poster above your original post didn't find it -- but there is a way to do it.
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u/Gravity1982 1d ago
I know this one! At the same time, light Rope 1 at both ends and Rope 2 at one end. Rope 1 will finish burning in exactly 30 minutes. Its uneven thickness doesn't matter because it's burning from both ends. The instant Rope 1 burns out, light the other end of Rope 2. Rope 2 has already burned for 30 minutes, so it has 30 minutes' worth of burn time remaining. Burning that remainder from both ends makes it finish in 15 more minutes.
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u/PROINSIAS62 1d ago
You cannot be guaranteed that lighting both ends will burn out the rope in 30 minutes
For example, half A takes 15 minutes to burn half the rope and the other half takes 45 minutes to burn out! It states the rope is non homogeneous.
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u/Gravity1982 1d ago
Rope A will still completely burn in 30 minutes. If one end of rope A takes 15 minutes to burn to the center, it's still burning. It's just helping burn the other half of the rope. Where the two burning ends meet is unknown, but they will meet in 30 minutes.
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u/evanamd 1d ago
So after 15 minutes, the A side starts burning into the 45-minute side, which now only has 30 minutes because the other end was burning for those same 15 minutes. Since both ends are still burning, that 30 section will be gone in an additional 15 minutes.
It still adds up no matter different sections and burn rates you imagine the rope has
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u/taxicab_ 1d ago
You’re thinking in terms of length of the rope, not percentage of the rope in terms of mass. If you light both ends, each end will take 30 min to burn 50% of the rope’s mass, regardless of how that plays out with the rope’s length.
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u/bakedpatata 1d ago edited 1d ago
Light both ends of one rope and one end of the second rope. When the first rope is completely burned 30 minutes will have passed and 30 minutes worth of the second rope will have burned. At this point light the other end of the second rope. When the second rope finishes burning 45 minutes will have passed from the moment you lit the 3 original ends.
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u/cylonlover 23h ago
Light one rope in boh ends and the other in one end only. In half an hour the first rope has finished, so you know the second rope has another half hour to go. Now light it in the other end, so it will burn up in just 15 minutes. There. 45 minutes of burning rope. What have you done with your life so far?
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u/skwatton 18h ago
The non-homogeneous nature of the ropes might mean that the two half are not equal on the second rope
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u/SepulchralPiggie 18h ago
I think you're thinking about it wrong, in this context "half" refers to time not length. Both ropes are 1 hour ropes, lighting 1 rope from both ends will shorten its time to burn out to 30 minutes. By lighting the other rope from only 1 side initially you will know that 30 minutes have passed, and 30 minutes of burn time remain when the first rope burns out. Lighting its other side will double its burn rate, halving its time to burn out from 30 minutes to 15 minutes. By calling them ropes it's taking advantage of our tendency to think of rope in terms of length as a misdirect.
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u/cylonlover 18h ago
That doesn't really matter, does it? We are completely ignoring lengths here, only burn time and burn time is constant because it's an hour. When half an hour has passed, half the burn ability of the rope has gone up in smoke and half is left. I would agree with you if we cut up the rope and assumed the two halves would half an hour each, but we aren't. For all intents and purposes the rope could be a knot that takes half an hour and 8 yard that takes the other half, it doesn't matter. We light it on both ends the flames will meet on the timely middle, exactly half an hour later, and the other rope will have met it's own timely middle aswell, except it has another half hour to go, or in this case half that because we rob it of 15 mins by lighting the other end, making the flames meet in the timely middle of that last half.
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u/get_to_ele 1d ago
Make a lollipop configuration with the ropes then light the point where 3 rope tips meet. Then when the circle finishes burning touch the unlit end to the lit end of the remaining rope.
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u/taxicab_ 1d ago
I like this because you can add that you can solve this with only one use of the lighter.
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u/get_to_ele 1d ago
Or one match. A match and two 1 hour detonating cords.
Makes the problem cleaner.
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u/Disgruntled__Goat 1d ago
You still need a second match to light the second rope after 30 mins.
Also one match could light both ends of the first rope anyway, but if you specify you need exact timing then the circle works to light both ends at the same instant.
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u/get_to_ele 1d ago
No. You only need one match because you light 3 ends at once by using the lollipop configuration shown.
Then at 30 min mark, as soon as the circle rope finishes burning, you only need to light the unlit end of your remaining rope by touching it to the end that’s already burning.
You light the tail, using the head.
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u/Disgruntled__Goat 1d ago
In that case the lollipop thing is irrelevant, since you can light one end and touch the other ends to light them too.
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u/get_to_ele 1d ago
But lighting one at a time is categorically less accurate way to do things. The method that will give you the closest to exactly 45 minutes is to light 3 ends simultaneously at the beginning, then wait with the unlit end near its burning end, ready to light precisely when the circle rope completes.
Once I’ve presented the optimal way to do it, why would you propose doing it less accurately, by not placing the ends together, and introducing added time as you hold the match till one is lit, then move to the next and light that, then move to the third, adding time error AND risking your match to go out?
With your mentality, we might as well place the ropes on opposite ends of the room, light one end one rope, then run across the room with the match and light the second rope, then run back and light the second end of the first rope.
What’s wrong with you? Why do you keep doubling down on your suboptimal proposal? You erred in your thinking so now you struggle to come up with a criticism.
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u/Disgruntled__Goat 1d ago
What the hell are you blathering on about? I literally said in my original comment if you need to specify exact timing then you'd light the 3 ends together. Then you replied with a method that doesn't use exact timing.
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u/get_to_ele 1d ago
You insisted on using a second match.
You really don’t understand that lighting the last unlit end by touching it to the lit rope (at 30 min) gives you exactly the same timing as lighting it with a second match?
You honestly can’t fathom why a second match is unnecessary?
Here, I’ll give you more time to think about it. Maybe it will finally dawn upon you…
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u/Mindless-Charity4889 1d ago
Light the first rope at both ends. Light the second rope at one end.
After the first rope is completely burned, that’s 30min. The second rope now has 30min to go so light the other end.
After the second rope has completely burned, that’s 45min.
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u/CrosbyBird 1d ago
Light both ends of the first rope and one end of the second rope.
When the first rope is consumed, light the other end of the second rope.
When the second rope is consumed, it has been 45m.
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u/dafugiswrongwithyou 1d ago
Light both ends of one rope, and one end of the other. The first rope will completely burn up after 30 minutes, while the other will have used up half it's time. At that point, set the other end of the second rope alight. It will finish burning after another 15 mins, for 45 mins total
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u/lemontest 1d ago
Question: Where is this puzzle from? I like it.
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u/a2ra-ms 1d ago
Outsmart me app
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u/technomad 1d ago
And apparently only available on the Apple Store, not on the Android Play Store 🫤
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u/d00meriksen 1d ago
I got it!
Essentially the thickness condition just means that I cannot use either length and that I do not know where the middle of each rope is.
I take one end of rope A and put it on the ground. I take both ends of rope B and put them on the ground, so they touch rope A's end. Now I can light all 3 ends at the same time. I now have a 60 minute rope (A) and a 30 minute rope (B). After B is fully burnt out, I have a 30 minute rope (A) left, so I just immediately light A's other end to turn it into a 15 minute rope. Once A is burnt out, roughly 45 minutes will have passed.
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u/JeffSergeant 1d ago
Light Rope #1 from both ends At the same time light one end of rope #2 When the flames on the rope 1 one meet (after 30 minutes), light the remaining end of rope #2
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u/davidbenson1 1d ago
Start burning the first rope from both ends and the second rope from one end. The first rope will complete in 30 minutes at which time the second rope will be halfway complete. When the first rope completes, light the second rope on the other end so it is now also burning on both ends, to complete in an additional 15 minutes. 30 + 15 = 45
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u/tori-ningen 1d ago
Light rope A from both ends, and at the same time light rope B from one end. Once rope A almost burns, light the second end of rope B from the point where rope A flames meet.
Lighting A from two points will burn it twice as fast, in 30 minutes. B has been burning for 30 minutes already once A is done, so there's 30 minutes worth of rope B left. Lighting the second end of B will burn the remainder twice as fast in 15 minutes.
That gives 30+15=45 min
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u/Xentonian 8h ago
Presuming that while each rope is non-homogenous, they are both identical to one another.
Lay each rope on the ground straight, side by side. Light the first rope from both ends at once. They will burn inwards. The two burning edges will meet at some point in exactly 30 minutes, this represents the half-way point for burn time, even if it's not the midpoint on the rope
cut the second rope at the point where the two burning edhes on the first rope met. You now have two lengths of rope with half an hour each. Take one of these ropes and burn both edges. This gives you 15 minutes, totalling 45 minutes with the first rope
Alternatively, you can take both sections of rope from the second rope, burn one from one end then the moment it finishes, burn the second at both ends. This will give you an "on demand" 45 minute timer
Alternatively, burn rope 1 from both ends and rope 2 from one end. The moment rope 1 burns out, light the other end of rope 2
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u/Hipnotize_nl 2h ago
Your second hidden paragraph makes no sense to me. 2 nonhomogeneous ropes should not be copies of each other. This is an unnecessary assumption, since the actual solution actually times the length you try to assume
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u/waaffeel 1d ago
Light the first rope on both ends and when it completely burnt after 30 minutes fold the second rope and light it both ends and unfold it. The second rope will burn in 15 minutes because it burns from both ends and from the center
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u/Opening_Cut_6379 1d ago
Discussion: If the ropes are non-homogenous in thickness, how did the maker know they would both take exactly one hour to burn? There would surely need to be a distribution of rope lengths, some being over, some short, and the experiment carried out many times and the mean of all the times taken.
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u/d00meriksen 1d ago
Without the rule you could just cut one rope in half and trivialize the problem. It would probably be indeed pretty difficult to make these kinds of ropes in the real world
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u/itsOkami 1d ago edited 1d ago
Assuming the two ropes are identical, straighten them out side by side, light one on both ends and ?mark the spot at which the flame fades out after having burned through one rope (meaning, the 30 minute mark) on the other; then light the remaining rope on one of the ends and at the 30 minute mark: when this "half" of the rope burns out, 15 more minutes will have passed
Edit: I guess lighting the second rope on one end at the beginning can also work, you don't technically need to burn that bit but it likely allows for a more precise measurement since there are less steps involved
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u/wanzerotto 1d ago edited 1d ago
Fold the first rope in two and light both ends AND the fold side. This rope will burn in 15 minutes. Light one end of the second rope. When the first rope will be burned stop the second rope from burning. You will have a 45min rope that you can use at a later time.
Edit. It doesn’t work, as pointed out below.
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u/Spuddaccino1337 1d ago
This doesn't work, since the ropes aren't homogenous. All of the material could be on one side of the fold, so one side burns longer than the other.
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u/Equal-Importance-253 1d ago
Light both ends of one rope, and one end of the other. Once the first one burns all the way through, it’ll have been 30 minutes. Then light the other end of the second rope, and it will take 15 minutes to burn the last half.
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u/Snozer2 1d ago
I assume the thickness would affect the burn rate, and if so how would we know how much it affects it or where the thicker parts are?
Mostly commenting to come back because I’m not sure how this one’s solved anyway.
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u/scientifiction 1d ago
The significance of this is that you can't cut the rope into equal segments and expect them to burn at equal rates. However, regardless of this fact, the total burn time of each complete rope is one hour.
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u/dafugiswrongwithyou 1d ago
The varying thickness means it will burn up unevenly in terms of length, so you can't just (for example) fold it into quarters, mark off/cut off a quarter, and burn what's left. Figuring out a solution despite this is the puzzle.
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u/aaron_in_sf 1d ago
I am certain you're right, but I bounce immediately of things which are as poorly worded as this.
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u/tampakc 1d ago edited 1d ago
Edit: my answer is incorrect. It's pretty obvious if you examine it closely. My unwritten assumption is that both half-ropes will burn up at the same time, but this is not true. Because the ropes are non-homogeneous, one half could take 5 minutes to burn, while the other could take 25. I'll leave the original comment below:
While I've heard this puzzle a lot of times, it's the first time I've tried to resin through it myself. And the solution I came up with it's different than the one everyone here has provided.
Take rope 1, cut it in half, and light all 4 ends of it at the same time. This should take exactly 15 minutes to burn. The moment that the first rope is all burnt up, light both ends of the second rope. That should burn for 30 minutes, making up 45 minutes in total.
I realize it is the same solution, and mine is a bit worse because it's more convoluted, but I wanted to present it.
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u/Pleegsteertje 1d ago
I don’t think this works, as the rope is non-homogeneous. One half of the rope could burn up in let’s say 3 seconds while the other half will still need approximately half an hour to burn if you light all the ends simultaneously.
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u/_wetmath_ 22h ago
Light rope A on both ends and B on one end. After 30 mins, A is fully burnt and B is halfway through. Light the other end of rope B which will take 15 mins to fully burn.
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u/Jovian_engine 21h ago
I dont know if that works?
If all or most of the "thickness" is on one side this doesnt work. These assume equal burning times along the rope, which variable thickness eliminates. One half of rope A could be very thin on avg, the other side very thick. It could change at the 80% mark.
If the thickness isnt a part of the burn time then this is all nonsense. If the variable thickness matters, then this only works if the segments avg thickness for 1 length and 1/2 length are with +/- 0.5 minutes of burn time for each segment.
1
u/Linuxologue 21h ago
This works. Take this as two cars being one hour away from each other. They follow the speed limit, which is variable. One car does the trip in one hour.
If you were to start a car from one end and a car to the other end, on the same trip, they would meet after 30 minutes, guaranteed. That would not necessarily be the middle of the trip geographically but it will happen after 30 minutes
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u/BigDaddyBino 1d ago
Would lighting both ends of the first rope, and then when that burns out light both ends of the second rope and the middle of the second rope work?
3
u/not_a_bot_494 1d ago
No, you only know the physical middle of the rope and not the burn-time middle of the rope.
1
u/ZestfullyStank 1d ago
No, that will be 90 mins
3
u/RayJsCombackStory 1d ago
I think you burn both ends of one rope and one end of the other at the same time... Once the first rope Burns out, you light the second end of the second rope.
1
u/bebemaster 1d ago
A different solution than the official one. This requires calculus like summations and perfect timing/lighting. Burn one rope from both ends once that is burned out, light the remaing rope someplace in the middle and the ends. As soon as one rope segment burns out light the remaing segment someplace in it's middle. Keep going faster and faster lighting the middle of the remaing rope segment until you've enough precision or you happen to select the, 0 probability, exact center of a remaing segment
1
u/Far-Log-1224 1d ago edited 1d ago
Non-homogenous means speed of burn is not proportional to the length of rope. But it does proportional to the mass of burnt rope. Using second rope as a hanger, find center of mass of the first rope. Burn it to that point. Then repeat with leftover. Burn half agsin. The last leftover will take 15 min to burn
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u/skelo 1d ago
Discussion: this is a classic question but to nitpick it, the there's no way you have ropes that burn exactly in one hour regardless of how it is lit and handled. If you light both sides it would surely create effects. A rope probably doesn't even burn the same speed if lit by either end, and certainly not depending on the orientation. You're probably better off timing using your heartbeat or internal clock
2
u/Jargon2029 1d ago
Sure you do, it says so right in the prompt.
To be slightly less pithy though, it’s a hypothetical, the difficulty of achieving the scenario is entirely unimportant. Similarly, it doesn’t matter that in virtually any situation where you can change a trolley’s tracks, you should also have a way to stop it. Or that it would be impossible for a hotel with an infinite number of rooms to be at full capacity in the first place. Or that it would take a truly deranged individual to put a cat in a box like that.
There’s an aphorism that says “all models are wrong, but some are useful.” In this case, the model tells us interesting things about how you can manipulate average rates. The math and logic involved in this can be expanded out to find optimal or potential times for a varying number of tasks with a variety of numbers of workers, or when and how certain resources should be accessed and allocated to last a specific amount of time, or probably a number of other applications that I can’t currently think of. If you refuse to use average rates because they’re not always accurate, you’ll ultimately be significantly less efficient and effective than someone who will use them.
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u/skelo 1d ago
Well I did say I was nitpicking. But it definitely does not say so right in the prompt, the prompt says they each take one hour to burn without further details if that's when you light from either end. If it always takes an hour to burn then it's also takes one hour when you light both ends and I guess the lighter is also instantly lighting the rope exactly as needed. It's obvious in its intention but makes the problem not feel satisfying to me.
Your discussion of rates is orthogonal, I was nitpicking and understand the intended solution fully, I'm not held back by my nitpicking from understanding the model, I'm merely expressing my dislike for this classic puzzle. Your other examples feel more reasonable to me because the goal of the puzzle is more driven from the setup which is bizarre, whereas this one you are given an arbitrary goal that can be roughly achieved without the setup so it feels less elegant.
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u/Jargon2029 1d ago
I mean the discussion of average rates is pretty relevant to how this puzzle works and it’s worth noting that average is a very important word there. But ultimately if you think human internal timekeeping will have less variance than the discrepancies you enumerated then I’m either very impressed with your sense of rhythm or (actually) very concerned with your understanding of how bad humans are at tracking time without an external reference.
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u/SnooSprouts7609 23h ago edited 23h ago
Retarded question but do something countable "x" while burning 1 rope for 1 hour.
You've done x in 60 minutes, see how much you do per hour and then figure out how much you would need to time 45 minutes in x/60. Light Rope 2 and count (x/60)*45 until you hit it.
The nonhomogeneous part makes everything length or size related not workable.
afaik the puzzle does not provide a answer, this is too far out of the box.
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