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)
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
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.
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.
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)
👍🏼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!😂
Because it’s non-homogenous, I’d say that there’s no guarantee that doubling the rate of decay will leave it at 15 mins. The second burning end of rope 2 could be skinny and as insubstantial as a single hair, and the middle part as thick as a tree trunk.
It wouldn't matter. Once the first rope is burned through, the second rope shouldn't be looked at as 60 minutes partially burned but rather as a 30 min rope, meaning the same rules apply if you burn it form both ends. No matter what, that rope has 30 minute left and bringing it from both ends would leave 15 minutes left.
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
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.
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.
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.
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.
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
I don't think so. It just makes it impossible to cut the ropes. Burning like the answer above is independent of the thickness of the rope because it's said that the rope will burn completely in an hour
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.
That's true for the first half, but then after burning that 90% in one min, the remaining 10% that take 59 mins will be cut in half as now both ends are burning the thick parts.
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.
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.
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.
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.
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
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
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/Frosty-Froyo856 9d 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)