The Burning Ropes Problem - a fun brain teaser
Both of them are different sizes, different length and each of them is also not uniform, different densities and all however both of them if you light them up, take exactly 1 hour to burn all the way through. So given these two pieces of ropes, how will you measure an interval of time that is exactly 45 minutes? And the rules are obviously no Googling for an answer. It's an honor system
Shahnaz Ahmed
@bookishpodcast · 0:55
So that's what I'd do. I'd measure each rope and go three quarters and burn it for three quarters of the time. But that doesn't seem like the right answer. It seems to, you know, it seems like I'm not even giving you an answer. So I don't know. So then I'm going to just say, I have no idea
Shahnaz Ahmed
@bookishpodcast · 0:15
Or just set a timer for 45 minutes. And there you go. When the alarm goes off, there's exactly 45 minutes. I mean, that has nothing to do with the rope. But that's the other thought I came up with
When the first rope completely Burns out, 30 minutes would have elapsed, and at that exact point, stop the second row from burning and then fold the second rope into half of the remaining of whatever is left over. Just fold it into half, and then again burn it from one end, and when it reaches the halfway Mark, extinguish the flame so that would give you 45 minutes
I just parted a gaping big loophole in my own answer because it looks like I have very conveniently ignored the time lapse involved or the time delay involved in folding up the a second rope and setting it a light again. So I guess that solution ain't working. Doesn't add up. No, it's
Shahnaz Ahmed
@bookishpodcast · 1:05
Hey, Ramya, just when you are about, you know, the first rope you burnt at both ends, right. So that's half hour. I like that. I like that. So the second rope, just when it's getting to the point of where the first rope is going to get burnt up, you can burn the other end right at that spot. It burnt out. Boom, burn it, burn the other end. And then you have your exact 15 minutes there. Yeah
Using a timer would have been much more easier. I agree. And I'm sure given a chance, we both would have, you know, opted for that, especially me, given how crazy I am and how bad I am with numbers. But then this time I just push myself. I'm like, yeah, I can think out of the box as well. So let me give it a chance. But Unfortunately, I just couldn't get it. I let's see
Shahnaz Ahmed
@bookishpodcast · 0:22
Rami. I'm holding the rope in place. I got it down. Measure it halfway. Cotton plier with a clip. And there you go. Boom. Rope burning from one end from another end. You're still holding it. Not the rope, but you're holding it with a cotton plier. Fire. Ask the dentist. She knows that answer. See, at least I got one answer. Right? Haha
Hey, merely human. The assumption you have made in your solution is that each 15, like each quarter segment of the rope, Burns at a uniform rate. So each quarter segment is 15 nets. That is not correct. The rope is of uneven density and even thickness. So parts of it burn faster. Parts of parts of it Burns. So just by measuring kind of a quarter segment of the rope, you can guarantee that that particular quarter segment will burn in 15 minutes