Since the rope is non-homogenous, and possibly asymmetrical, it's quite plausible that sections of it will burn faster in one direction than the other. This conclusion is not purely deductive, but rests upon an assumption about the physical properties of the rope: namely that each section of the rope burns at the same rate in both directions. Quote: You know that it takes an hour to burn the whole rope, and half that time is gone, so the remainder of the rope has to take an additional 30 minutes to burn. You're right, i'd better be more careful next time. When their digits are reversed? ' - Anonymous You know that it takes an hour to burn the whole rope, and half that time is gone, so the remainder of the rope has to take an additional 30 minutes to burn. It has to be a thirty minute rope, no matter the inhomogeneity. I like the kind of awnser Evan gave, but i don't agree it is 100% correct because after the first rope finishes burning you can't say rope 2 that remains is a 30 min rope, since it is non homegenous.īoldly going where even angels fear to tread. Very elegant - and it works, if not 'easily' than at least without any gotchas. By splitting it up, you give it a larger surface area, exposing more of the rope to the open air, and thus causing it to burn faster. The idea of separating the rope into small pieces has one serious drawback: it will change the overall burning time. I doubt you could rely on homogenizing it yourself. It's likely the ropes are non-homogenous because they're made of multiple different materials, some of which burn faster or slower than others. Burn three of them one after the other, and you have 45 minutes. Make a big pile, and (in this case) divide it into fourths. Use your teeth, or your pocket knife, to break it up into small, uniform pieces. « Last Edit: Dec 10 th, 2002, 12:18pm by william wu »Īctually, under the terms of this question, you can time any rational fraction of one hour using only one rope. When you light this rope on both ends it becomes a 15 minute rope allowing you to time 45 minutes. After 30 minutes of burning from one end on the second rope, you are left with a 30 minute rope. The first rope when lit at both ends only take 30 minutes to burn. Solution: Light both ends of one rope and one end of the other rope on fire, when the first rope is done burning, light the other end of the second rope. Topic: NONHOMOGENOUS ROPE BURNING (Read 28739 times) RIDDLES SITE WRITE MATH! Home Help Search Members Login RegisterĮasy (Moderators: Grimbal, william wu, Icarus, towr, Eigenray, SMQ, ThudnBlunder) « wu :: forums - NONHOMOGENOUS ROPE BURNING » So rather than 30 minutes, Rope B will completely burn in 15 minutes.Īdding up the 30 minutes it takes to completely burn Rope A, and the 15 minutes it takes to completely burn the remaining half of Rope B gives us 45 minutes.Wu :: forums - NONHOMOGENOUS ROPE BURNING This will double the rate at which Rope B burns. Rope A will take twice the rate of Rope B to burn, which means, Rope A will take 30 minutes rather than 60 minutes to burn completely.Īt the time Rope A burns completely, Rope B will have 30 minutes remaining to burn.Īt this point, we proceed to burn the other end of the Rope B. Let's label the ropes as Rope A and Rope B.įirst, burn both ends of Rope A, and at the same time, burn only one end of Rope B. How can you measure exactly 45 minutes by burning the ropes? For instance, if one end of the rope is lit, it may take 5 minutes to burn the first half of it, and 55 minutes to burn the second half. But the ropes do not burn at a constant rate, so you do not know that half the rope burns in 30 minutes.

Each rope takes exactly 60 minutes to burn completely. Objective: There are two ropes and a lighter.

You half to burn the rope