![]() Ergo, lit simultaneously at both ends, the rope is completely consumed in 15 minutes! However, it has the curious property that, in either direction, the first half of the rope (by length) burns in only 15 minutes. We have a "1 hour rope" - light it at either end, and it takes 1 hour to burn through. So do you have a method of for timing 45 minutes with such a rope? I believe you need more information about the rope before you can proceed, but since you have it before you start, any measurements needed can be made then. After all, we are told it is a 1 hour rope, not a "1 hour from one end" rope. If the variance is not continuous, it may at least be assumed that the changes have some symmetry. That being the case, it should burn at the same rate for either direction - assuming that the thickness varies in a continuous fashion. However, the puzzle statement explicitly states that the inhomogeneity in burn time is a result of varying thickness. It's true that this does assume that the rope at each place burns just as fast in one direction as it does in the other. 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 28630 times) RIDDLES SITE WRITE MATH! Home Help Search Members Login RegisterĮasy (Moderators: william wu, ThudnBlunder, SMQ, Grimbal, Icarus, towr, Eigenray) « wu :: forums - NONHOMOGENOUS ROPE BURNING » Wu :: forums - NONHOMOGENOUS ROPE BURNING ![]()
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