The solution presented in the book, as written, is wrong, at least in English (I can't speak for the original phrasing of the problem). This might be a dead thread, but it's one of the first hits on google, so maybe someone else will see this. Keep in mind that in theory you might need to ignite the remaining part infinite number of times (and also infinitely fast in the end, which would create a nice link with question 1) in case no 2 parts finish burning at the same time. The canonical solution to the problem is to start burning the rope from both ends and anywhere in the middle at the same time and then repeatedly ignite the remaining part after the other one has been burnt, anywhere in the middle, until the whole rope is burnt. On the other hand if they mean that the both halves should touch and the faster burning part will ignite the slower burning parts, this does not work either because the faster burning part would ignite the slower part in multiple places, leading to faster-than-15 minutes burning of the entire rope. If by folding they mean to combine them and create a new, shorter rope from these 2, then we cannot be sure what the burning time is for such a constructed rope. In common versions of the problem, each fuse lasts for a unit length of time, and the only operations used or allowed in the solution are to light one or both ends of a fuse at known times, determined either as the start of the solution or as the time that another fuse burns out.I had the same issue with the solution from the book. Visualisation of the smallest fusible numbers larger than 0, 1 and 2: 1 / 2, 1 1 / 8 and 2 1 / 1024, respectively (bold) Many other variations are possible, in some cases using fuses that burn for different amounts of time from each other. Once the first fuse burns out, 45 seconds have elapsed.Once the second fuse has burned out, 30 seconds have elapsed, and there are 30 seconds of burn time left on the first fuse.Light one end of the first fuse, and both ends of the second fuse.One solution to this problem is to perform the following steps: The assumptions of the problem are usually specified in a way that prevents measuring out 3/4 of the length of one fuse and burning it end-to-end, for instance by stating that the fuses burn unevenly along their length. 3 Lighting more than two points of a fuseĪ common and simple version of this problem asks to measure a time of 45 seconds using only two fuses that each burn for a minute.The fusible numbers are defined as the amounts of time that can be measured in this way.Īs well as being of recreational interest, these puzzles are sometimes posed at job interviews as a test of candidates' problem-solving ability, and have been suggested as an activity for middle school mathematics students. In recreational mathematics, rope-burning puzzles are a class of mathematical puzzle in which one is given lengths of rope, fuse cord, or shoelace that each burn for a given amount of time, and matches to set them on fire, and must use them to measure a non-unit amount of time. In theory, the second rope burns out in 15 s, giving a total of 45 s. Each time a segment burns out, a random point on the remaining rope is lit. The first rope burning out triggers lighting of both ends of and a random point on the second rope. An alternative solution with the second rope initially unlit. The first rope burning out triggers lighting of the second end of the second rope (blue arrow), burning it out in a total of 45 s.Ĥ. The standard solution with two ropes, initially the first with both ends lit and the second with just one. Lighting both ends burns it out in 30 s.ģ. ![]() ![]() Lighting one end (red line) of a rope (brown line) burns it out in 60 s.Ģ. Visualisation of the rope-burning puzzle, the horizontal axis denoting time elapsed in seconds and vertical axis denoting burn time remaining on a rope.ġ.
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