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I have this riddle:

You have two fuses. Both fuses will burn completely in one minute, but they burn uneven and differently. Can you with the help of these two fuses measure exactly 45 seconds? Can you measure 10 seconds?

This post describes how to do 45 seconds:

Puzzle : There are two lengths of rope ...

But what about 10 seconds? I do not have the answer, so it may be that it is not possible. But then there has to be an argument to show that it is not possible? By using the argument in the link you can measure 15 seconds(from 30 t0 45). So maybe it can be solved by subtracting 5 seconds from these 15 seconds in some way. But maybe it is not possible.

This problem is from the first chapter in an introductory book about logic.

user394334
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  • This shows how to do 50 seconds: https://www.youtube.com/watch?v=z7LhQrZdpIc – Gerry Myerson Sep 23 '21 at 11:12
  • @GerryMyerson Thank you, but I think that solution is wrong. If we were able to get 20 minutes we would have solved the problem. But the way he gets 20 minutes in the solution seems wrong. Because he starts by lighting 3 flames, if you were able to have 3 flames all the time, it would work. But the way he explains it seems to give us a probem: He talks about burning from one end, and in middle: we could get the situation that the part of the rope with 1 flame burns out first. Then you are left with a rope burning at both ends, if you add a flame in the middle, then you actually add two flames. – user394334 Sep 23 '21 at 14:24
  • And then you are left with 4 flames. It seems that some comments of the video also mention this. – user394334 Sep 23 '21 at 14:29
  • A "mathematical" way may be to keep cutting the rope and let there be 3 flames at all times, then it would be 20 minutes in the limit. But this may entail an infinite number of cuts and lightings. If we start this with the 30 minute algoritm for the other rope we get that it is 10 minutes left when the 20 minutes is over. But I do not know if we are allowed to cut the rope, and I do not know if we are allowed to do an infinite number of operations. – user394334 Sep 23 '21 at 14:35

1 Answers1

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This way could be inefficient and impractical, but if you cut a fuse into enough pieces so that you could have 6 places burning at once, you would be able to measure $\dfrac{60}{6}=10$ seconds.

PiGuy314
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  • How. Considering that you don't know the burn rate of different parts of the fuse, how would you measure ten seconds if the pieces burn at $1,1,1,1,1,55$? – Moko19 Aug 31 '22 at 12:16