Thread and lighter. (Two strings and a lighter - 2).

Question

But it is more difficult for you: After an unsuccessful experiment from the previous task , we have only one thread left. It still burns for an hour. It is necessary to measure 15 minutes. :)

Prizes are not allowed. Current thumbs up all correctly answered, a check mark to the first, 20 points from me personally, if strict evidence is presented.

UPD : Thank you @ Asen2 for the comment. The problem has a solution, at least at the level of the algorithm. Just in case, I note that the uneven burning is finite. That is, instantly 99.9999% of the thread can not burn, leaving for the remaining 0.0001% the whole hour.

UPD : burning rate changes quite smoothly.

UPD : the solution has already been published. It is better than what I wanted to offer. Therefore, a bit of points went and @nike. I am waiting for strict evidence. (I already did, that's why I awarded Nike)

Since the thread burns unevenly along its entire length, I think that it can be proved that the problem is unsolvable.
Or folded 4 times and weakly twisted will ensure synchronous combustion of their parts?
@knes I correctly understand that uneven burning is some instantaneous value?
That is, can it be that the thread burns quickly, slowly, quickly and it is not deterministic (except for the fact that the entire thread burns in an hour)?

nopster nopster 76 five · Accepted Answer · 2012-07-20T12:55:39

we set fire to the thread at the beginning, at the end and approximately in the center. We wait until one part burns out and we set fire to the center of the thread that is still burning, and so on until the thread burns, the main thing is that the thread burns all the time in 4 parts, after all the parts burn out, it takes 15 minutes

See the answer @nike, we do not need to look for the middle.
@Spectre, I answer here: in the first case, you have two burning points saved until the entire rope burns.
In this case, you have 4 places of burning turn into 2, if one of the parts burns out.
@nike and @nopster suggested how to save 4 points of burning to the very end.

nike nike 51 one · Answer 2 · 2012-07-20T12:56:41

It is necessary to set fire to the thread at both ends and in any third place. As soon as one of the parts burns through, we ignite similarly the remaining part. And we do it until the whole thread burns down. 15 minutes

Perhaps you `re right. I'll check now. If yes, then @nopster was the first. =) - knes

temoffey temoffey 345 2 22 · Answer 3 · 2012-07-20T12:43:48

We set fire to the thread from two ends, and from the middle. As an option, fold it in half and set fire to the resulting double thread from both ends. As it burns down - 15 minutes passed.

temoffey

345 2 22

The problem is that the two resulting pieces do not necessarily burn an equal time. More carefully: the speed is uneven. - knes
This is the most obvious option, but it does not suit the TSA - Specter
Perhaps as one of the pieces burns down, set fire to the middle in the middle - temoffey
Oh, warmer. So, set on fire, then what? - knes
Although a double thread folded in half, and rolled up with a rope, will exclude the difference in burning rate of individual threads ... - temoffey

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Answer 4 · 2012-07-20T12:50:21

We divide the thread into many, many parts, mix these parts, divide into four groups of equal parts by the number, we light each of them. when the two parts burn out, we wait a little bit (or after the third part burns out) - about 15 minutes has passed. Although, in reality it will not work - the rope, divided into many parts, will burn faster than usual. And the lighter does not divide the rope, but we do not have scissors.

caravaneer

1,154 6 12

Nice try. But even if you had scissors: what if, by dividing the rope in this way, you would get heaps with sharply different contents? How do you know that the “little bit” that you have waited is sufficient? Is it possible to somehow increase the accuracy of your decision? - knes
Perfect solution! I will slightly reformulate (@knes search for errors))): We divide the thread into infinitely many identical parts, absolutely randomly choose every fourth part (that is, choose one out of four, and ignore the remaining three), add them into one thread and ignite. Because there are infinitely many parts and we chose them absolutely by chance, then this thread will burn FOR EVERYTHING 15 minutes. - Alexey Lobanov
> Because There are infinitely many parts and we chose them absolutely by chance. The probability distribution of the burning time will have the most accurate maximum at a point of 15 minutes. However, it will not save you from the most significant mistakes. There is a nonzero probability in this way to select only slow or fast pieces. - knes
The decision above is absolutely theoretical and has nothing to do with practice! - Alexey Lobanov
@knes This non-zero probability takes place if there are a finite number of pieces, but there are infinitely many! Therefore, if it is non-zero (as it will be on the wall), then it is scornfully close to zero. - Alexey Lobanov

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Answer 5 · 2012-07-20T13:08:52

The denial of popular opinion "Light a thread at both ends and in the middle"

[|] ----------- |----------- [|] ----------- |----------- [|] 5мин. 10мин 15мин 30мин

[|] - arson sites

in five minutes we will have:

 [|] |----------- [|] ----------- |----------- [|] < 5 мин 10мин 25мин

after another five (the second half of the thread will remain, although the first will burn in less than 5 minutes, since it will burn at both ends):

 [|] | [|] ----------- |----------- [|] 5мин 20мин

after another 5, 15 minutes will pass, but the most resilient piece will still burn

 [|] | [|] |----------- [|] < 15мин

Thank you. =) But according to the rules, I can’t put a thumbs up.
What is really there can be easier: [|] 2 minutes [|] 58 minutes [|]
It is easier to disprove - they took the thread evenly thick on the left and uniformly thin on the right: ==== ---- .
Let the left part burn in 45 minutes, the right - in 15 minutes.
Lit in the middle and from two ends - the left side will burn in 45/2 minutes, the right - in 15/2 minutes.
If the burning rate depended on the thickness, we would have managed to measure this thickness.

obivan obivan one · Answer 6 · 2012-07-20T12:48:08

Light a thread at both ends and in the middle?

Thread and lighter. (Two strings and a lighter - 2).

6 answers 6

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