Lateral thinking IV: Two strings

[ayw]

 
 
You have two pieces of string. The only property known about the strings is that, if lighted at one end, a string will burn for one hour minute. The strings may differ in every other aspect, including length. In particular, the strings do not burn away uniformly in length with time.

Your task is to accurately measure 15 seconds using only the two strings (and some matches).

Spoiler:

This one is dedicated to Holmes.

 

[Holmes]

Hey man, thanks for dedicate me this, very interesting one.

But I have a few questions:

if the two strings are lighted in one end, the two of them will burn for an hour or just one?

And it might be silly, but I didn´t understad it very well: the strings have the same length?


Thanks again mate. 

[Sayumi]

@Holmes
Each of the strings will burn for one hour. But if you light both of them at the same time they will both be burned down after one hour of course.
They don't need to have the same length, material, colour, thickness or anything like that. They just burn for one hour each.

@awy
I never heard of this one before, it's quite interessting...
But is the task really to measure 15seconds, not 15minutes or one minute instead of one hour? I would know how to do that...
Well, I will just post my answer for the 15min anyway 

Spoiler:

1. Light both ends of one string and one end of the other string at the same time.
2. Wait until the string with both ends lit is completly burned down (it will be eactly 30min), then light the other end of the second string and start measuring the time.
3. When the second string is completly burned down exactly 15min will have passed since you lit the second end.

->The first 30min will have passed while the first string was still burning (it will burn double as fast with both ends lit), so you have 30min of the second string left. By lighting the other end of the second string as well you will divide these 30min by two and the amount of time it takes to burn down the rest of the string will be exactly 15min.

I really wouldn't have a clue on how to do 15sec but maybe someone will come up with an idea. 
Thanks for posting this....

[Holmes]

I agree with Sayumi, I directly say this so I don´t have to type samothing identical.

And of course, thanks for these, it keeps brains working. 

[ayw]

Sayumi: My mistake, I meant to write that a string burns one minute, not an hour. It would be hard finding a string that burns an hour.
Anyway, spot on, Sayumi!

Holmes: Light any one of the strings at one end and it will burn for 1 minute. (Of course, If you light both strings at one end at the same time, the two will also only burn for a minute. If you burn one string off first, then the other after the first has extinguished, then the total burning time is two minutes.) No, the strings don't have the same length. In fact, it doesn't matter what length they have; Nothing is known except that a each burns for one minute.

ps Holmes: Yes, they're a healthy distraction! 

[sstimson]

even though you already have an answer. I do have a question. Are you allowed to fold the string?

Later

[ayw]

even though you already have an answer. I do have a question. Are you allowed to fold the string?

Later

Yes, you can fold the string. You can set it alight anywhere you like. But remember, the strings don't burn uniformly, i.e. burning half the string doesn't necessarily take 30 seconds.


 

[Holmes]

Here´s my answer:

Spoiler:

If lighting and end of a string will take 1min, then if you light boths ends it will take half the time, 30 secs. So, first you light both ends ends of one and one end of thesecond one. When the first one is all burnt out it would have passed 30 secs, inmidiatlt after the first one is burnted out, you light the other end of the second one. The second one would have left 30 secs. to go, so if you light the other end only 15 secs. is neccesary to burn all the string. So when you light the other end of the second one, you can measure 15 secs.

It took me almost the whole night to think of this.

Lateral Thinking V is coming.

[ayw]

Here´s my answer:

Spoiler:

If lighting and end of a string will take 1min, then if you light boths ends it will take half the time, 30 secs. So, first you light both ends ends of one and one end of thesecond one. When the first one is all burnt out it would have passed 30 secs, inmidiatlt after the first one is burnted out, you light the other end of the second one. The second one would have left 30 secs. to go, so if you light the other end only 15 secs. is neccesary to burn all the string. So when you light the other end of the second one, you can measure 15 secs.

It took me almost the whole night to think of this.

Lateral Thinking V is coming.

Well done!
Looking forward to LTV

 

[sstimson]

even though you already have an answer. I do have a question. Are you allowed to fold the string?

Later

Yes, you can fold the string. You can set it alight anywhere you like. But remember, the strings don't burn uniformly, i.e. burning half the string doesn't necessarily take 30 seconds.


 

If that is true, then burning each end does not mean that 30 seconds have gone by. For that to happen at least one string must burn completely uniformly.
I show you what I mean

Let A = Fast burning B = Normal Burning and C= slow burning

Lets say the string looks like this: BBBBBAAAAA. If both ends are lite. that The fire should meet is the B section Or Even better say the string looks like this: CCCBBAAAAA then then the fire should meet in the b zone. It would still take a minute to burn all the string one way. but these kind of strings might burn faster or slower if started on both ends right?

Later

[Sayumi]

I show you what I mean

Let A = Fast burning B = Normal Burning and C= slow burning

CCCBBAAAAA then then the fire should meet in the b zone. It would still take a minute to burn all the string one way. but these kind of strings might burn faster or slower if started on both ends right?

Later

Not sure if I got right what your problem is but I'll try to explain 
Let's say that if you light your CCCBBAAAA on the C end end. It might reach B after 30sec. Then it necessarily has to take 30sec to burn down BAAAA. So if you light it on A end it also has to take 30sec to burn AAAAB until it reaches B. So if you light both ends one would burn down CCC and the other AAAAB, but both would meet at the red B after exactly 30sec (not in the middle of the string).

[ayw]

As Sayumi says it does indeed mean that the string will burn half the time when lighted from both ends.

The proof is simple: Imagine setting alight both ends of the string. After some time, the flames will meet at some point on the string, and the whole string will have burnt away. This must occur after exactly 30 seconds, because if it didn't, then the total burning time of the string would not be 1 minute.
(For example, if it occurred after 40 seconds, then the parts of the string either side of the meeting point would have burnt 40 seconds and the total burning time of the string would be 1 minute 20 seconds.)

Maybe this will help the "penny to drop": Imagine you burn a string from one side for 30 seconds, then extinguish the flame. No matter what burning rate the burnt string had, you will have exactly 30 seconds worth of string left over. Now imagine you had the string again and think of it as a composite of the two parts: the burnt part and the left-over part. Each part will burn for exactly 30 seconds, so lighting the string at both ends will burn off the whole string in 30 seconds.