I got a MENSA riddle in my email and wanted to present it to all of you to see if you had any other solutions then mine. Please make your text color white so you dont spoil other answers ;).

Here is the riddle:

You have two lengths of string, which although they are not the same length, will each take exactly 30 minutes for a flame to burn from one end of the string to the other. The strings do not burn evenly, so the position of a flame, as it burns through a string, will not afford you any specific knowledge of how much time the string has been burning for. All you know is that it takes exactly 30 minutes for a flame to burn from one end of each string to the other end. How can you use these two strings and matches to measure out exactly 45 minutes with almost perfect accuracy?




Highlight to see what my answer is:

I had alot of ideas, but the only one that I couldnt disprove was this one. If you were to burn one string from only one end, and then when that string finished burn the other string from both ends, the first one would burn for 30 minutes and the 2nd one would burn for 15. No matter if the 2nd string burned evenly or not, the flames would still meet in the middle amount of time it takes to burn the string--hence 45 minutes, nearly exactly.(minus reaction time to lighting the strings.)

what about using half the other string that would be 15 minutes, tying it to the other string. that way it would be 15 minutes?

I did not look at your answer yet... The key is the fact that the string has an average burn time of 30 minutes.

The best answer (but still not guaranteed to work) is to fold the second string in half and attach it to the first string.

Me :D

Take string I and string II (bend it perfectly into two) -
then start string II burning as I is burnt out
?maybe burn from the 2 waggling ends - or from the bent centre -
and when string II is burnt out -
45 minutes (30 + 15 mins) will have elapsed.

-<-

Suggestion of solution in white as per Speedo request in #1.

what is the surface that these strings are on, maybe the longer one could be positioned in a way that is more vertical to the shorter one and that would cause the flame to burn it as fast as the other one, maybe it is all about position? Can't really think too long now the dexedrine has worn off LOL

umm, no clue on the surface, that is all the detail the email gave me. i considered sb_uk's idea of burning the 2nd one from the center, but i dont think that would work because the string doesnt burn evenly-- if you burn it from the center, i believe it would burn faster because it has 2 directions to go, but you would have no way of knowing how long it had been burning when it went out because it doesnt burn easily, since each direction of the flame would be exposed to different sides of the string, yet when one side of the string finished burning it would be unable to help the other side of the string(which had the harder path to burn) finish its side--so it could burn longer, could burn shorter, but we would have no way of knowing how long or how short.

How can you use these two strings and matches to measure out exactly 45 minutes with almost perfect accuracy?
Why would I do that when I can just use a watch? :p

If lighting one end takes the flame 30 minutes to get to the other end, then lighting both ends of a string will cause the two flames to meet at 15 minutes. It would not necessarily be at the middle though.

To do this, you would have to attach the two ends of one string to one end of another... such as this...


/------\
------------+ |
^ String 1 \------/
(30 min) ^ String 2 (15 total)
^ Both ends of string tied here...


Note that this is not the same as cutting a string in half. The second string should be looped so that the two flames burn independently.

Proof:



String:
|-------------------------|
(30 minutes)

No matter how it is broken down....
|-------------------------|
********************+++++++
| 15 | 15 |

Or
*****++++++++++++++++++++++
| 15 | 15 |



For any point on there that is declared as 15 minutes, the rest of the string must be also 15 minutes, because the total time can't be anything other than 30. So if two flames burn toward each other, they will always meet at the same time (obviously because one meeting the other depends on the other flame, and they were lit at the same time).

the problem lies in the fact that the string has a non-uniform burn rate:

for example: the first half of the folded string might burn in 10 minutes and the second half of the string might burn in 20 minutes yielding a total burn time of 30 minutes.

Folding the string and lighting it in the middle yields a burn of either 10 or 20 in adition to the 30 minutes of the first string

The ONLY way to get a burn time of exactly 45 minutes for two strings is to fold the second string into a loop, so that all of the second string burns completely in 15 minutes.


Me :D

You post it as a riddle to a bunch of ADDers and by the time they get bored with all the different posibilities ,go outside for a smoke and use the matches to light a cigerette.

By the time your done and come back inside to the computer 45 minutes will have elapsed and you will move on to the next post as theres no way to prove your theroy anyway

nah, the theory can be proven with math, but finding 2 strings that take exactly 30 min to burn unevenly is a challenge...

It's easy: Light a string. Using your watch (which is in no way prohibited by the riddle), wait 15 minutes. Light the second string. When both strings have burned completely, 45 minutes has elapsed.

How can you use these two strings and matches to measure out exactly 45 minutes...


actually it is kind of restricted--inherent limitations. i am wondering though if that sentence means two strings and two matches, or 2 strings and an unlimited supply of matches...

You had the right answer from the beginning.

Light one string, when it burns out light the other string from both ends.