Fuse Timer Puzzle

[pdurrant]

This one's adapted from http://www.rinkworks.com/brainfood/p/discrete5.shtml

You like your boiled eggs to be boiled for exactly three-and-a-half minutes.

Unfortunately, you've broken your three-and-a-half minute egg timer, and the only other timing mechanism in the house are some slow-burning four minute fuses*. NB. I mean fuses that burn for exactly four minutes, not four fuses that burn for a minute each!

Unfortunately (again), you know that the fuses do not burn at a uniform rate, so you can't just cut one of them to a three-and-half minute length.

Can you time exactly three-and-a-half minutes for your egg using the four minute fuses? If so, how?

Oh - and spoiler tags around answers please. Many thanks to all of you who remembered without me reminding you.


*No, I don't know why you have four-minute fuses in the house either. And yes, you do have some matches as well.

[clarknova]

Spoiler:

Wouldn't you just light the first three fuses in succession to count three minutes, and then the fourth fuse at both ends to get it to burn for only 30 seconds?

I'd probably end up contacting the Chinese manufacturer of these timing fuses to figure out what math they used to calculate these non-uniform fuses' burn times.

[HarryT]

Originally Posted by clarknova

Spoiler:

Wouldn't you just light the first three fuses in succession to count three minutes, and then the fourth fuse at both ends to get it to burn for only 30 seconds?

I'd probably end up contacting the Chinese manufacturer of these timing fuses to figure out what math they used to calculate these non-uniform fuses' burn times.

Spoiler:

I think Paul means that you have "fuses that burn for four minutes", rather than "four one minutes fuses" .

[clarknova]

Originally Posted by HarryT

Spoiler:

I think Paul means that you have "fuses that burn for four minutes", rather than "four one minutes fuses" .

Ahh... I see. I re-read, and it seems you're correct.

[omk3]

Okay, after looking at this for some time thinking it can't be possible, or that I'm missing some special physics of fuses , here's my idea:

Spoiler:

We take 3 fuses and light them all at the same time.
We light fuse A from both ends. This should make the fuse burn in half the time, ie 2 minutes.
We have lit fuse B from one end only, but on the 2 minute mark, when A is burned, we light the other end of B too. The time remaining on B was two minutes. Now, with both ends lit, it will burn completely in one minute. We are now on our third minute.
We have lit fuse C from one end only, but on the 3 minutes mark, when B is completely burned, we light the other end of C too. The time remaining for C to burn completely would be 1 minute. Because it is burning from both ends, it will take half the time, so it will burn in half a minute.
When C is completely burned, we are at exactly 3 and a half minutes from when we started.

[HarryT]

Originally Posted by omk3

Okay, after looking at this for some time thinking it can't be possible, or that I'm missing some special physics of fuses , here's my idea:

Spoiler:

We take 3 fuses and light them all at the same time.
We light fuse A from both ends. This should make the fuse burn in half the time, ie 2 minutes.
We have lit fuse B from one end only, but on the 2 minute mark, when A is burned, we light the other end of B too. The time remaining on B was two minutes. Now, with both ends lit, it will burn completely in one minute. We are now on our third minute.
We have lit fuse C from one end only, but on the 3 minutes mark, when B is completely burned, we light the other end of C too. The time remaining for C to burn completely would be 1 minute. Because it is burning from both ends, it will take half the time, so it will burn in half a minute.
When C is completely burned, we are at exactly 3 and a half minutes from when we started.

Spoiler:

That looks right, but one can't help thinking that it would be a lot easier just to look at your watch.

[omk3]

Originally Posted by HarryT

Spoiler:

That looks right, but one can't help thinking that it would be a lot easier just to look at your watch.

Where's the fun in that?

[pdurrant]

Originally Posted by clarknova

Spoiler:

Wouldn't you just light the first three fuses in succession to count three minutes, and then the fourth fuse at both ends to get it to burn for only 30 seconds?

I'd probably end up contacting the Chinese manufacturer of these timing fuses to figure out what math they used to calculate these non-uniform fuses' burn times.

Sorry, the fuses each burn for four minutes, not one minute. Question changed to emphasise that each individual fuse burns for four minutes.

[pdurrant]

Originally Posted by omk3

Okay, after looking at this for some time thinking it can't be possible, or that I'm missing some special physics of fuses , here's my idea:

Spoiler:

We take 3 fuses and light them all at the same time.
We light fuse A from both ends. This should make the fuse burn in half the time, ie 2 minutes.
We have lit fuse B from one end only, but on the 2 minute mark, when A is burned, we light the other end of B too. The time remaining on B was two minutes. Now, with both ends lit, it will burn completely in one minute. We are now on our third minute.
We have lit fuse C from one end only, but on the 3 minutes mark, when B is completely burned, we light the other end of C too. The time remaining for C to burn completely would be 1 minute. Because it is burning from both ends, it will take half the time, so it will burn in half a minute.
When C is completely burned, we are at exactly 3 and a half minutes from when we started.

Yes, exactly right! Well done.

[pdurrant]

Originally Posted by HarryT

Spoiler:

That looks right, but one can't help thinking that it would be a lot easier just to look at your watch.

But no, no watches or other timing mechanisms are available.

You really ought to give your own answer before reading the spoilers — much more fun!

[obs20]

Am I along the right path?

Spoiler:

If I light a fuse at both ends it will bun for 2 minutes

[dreams]

I sure hope we have an unlimited supply of fuses, because I keep lighting them as I play with how to time subsequent burn rates.

[omk3]

Originally Posted by obs20

Am I along the right path?

Spoiler:

If I light a fuse at both ends it will bun for 2 minutes

Yes

[pdurrant]

Originally Posted by dreams

I sure hope we have an unlimited supply of fuses, because I keep lighting them as I play with how to time subsequent burn rates.

You may have as many as you think you need.

[dreams]

I couldn't figure this one out. I was able to start, but once again was lost.

Spoiler:

I had the control candle burning as I used subsequent candles and stopped and started them at various points related to the control candle. But I still couldn't get a way to figure out exact timing.