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A Short-Fused Conundrum: September 2022 Challenge Question

Posted August 31, 2022 12:00 AM
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You have two segments of TNT fuse. Each is rated to burn in exactly one hour; however, the fuses are not identical and do not burn at a constant rate. Some sections burn fast, others slow.

How do you measure 45 minutes using only the fuses and matches?

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#1

Re: A Short-Fused Conundrum: September 2022 Challenge Question

08/31/2022 7:54 AM

If you double 1 fuse over and light one end, it will burn in 30 minutes. If you double it again (4-ply), it will burn in 15 minutes. Double one fuse once and the other twice. Burn one first and then the other.

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#3
In reply to #1

Re: A Short-Fused Conundrum: September 2022 Challenge Question

08/31/2022 8:55 AM

"If you double 1 fuse over and light one end, it will burn in 30 minutes."

Why wouldn't the fast half still burn fast and the slow half still burn slowly?

Does the OP need to explain more about these fuses?

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#4
In reply to #1

Re: A Short-Fused Conundrum: September 2022 Challenge Question

08/31/2022 8:56 AM

That would work if the different sections with various rates of burning are spaced along the length of the fuses such that 1/2 and 1/4 of the length will burn in 30 min. and 15 min. respectively, but if the various rates of burning are randomly spaced, resulting in, say, 1/2 the length burning in less than 30 min., the other half burning in more than 30 min., then folding the fuse in half and twisting it into one shorter fuse will not average the rate to 30 minutes.

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#2

Re: A Short-Fused Conundrum: September 2022 Challenge Question

08/31/2022 8:46 AM

A TNT fuse burns at about 5 to 6 Km per second! So one of these fuses is about 20,000 Km long: this will require a lot of work.

Take one of the fuses and cut into 100 equal length pieces labelled 1 to 100; join lengths 1, 5, 9, 13... etc. up to 97 together: this should have averaged out the burn speed, and give you one 15 minute fuse.

Light the 1 hour and 15 minute fuses at the same time. The 45 minutes starts when the 15 minute fuse runs out, and, finishes when the 1 hour fuse runs out.

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#5
In reply to #2

Re: A Short-Fused Conundrum: September 2022 Challenge Question

08/31/2022 9:34 AM

I like it, but it's still guess work. There is no certainty that your given sampling and joining will result in a 15 min. fuse.

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#19
In reply to #2

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/03/2022 8:14 AM

Re: Fuse burn rate: That sounds like an extraordinarily fast burn rate you describe. Surely fusing is available with a slower burn rate.

In my early teens I went through a phase of building pipe bombs - to "soften up" enemy positions in the back garden. My father was an enthusiastic participant in this activity. Somewhere he obtained a length of fuse. It looked like an off-white piece of sash cord. You cut off the length needed. A 3-4" piece, when lit, gave us lots of time to get to cover - a very slow burn rate. Only the core of the fuse burned, leaving the heavy braided cover intact - so the strategy suggested by others here that the fuses in the problem could be cut into pieces and paralleled together to average out the burn rate is unworkable.

When we ran out of fusing we went to high-tech electrical detonation. We connected leads to a ball point pen spring, inserted the spring in the pipe bomb and ran the leads back to a toy train transformer. When power was applied the small spring glowed white hot - and boom!

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#20
In reply to #19

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/03/2022 9:15 AM

https://www.britannica.com/technology/explosive/Detonating-cord

Detonating cord (detonating fuse) resembles safety fuse but contains a high explosive instead of black powder. The first successful one, patented in France in 1908, consisted of a lead tube, about the same diameter as safety fuse, filled with a core of TNT. It was made by filling a large tube with molten TNT that was allowed to solidify. The tube was then passed through successively smaller rolls until it reached the specified diameter. In France the product was called cordeau détonant, elsewhere shortened to cordeau. Its velocity was about 4,900 metres (16,000 feet) per second.

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#21
In reply to #20

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/03/2022 1:52 PM

Then the fuses in the problem must be of the black powder type my father and I used back in the day.

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#28
In reply to #2

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/21/2022 2:37 PM

Laid out straight, 20,000 km would be around the opposite side of the world. Is there something that needed to be blown up with 2 fuses at the same time. Maybe it didn't need to be the opposite side of the world after all and could go 45min instead. A 1 hour fuse is a long time. Generally 30 - 60sec is good for most things I've been involved with. It gives enough time to get somewhere safe and not too long for someone new to turn up and put themselves in dangers way It would have to be fairly significant to lay out 20,000km of fuse

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#29
In reply to #28

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/22/2022 5:29 AM

These are logical challenges rather than practical ones, but, you're right: some of the practical implications of this one are problematic/entertaining.

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#6

Re: A Short-Fused Conundrum: September 2022 Challenge Question

08/31/2022 10:54 AM

Simultaneously light both ends of one fuse and one end of the other. At the moment the fuse that has been lit at both ends burns out, 30 minutes have elapsed. At that moment, light the second end of the other fuse. At the moment it burns out, another 15 minutes have elapsed, for a total of 45 minutes. This method compensates for any and all variations in rates of fuse burn, random and non-random along the lengths of the two fuses.

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#7
In reply to #6

Re: A Short-Fused Conundrum: September 2022 Challenge Question

08/31/2022 11:56 AM

GA

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#8
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

08/31/2022 4:22 PM

Very good, I agree. Good answer.

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#9
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

08/31/2022 7:14 PM

Thanks to both of you. I initially also thought that some info must be missing. Then after some rumination the solution just popped into my head.

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#13
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/01/2022 4:13 PM

Here is my mental picture. Red lines represent the position of the flames on fuse 1 and the green (*), the position of flames on fuse 2.

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#16
In reply to #13

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/01/2022 8:55 PM

Sure. Rated time duration of the two fuses on the Y-axis. Individual and total elapsed burn time on the X-axis. Simpler than my visualization. I saw, in my mind's eye, fuse 1, lit from both ends, burning out in 30 minutes at an indeterminate point on its length; and at that moment, fuse 2, which had been lit at only one end, having an indeterminate length remaining, but that indeterminate remaining length would be rated at a 30 minute burn time, so lighting the 2nd end of fuse 2 at that moment would result in it burning out in 15 minutes at an indeterminate point on its length.

Not sure how my thinking could be pictorially represented, since I was thinking about indeterminate points on fuses of indeterminate lengths, but nevertheless placing time stamps on those indeterminate points and lengths.

However, at least I know my thinking process. When savant Daniel Tammet is asked how he does his astonishing calculations, he doesn't seem to know. He will say something to the effect that he sees numbers in different sizes, shapes, and colours - but this gives us no insight as to how he knows, in a moment, whether some large given number is a prime number or not.

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#17
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/01/2022 9:22 PM

The fact that the fuses don't burn at a steady rate is a red herring.

If one flame burns a fuse for an hour, 2 flames will burn it in 1/2 hour.

If you have 30 minutes left with one flame on a fuse, if you add a second flame, it will burn for 15 minutes.

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#18
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/02/2022 8:52 AM

A very good red herring, since in actual practice a fuse is never lit from two ends, so that possibility is overlooked, which results in various failed cut and paste fuse configuration strategies wherein the fuse or fuses is/are still lit from one end.

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#10
In reply to #6

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/01/2022 9:59 AM

Good Answer but a couple of questions come to mind...

How do you know where to connect it to the TNT?

How many tons of TNT is being set off that you need to be 45 minutes away!

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#11
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/01/2022 11:05 AM

"How many tons of TNT is being set off that you need to be 45 minutes away!"

Since the question is talking about a TNT fuse as opposed to a fuse for TNT: but could be, then several tons. since TNT fuses burn at between 5 and 6 Km per second; a 45 minute fuse would be about 15,000 Km long.

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#12
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/01/2022 3:12 PM

How things have changed. In central Ontario, when I was a kid, any adult could go into a country hardware store and buy TNT. All that was required was to sign a pledge that it was for farm use.

My father bought a wooden box of TNT to blast out some bedrock for a boathouse at our summer place. He loaded the box into the trunk of his car and away we went (to blow up the Parliament buildings for all the store proprietor knew). I think it was TNT. Inside the sticks was a yellow brown substance that had the consistency of a banana. The blasting cap, electrically detonated, was about the size of a .22 short cartridge and was pushed into the end of the stick. He placed the sticks in holes he had drilled into the granite, covered everything with a pile of heavy brush, and set them off with a car battery from a safe distance away. Great fun!

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#30
In reply to #6

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/23/2022 11:25 AM

*Ding, ding ding*

Winner, winner, chicken dinner.

(BYO chicken dinner.)

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#14

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/01/2022 5:37 PM

My thoughts would be to cut the fuses into 4 equal pieces providing 8 pieces.

Mix then up then parallel 3 and connect end to end to another 3 parallel fuses and finally connect the remaining 2 in parallel to the the end of the last 3. Each section should be close to 15 minutes of burn time giving a total of 45 minutes.

Of course the fuses can be cut into half again and connected into the series parallel arrangement.

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#15
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/01/2022 7:30 PM

There is no certainty that the cutting and random selection of the cut pieces into the configuration you describe would yield sections with 15 minute burn times. Each three piece parallel section will burn at the rate of the fastest leg - like an electric current following the least resistive path. Conceivably your construction could burn up in a few seconds.

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#22
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/05/2022 5:28 PM

GA

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#23

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/06/2022 7:45 AM

Wouldn't it be easier to use a sextant?

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#24
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/06/2022 11:00 AM

Not if you don't want to be anywhere near the event which is triggered when the timer matures:-

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#25

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/08/2022 6:45 AM

I think it is more simple - just fold both fuses 2 times and lit one end of first - 30 min, . Then after first half burn, at the same time lit the other end. When the flames meet, there are another 15 min, and at the same time lit up the first end of second fuse. Then the flame is in the middle, you will have 45 min.

PS: in the original riddle, there is no mentions of "fragmented fuses burn faster or slower sections"!

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#26
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Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/08/2022 10:01 AM

"You have two segments of TNT fuse. Each is rated to burn in exactly one hour; however, the fuses are not identical and do not burn at a constant rate. Some sections burn fast, others slow."

By these problem specs, one-half of each fuse could burn in one minute, the other half in 59 minutes. Would your method work if that is the case?

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#27

Re: A Short-Fused Conundrum: September 2022 Challenge Question

09/13/2022 9:59 AM

Often, with these monthly challenge questions, silly solutions are also proposed. In keeping with that tradition:

Tie a weight (a stick of TNT will do) to the end of one fuse. Suspend it from the other end and swing it, pendulum fashion. Light both ends of the other fuse, and as it burns count the oscillations of the fuse/stick-of-TNT pendulum. When the lit fuse burns out, take note of the number of pendulum oscillations, multiply by 1.5, and allow the pendulum to continue swinging until that number of oscillations has been reached. Forty-five minutes will then have elapsed.

A bonus of this method is that since the oscillation rate, the period, of the fuse/stick-of-TNT pendulum is now known, it can be used as a general purpose timer.

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