# Can you solve the two-fuse puzzle?

Originally published at: https://boingboing.net/2019/05/10/can-you-solve-the-two-fuse-puz.html

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Light both ends of one fuse, and one end of the other. When the the first fuse has burnt through in 30 minutes the second fuse is half-way through (30 minutes remaining). Light the second side of that fuse in order to halve the burn time to 15 minutes. When the second fuse has burnt out it’s time to stir.

30 min + 15 min = 45 min - stir baby stir.

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does “irregular consistency” mean they burn at irregular rates? like so you couldn’t just measure, divide into 60 & count off 45 segments?

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This was a simple one: Hit the bong 2 or 3 times and go get a pizza.

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My thought process was that you could use a full fuse to measure when the other is half done and sort of do what is the actual answer.

Also I’m having a small WELL ACTUALLY moment: if the fuse is “rated” to burn for an hour, is that rating inclusive of being burnt at both ends as that’s not what fuse is actually designed to do? “Burning from one end to another” is not the same as “burning from both ends to the center.”

I’m picturing going to lodge a complaint:
Me: SIR THIS FUSE WAS OFF BY A MINUTE.
Fuse Manufacturer: Well did you light it at both ends like a completely insane person?
Me: I CARE NOT MY POTION IS RUINED
Fuse Manufacturer: Please leave my factory.

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Lay out both of the fuses side by side. Light one at one end, and at the same time light the second from the other end. When the two burning fronts of the fuses pass each other, exactly 30 minutes have passed. Then move the remaining unburnt portions of both fuses so that they are side by side, as before one burning at one end, the second one at the other end. This time when the burning fronts pass each other exactly 15 minutes have passed.

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Correct, you can’t do that because the fuse won’t be burning at exactly the same rate the whole time, your only guarantee is that it takes exactly 1 hour for the entire fuse to burn.

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My thought process: “Is this a simple math/logic problem, or is the statement that I am a wizard with a long beard important? Oh well, guess I’ll look at the comments.”

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Use one of the fuses to calibrate something else that has a regular beat/cycle of unknown duration. Eg, water dripping at a fixed but unknown rate. Use information to time potion with second device. Discard extra fuse

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“Hey, you there! Do you have a watch? I’ll let you have this nice fuse if you let me time something for 45 minutes.”
“Does the fuse burn at a regular rate?”
“Well, no.”
“Sorry, no deal.”
“Would you do it for … two fuses?”
“I still don’t like it, but I am too intimidated by your long beard to refuse such a generous offer.”

-fin-

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Only possible if they are the same length, which isn’t clear from the instructions. It does specify that they burn inconsistently so you cant rely on an even burn length.

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That’s only true if both fuses are identical in their rates of burn – something the problem does not assert.

For example, assume fuse 1 is 12" long and burns through its first inch in 30 minutes and that fuse 2 (also 12" long) burns through its last inch in 30 minutes. After 30 minutes, the burning fronts of the fuses are still 10" apart.

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This is what I thought too, then I remembered the ‘irregular consistency’ part and thought that might be a problem.

But then, after thinking about it, this would still work. Let’s say, for example, you COULD time it and light one side of the fuse and let it burn for exactly thirty minutes. By definition, whatever is left over MUST be exactly 30 minutes worth of fuse. The lengths might be different, but the time is guaranteed to be 60 minutes. That being said, there’s no way, if you lit both sides at the same time, one side could burn for 25 minutes and the other side burn for 35 minutes. Regardless of consistency, you can’t tell where they would meet, but you can say that they meet after exactly 30 minutes.

If you lit the second fuse at the same time as the first, you’ll know then that there’s exactly 30 minutes left on the second fuse, and the same logic applies. They’ll meet halfway through, timewise. Again, you can’t tell WHERE they’ll meet, but they have to meet after exactly fifteen minutes.

So, yeah.
That’s it.

Blockquote

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Oh THAT’S what the detail about “burning inconsistently” is supposed to mean? I.e. you can’t use length?

This riddle is insane.

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You’re a wizard. Make the damned owl keep track of the time.

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Having that same concern my solution to this problem was to fold one fuse in half for 30min and the other in half twice (quarters) for the 15min.

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Forget the fuses. Leave, and then return just in time to stir the potion. If you are in fact a wizard, you will arrive exactly when you mean to.

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The burn both ends solution won’t work because of the irregular consistency.

You have to make a sun dial or some other sun based time measuring device. Once feel like the device is close to being correct, burn one fuse at a time to calibrate the device to measure exactly one hour. You can then measure 45 minutes exactly provided you knew what you were doing when you built your time contraption.

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Like a pendulum, made from one fuse and calibrated with the other fuse burning from both ends. Then you can time any arbitrary duration.

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