Did anyone else click on this one expecting the kind of fuse problem that can be correctly* solved by shoving either pennies or bolts into however many spots the constraints of the puzzle make it seemingly impossible to fill?
Because I sure did.
2 Likes
This is clearly the correct answer. Turns out it’s one of those lateral thinking puzzles after all.
8 Likes
Because irregular consistency could mean anything. You have to make an assumption on the burn rate (like you did), and that almost certainly will be wrong.
You need to find or build a consistent time guage, then find how long the consistent guage takes to go an hour, then use math to back into 45 minutes. The riddle is to think out of the box in the way the fuses are applied.
You beat me to it. And as a bonus, you still have 1 fuse left.
A few other solutions:
- Build a sundial by hanging one fuse.
- Have your two assistants alternately drop the fuses from a known height (creating a clock).
- Rent a watch for one or two fuses.
- Bet some dude with a watch one fuse that he can’t time 45 minutes exactly.
- Steal a watch from someone you tied up with a fuse.
- Build a pendulum … which you use to hypnotize someone with a watch into timing 45 minutes for you.
- Send a quipu message asking your Incan buddy for a water clock.
- Go on BoingBoing and ask someone to solve your problem.
7 Likes
Folks should watch the video because he answers a lot of these questions. Before he gives the answer he says, “Do you give up? Are you ready for the answer” so you can stop and think about it for as long as you like before finding out the answer.
1 Like
Place a glass vessel of known volume above the first fuse. Burn the fuse, trap the smoke, and mark the volume used by the smoke. Empty container of smoke and fill up with water to determine how much volume is used by the smoke. Reduce the equivalent volume in water by 1/4 and mark the volume on the vessel.
Light the second fuse and capture the smoke. When you reach that new volume of smoke, 45 minutes has passed.
6 Likes
Trade the fuses for a stop watch at a pawn shop.
5 Likes
But the total burn length is always 1 hour - so regardless of the distribution of the irregularity, the total burn length will be 1 hour over the whole string. Burning from both ends works - it doesn’t matter where along the string the burned ends meet, but when they meet - it will always be 30 minutes, even if the “midway” point is an arbitrary point along the string.
There’s no real assumption, as the defining information is provided in the riddle. The lateral thinking comes from thinking of time as a dimension to an object, rather than length, in my mind.
9 Likes
Hmm without looking at other answers yet, I say:
Light both ends of one fuse. As soon as it burns out completely (30 minutes) light both ends and the middle of the second fuse which should burn out in 15 minutes. I’m thinking this should work regardless of irregularities because we aren’t measuring anything except “completely burnt.” Even though we pick the middle in the second case, that’s just a convenience and not really necessary. Any point will probably work. What matters is that ALL of the fuse burns.
Aha. So the real answer is slightly simpler than mine, but would mine work?
2 Likes
Algebra:
L: length of fuse 1
Light at fuse 1 at both ends. (Light fuse 2 at one end.)
M: distance from left end at which flames meet.
tl(x): time for left flame to reach x
tr(x): time for right flame to reach x
tl(M) = tr(M)
but we are guaranteed that tl(M)+tr(M) = 60 (assuming fuse burns at same instantaneous rate in both directions) so
tl(M) + tr(M) =60
therefore
tl(M) = tr(M) = 30.
Now light other end of fuse 2, which has 30 mins left, guaranteed. Repeat argument above, halving the times.
There’s probably a way to frame this using the intermediate value theorem, but I can’t be arsed.
What’s more interesting is the notion of irregular consistency. How does the fuse ‘know’ to speed up burning if it is behind schedule, or to slow down if it is ahead of schedule? It can’t, unless you live in a world of sentient fuses, which might be the case if you have wizards etc. Maybe the fuse manufacturer produces fuses with erratic instantaneous burning rates, but it can integrate the rate to cut the fuse at the right length to guarantee one hour total burn time.
3 Likes
I’m not going to pretend that I can work out the maths for this given that I’ve not done any real algebra in 20 years and how drunk I am (autocorrect has proven it’s worth today I swear)
I think the more interesting question really is: how did the manufacturer of the fuse guarantee that the entire fuse length burns in one hour, given that their manufacturing process makes fuses of an irregular burning rate?
7 Likes
Alas, we cant assume that since its explicitly stated that the fuses have erratic burn rate.
How does the manufacturer know that the fuses will burn through in an hour? Perhaps the manufacturer weighs the amount of combustibles and adjust the amount of filler. Maybe there is a way to measure some inherent property that tells the manufacturer what the burn duration will be. Perhaps just through years of trial and error they perfected a one-hour burn time even if they dont know why (in industry this is called black magic). Or since this world has real wizards, maybe they have a wizard working in the manufacturing process ensuring proper quality.
1 Like
Blah blah
die hard with consumption
Just to be clear. I have not assumed a constant burn rate through the fuse. What I (and others, implictly) have assumed is that the instantaneous burn rate at position x for a flame burning from left to right is the same rate at the same x for a flame burning from right to left.
1 Like
I thought the solution would be something like cutting the beard and make new fuses out of the hairs. Then use the irregular-fuse to time how fast the beard-hair-fuses burns.
2 Likes
I think that’s a perfectly reasonable assumption, otherwise I can’t see how the fuses could be guaranteed to burn for exactly one hour: they could surely only be guaranteed to do so if you lit them from a specified end.
Well, it’s a constraint of the puzzle. We cant suspend constraints that dont agree with our experience or dont pass the smell test. This puzzle involves wizards too.
If the manufacturer had decent QA processes in place, they would’ve burned each fuse before it left the factory to make sure it worked as advertised.
2 Likes
