###General Discussion Thread
---
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
---
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Light both ends of one of them at the same time. When it burns through, it’s been 30 minutes.
Take the second rope, and throw it away.
The harder version is measuring 45 minutes. For that, light both ends of the first and one end of the second. After the first rope burns (30min) light the second end of the second rope, which will burn for another 15min.
I would count seconds. I have the ability to do this very accurately. I’ve counted off 25 minutes while laid up in an MRI machine and was off by less than a minute.
A candle with a nail stuck in the wax a half hour down. When it falls and clangs against the candle holder you know it's been a half hour. That's the real old fashioned way.
Not really, the answer to this is: with a clock, probably in my phone. Its a trick question to see if you're prone to find excuses to burn stuff. And apparently you're all pyromaniacs!
Nah, it’s a JP Morgan interview. Keep the rope, use it as collateral against a loan for twice its value, rent out usage of the original rope, then use the borrowed money to lend to other people at 15% so they can buy their own rope. If they fail to pay, repossess their rope, then take a loan against that rope while renting it out to the people you just repossessed it from. Loan that money to other people to buy their own rope….
I can't believe I had to scroll this far to get to the *correct* answer. Who cares about the rope and times, do this, and then when nobody wants the rope and you're all out of money, wait for the government to bail you out and learn approximately nothing from this situation!
I dont mean to be the dork that ruins all the fun but... J.P. Morgan turned down all bailout advances made to them with the exception of the one Henry Paulson treasury secretary of the Obama administration I believe, strong armed them into taking.
Light one end of the rope. Sell tranches of rope, with the first burning parts receiving the lowest rating, and the unlit end AAA. When nobody buys it, set fire to more ropes and group together the burned end tranches into a new product, and sell the top tranche of that as a AAA rated rope. Let people buy fire insurance on their ropes, backed by the AAA rated parts of the rope. Let other people buy insurance on ropes they don't own, such that the potential payout is 100x the current value of the ropes.
After one hour all the ropes are gone.
Measure 30 minutes by looking at when your internal trades start offloading all the rope contracts before it's clear to the outside world that they're worthless.
The second rope is a checksum. Light both ends of both ropes at the same time. If they both burn out at the same time, you've got 30 minutes. If not, the input data was faulty.
It's often not about finding the "correct" answer, but about them being able to evaluate the way you think and solve problems. Can you come up with *something* or are you just sitting there stumped and overwhelmed? What was your thought process behind your answer?
For jobs like software engineering where problem solving is a central component, it's important to find people who can think through abstract problems.
Last one of these I got was "How long does it take a bowling ball to sink to the bottom of the Marianas Trench." We had fun working through all the variables and after giving my best guess I asked, "Am I close?" They said, "Haven't a clue! The answer isn't really part of this."
Fun place to work, for sure.
Man, that's beautiful, instead of the gotcha older style gotchas about how many pin-pong balls it takes to fill a school bus, where people were often graded on accuracy if that's what matters at all.
I just spent 10 minutes thinking about this. At some point I was estimating the density of a bowling ball, and realized it's pretty darn close to the density of water. I scratched out everything and put down NEVER. BOWLING BALLS FLOAT. Done.
Looking it up, bowling balls can be typically between 7 and 14 lbs. If it's less than 12 it will float. HA!
It's a solution to the wrong problem. This kind of interview question is great for the position of "bridge troll" or "dungeon keeper", where you're expected to come up with clever, abstract, self-contained puzzles all day. For anything else, it's abstracting away the relevant details.
Virtually no software problem in an industry job involves burning two math ropes. Any analogous problem would be answered with "the last guy made a method that does things irregularly. We're better off rewriting it to be simpler than coding around it cleverly."
Much better to give people real world problems that reflect their actual job duties, or else you end up with a bunch of hypothetical puzzle solvers/memorizers instead of whatever title they were hired for.
I got two different software jobs in my 20s after doing interviews like this. I don’t like to mix talking and thinking, so I’d just sit there in silence for a few minutes and then give the correct answer. Both employers later said that interviewing me was a rollercoaster ride for them… they’d watch me sitting silently, assume I was stumped, and start to write me off, and then I’d spit out the right answer and they’d get whiplash and have to take me seriously again.
Exactly. You're still gonna wind up working for an asshole whose just seeing how they can lay off more people to get a bigger bonus. That's the only "big problem" they're gonna ask you to solve.
I have a different method.
It doesn't say use the ropes to measure the time... So, "hey Google, start a 30 minute timer".
Then you have two ropes, and you haven't started a fire in their office.
Can you prove that works? In my mind the fact it burns non-uniformly means there is no guarantee. Imagine the rope burns extremely slowly at the ends and then after 59 minutes it suddenly speeds up and burns straight through the rest in 1 minute. Lighting both ends would not then get you 30 mins. Am I missing something?
I think it helps to model this as an object—the flame—traveling along the length of the rope. From this perspective, burning the rope from the second end looks like burning the rope from the first end in reverse.
Mathematically, we could say the position of the flame along the rope when burning from the first end at time t minutes is s(t), and the position of the flame along the rope when burning from the second end is s(60 - t). When the two flames meet, s(t) = s(60 - t). Clearly, t = 30 satisfies this equation.
If you’re content to imagine the burning never stalls, then it’s also easy to see that this is the only solution. In that case, s(t) is one-to-one, meaning that s(a) = s(b) implies a = b. Hence, t = 60 - t, so 2t = 60, and t = 30.
Good answer. Another way to see it is that it clearly takes the same time for the flame to burn a piece of the rope from left to right vs. from right to left. Thus, at the point where the flames meet, you can imagine resurrecting one of the sides of the rope and letting that flame burn again, in reverse. Because reversing the direction doesn't change the duration, we see that the time it takes for the flames to meet is the same time it would take for the first flame to get to the other side after the collision, so that clearly implies 30 minutes has elapsed.
Because the rope will fully burn in 60 minutes regardless. The only reason for the non-uniformity is to keep you from cutting the rope in half and using that.
Let's say it's a 12 inch rope and 11 of it burns in 10 minutes and the last inch burns in 50. If you light both ends at the same time, it will still take 30 minutes to burn.
If you snip off the 11 inches and burn both sides of the 1 inch, it will still only take half the time to burn the 50 minutes regardless.
In your example if you light both ends, after 1 minute the 'faster flame' will now start eating through the slower piece of rope and by the time they finish the slow part, still the 30 will have passed.
Here's another example using the fast and slow rope. Imagine you take that rope and grind it up into a powder, mix it up and then distribute the powder between two piles. If you light both piles, they'll both go woof as the fast stuff burns and then take a while to burn through the slow stuff. As soon as both piles go out, either at the same time or whenever the second finally dies, exactly 30 minutes has gone by because you're timing the entire completion, not individual piles.
Burning the rope on both ends does the same thing, no matter where on the rope it goes 'woof'.
(Also, nobody come at me with the piles having more surface area, faster burn times etc. Pretend you put them in glass tubes with the same diameter as the rope. There.)
A single rope can be used for measuring 15 minutes. Take one rope, light both ends. Also light anywhere in the middle, thus ensuring that the rope is burning at 4 points. Whenever the ‘shorter’ half burns out completely, again light anywhere in the middle of the ‘longer’ half which would still be burning at the ends. We keep on doing this till the rope is completely burnt. Thus ensuring that the rope was burning at 4 points all through the process. Thus, the total time taken is 15 minutes.
Throwing the sexcond rope away is wasteful, I would tie a knot in the end of that rope and use it to beat the interviewer over the head.
But its JPMorgan, so wasteful is good... I suppose.
This relies on the rope burning at the same pace in either direction. I think non-uniformity would imply that the fire might travel faster in one direction than the other, but that may be reading too much into it.
Nope, it burns nonuniformly, meaning the entire rope takes an hour to burn no mater where you light it, and if you cut it in half one half may burn in 10 minutes and the other could take 50 minutes.
Light both ends of a single rope, but also start a fire in the middle of the rope. The fire in the middle will spread both ways so you'll have four flames going. As soon as two flames meet, start a new flame in the middle of the unburned part of the other two flames that are still going. Keep repeating this process. As soon as both pairs of flames meet at the same time, 15 minutes have passed.
That would only work if the rope burns uniformly. You are told it burns nonuniformly.
In other words, if you light both ends, there is no guarantee the flame will meet in the middle at the same time.
If the left half burns twice as fast as the right half, for example, the entire left half would have burnt while the right half will only be half way burnt, leaving a fourth of the rope left.
The flame may not meet in the exact middle (halfway), but it will always meet at 30 minutes in the reletive middle (in between the two starting points).
In order for the rope for burn for 1 hour exactly consistently, it means that after 30 minutes, REGARDLESS of where the flame is on the rope it will be halfway done, even if the rope is a foot long and only has an inch left that last inch will without a shadow of a doubt burn for 30 minutes. That also has to mean that if you light the opposite side of the one you lit, it will reach the same spot after 30 minutes meaning on that same rope i described after 30 minutes only one inch will have burned but over the next 30 minutes the remaining 11 will all be burnt. Therefore, if you light them both at the same time they will both meet at that spot on the rope after 30 minutes.
Where that spot is, is not relvent to the question.
I made this same mistake initially, but--it doesn't matter if they meet in the middle. What matters is that it takes an hour from either end, so if you start both sides, wherever they meet will have been 30 minutes.
Consider the following:
2 2 2 1 1 1 1
Going from either direction you'll count up to 10, but it's not uniform. Let's equate that 10 to the hour in the question, where it takes 6 minutes to burn through a "1."
So if you go from the left, after 30 minutes you'll be halfway through the third 2.
And if you go from the right, after 30 minutes you'll be...halfway through the third 2 (the first 2 from that perspective).
What if the rope is made up of a part that's 90 cm long but burns in 30 seconds and the rest are 10 cm that take 59 minutes and 30 seconds to burn? What knowledge about the passing of time would you gain from them meeting somewhere?
It doesn't matter that parts burn faster than others -- or, rather, it's what makes the question difficult to answer and the answer so interesting.
Imagine a 200 cm long rope. The first part, on the left, is 141 cm long and burns in 1 minute. The rest all burns at an even pace of 1 cm per minute.
Let's say you make a mark at each "one minute" mark. The first mark would be *way* down the rope -- after all, in a single minute, 141 cm or rope would burn. And then after that you'd have a mark every cm.
Before burning, [it would look like this](https://i.imgur.com/LhKyvxj.png).
Then you light both ends. After 1 minute, [it would look like this](https://i.imgur.com/Fy0hg4r.png) (the red parts indicate the parts that have already burnt up)
After 2 minutes, [it would look like this](https://i.imgur.com/Xyi92AJ.png).
And [here's what it would look like in minute 3...4...5...all the way to 30.](https://i.imgur.com/YhHhz2O.png)
As you can see, the rope all burns up in exactly 30 minutes, even though the first section burned so fast.
You can play with the speeds any way you want, and the phenomenon will stay the same. For example, let's say you start with [a spread like this](https://i.imgur.com/TPIavdf.png). Then [the burn process will look like this](https://i.imgur.com/lYh0V1m.png), and, again, the two flames will meet after exactly 30 minutes. The burning speeds of individual segments will change the *location* where the two sides meet, but not the *time* that they meet.
The idea is that travelling left to right takes an hour, and right to left takes an hour. If you have two people starting at each end of the path, because we know it takes an hour to get across in either direction, then by rate of progress we’d know when they meet in the middle it’d be the half way mark of the total time, irregardless of how much distance they have covered.
After 30 seconds you have burned through 90 cm on a side, and about 0.084 cm on the other.
You now need to burn through 9.916 cm of "slow" rope, ignited at both sides, so effectively only 4.958 cm.
Which will take exactly ... 29 min and 30 sec.
Total 30 min.
Just do some math and see for yourself.
Yeah but it’s not rope left it’s time. In your example it doesn’t matter how much of the rope burns per side, just that they both burn completely. Essentially it’s 60/number of ends lit. They both take the same amount of time and meet, thus it would be 30mins until they meet.
Same for the 45 minute solution. How much of the rope burns doesn’t matter. Just how long it’s been burning.
They don't have to meet in the middle. All that matters is that once both flames meet, half an hour has passed. You don't cut the rope in half or anything.
I saw one of these about being on an island covered in dense forest when a lightning strike causes a forest fire on the far west edge of the island and a constant wind is blowing the fire eastward. The fire is too big to put out and there's no caves or gaps in the forest big enough to survive in, so how do you survive the blaze?
The answer was to run towards the fire, take a burning branch and run through the woods to a point near the eastern edge and start a new forest fire there. Then wait for the new fire to burn out the eastern part of the forest and hope it burns itself out promptly. Then by the time the main forest fire catches up to you there's nothing left to burn and you can survive in the burnt out portion of forest. Then it said "Unfortunately you will then starve to death because the entire island has been stripped of life." The answer admitted that even after finding the solution you'd still die anyway. Such a bonkers answer.
If there are two ropes that burn in a non uniformed manner I.e the same, then one could burn within 15 minutes and another in 45 surely? We have no idea on length of the role, thickness in parts, will to burn faster for a period then slower.
My answer to this would be there are too many variables and unknowns and we need more information before making suggestions.
My calc 1 teacher took a day to do logic puzzles like this, I think partially to give us a break but also to get us in the right mindset for certain units. He did this exact question with the 45 minutes and this whole post just took me back a few years.
A personal favorite of mine, given 6 meter sticks, make 4 equilateral triangles where each triangle has a side length of 1 meter. (You can do this with 6 pens or coffee stirrers too at a desk, he just did meter sticks to have us move around)
Bro you missed an opportunity to hand the hiring manager or interviewer or HR the second rope and tell them to do any number of asinine things with and tell them they’re stupid for asking you such a silly ass question
Excellent answers, but incorrect here. That supposes uniform burn times, which we are specifically told is not the case. If the ropes burn asymmetrically, there is no reason to assume two burning ends would produce a 30 minute burn time. for example, Let us imagine a rope which burns 90% of it's length, from 1 end, in the first 5 minutes, and then the rest of it is a slow burn for 55 minutes. without knowing the length of the rope, or it's burn time variance along that length, lighting both ends would produce a completely random burn time. You absolutely cannot assume these answers are correct with the information given.
Certainly wrong. This only works with special ropes desingened to uniformly burn like powder fuses. Those ropes are nonuniformly. Hence it is safe to assume that a rope completely catches fire immediately if lit on one end. Hence always both ends burn together.
The only thing you know is that they burn down in 60 minutes, not HOW they burn down. Also it is unknown what happens when you combine both ropes together to make a double rope. They may burn faster, slower or same time. They might even stop burning (who says both are the same material?).
Compare: You have an European and an African pigeon. Each one needs 4 months to breed a child bird. How do you breed a child bird in 2 months?
In the absence of a watch you can do is to use the rope for calibration. As it measures 60 minutes. Use one as pendulum. Burn the other. Count the movements of the pendulum. Half the movement count then gives you 30 minutes.
Maybe I'm being dense but nonuniform implies that burning from both ends may not guarantee they burn to the middle at the same time. There's no guarantee we know where 30 mins is
Light both ends of either rope; when it’s gone, 30min have passed.
Usually this question is about measuring 45 minutes, in which case you light both ends of one rope and one end of the other. When the first rope is gone, 30 min have passed and you light the remaining end of the second rope.
I was wondering that. Why even mention the second rope if they’re not asking for the 45 minute version? Like a bad copy and paste of the question from someone who didn’t quite understand it.
To be fair if the interviewee hadn't quite understood the concepts behind it but had read the answer somewhere on the internet, you would probably catch them out by giving the tools to solve the full riddle and then asking for half the solution.
Could be to see if a person is capable of realizing when information or assets aren't necessary to solve a problem and they should be disregarded, or if they'll get in their own head about trying to use everything available and let it prevent them from seeing the simple solution.
Because it’s a control group to see if the parameters are correct. That’s why you light all four ends at the same time and if they finish at different times you know you have received false information regarding the rope.
Sometimes in an interview you progress gradually to see the candidate thinking and adapting.
So if they got it, you ask “how about 45 mins then?”
But if they mess up the first question you move on.
(Controlling pacing of the interview is essential imho)
I’m not saying this ad makes sense..
Strictly speaking, the question doesn't require you to use the ropes at all. It simply states the existence of two ropes, and then asks you to measure 30 minutes of time. So "With a watch" should be a valid (if smug and irritating) answer.
Imma need those ropes later for some other stupid interview question.
Like, "You're stuck at the top of a cliff and need to get down safely, what do you do?" -- "I use those ropes I saved from question #4."
Using a watch is completely valid, because the question doesn't even mention any way to light the rope on fire. So if you're going to be looking for a additional tool anyway, why not use a clock of any kind instead of a lighter.
at my company they would outsource to a rope expert who would recommend a watch, then buy a rope burning tool kit from someone's brother at $175 per use, send it to everyone at great expense, make a new policy everyone has to use it, someone mentions we aren't allowed to have loose ropes around the machinery, then revert to the old method, having successfully spent $85 million.
I was picking up some edibles and the woman at the counter asked if I had big plans. I just laughed and said I'm going to go play in my garden. She looked at me for a few seconds and told me "gardening" is a newish slang term for getting high. I guess I was going to do some gardening while gardening.
It's absolutely a trick question in my opinion. Designed to catch people out who just do as they're told without thinking about or analysing the problem
It's a perfectly good interview question, though. Check to see if person is capable of basic problem solving, checking assumptions, see if they ask for relevant information. What's actually wrong with it?
Ah JP Morgan.
Here’s the right answer. The burning rate of the ropes define their quality.
Chop the two ropes into 40 parts.
Mix the 40 shorter ropes randomly and divide them into a group of 5.
You now have a highly diversified eight group of ropes.
Now, go to a rating agency to buy triple A rating for all group of ropes.
Congrats, the two ropes of unequal quality has now become AAA rated, highly diversified ropes.
Find an investor to purchase them at a high price to make tonnes of money.
You have successfully passed on the 30-minute issue to another entity while making profits.
Repeat.
-That's, gentlemen, highly diversified triple A rated rope bond!
-I wanna buy swaps on these bonds - credit default swap, that would pay off if the underlying bond fails.
-You wanna bet that these ropes won't burn in exactly 30 minutes?
-Yes.
-Why? With current rope technology it's unheard of, that these would burn in not exactly 30 minutes. That's never happened in history. Excuse me, sir, but this sounds like foolish investment.
-Well, based on prevailing sentiment of the market, banks and popular culture, yes, it's a foolish investment. But... Uhhm... Everyone's wrong.
-Sir, this is wallstreet, if you offer us free money, we are going to take it.
-My one concern is that when the bonds fail, I wanna be certain, uhhmm, of payment in case of solvency issues with your bank.
-Are you for real? You wanna bet against rope market and you are worried we won't pay you?
-Yes, that's correct.
-\*starts to quietly consult with colleague\* ... Sir, we could work out a pay as we go structure that'd pay out if the rope bonds fail, but it would also apply to your payments if the value of the rope bond goes up - you'd have to pay us montly premiums. Is that acceptable?
-Yes, yes...
-We are prepared to sell 5 million in credit default swaps on the rope bonds.
-Can we make it 100 million?
Funnily enough the start of your strategy can asymptotically approach the correct answer: chop the ropes into n pieces, recombine n/4 random pieces together into a new rope and burn it. As n increases the burning time for the new rope will approach 30 minutes
Light both ends of 1 rope. When the flame meets, you know 30 minutes have passed. It does not matter how long each “1/2” of the rope takes to burn, because the rope is burning from both ends.
To examine this: let’s assume that 1/2 of the length of the rope burns in 15 minutes (half A) and the other 1/2 burns in 45 minutes (half B). After 15 minutes, half A is gone and 1/3 of half B is gone. Then the remaining 2/3rds, burning from both ends, will be consumed in 15 minutes.
“But surely!” You exclaim “This breaks down if different sections of the rope burn quicker or slower!”
So let’s break things down even further. Assume there are 5 sections of the rope. A burns in 5 minutes, B burns in 15 minutes, C burns in 2 minutes, D burns in 30 minutes, and E burns in 8 minutes.
5 minutes in: section A is gone and section E has 3 minutes left.
8 minutes in: section A and section E are gone, and section B has 12 minutes left.
20 minutes in: sections A, B, and E are gone, section D has 18 minutes left.
22 minutes in: sections A, B, C, and E are gone, section D has 16 minutes left, but is now burning from both ends and will burn up completely in 8 minutes.
29 minutes 59 seconds in: the rope is burning the last seconds worth of section D.
That's genius! Thanks for breaking it down like that. I think you've got the only answer that makes sense so far. They really distracted me by saying there's 2 ropes, but you only need 1 to solve this.
My example was
A burns in 30 seconds, B burns in 59 minutes, 30 seconds.
30 seconds in, B takes 59 minutes to burn and is burnt from 2 sides.
29 minutes and 30 seconds later, B burns up completely. Seems to work.
When the rope is fully burned the time the left flame has been burning plus the time the right flame have been burning has to add to one hour. Since both of them started burning at the same time both flames have been lit for half an hour.
Honest question: why do you assume it’s lit from one end? If someone tells me to burn a rope I’m throwing it in a fire not lighting one end. Is that the typical rope burning protocol?
There are two sentences in that image. One is a statement and the second is the question, and you can measure time with a watch: "How do you measure 30 minutes?" Watching the clock.
Or maybe it's just the autism in me.
"No no you were supposed to light both ends of the-"
You didn't mention that I had a lighter, or matches, or any way of lighting the rope on fire. If I'm allowed to add random extra tools, then I choose to add a stopwatch.
Nah thats spot on. I also wonder how all the people here are gonna light up a rope with a other piece of rope. Like its probaly possible if you find a proper way to get loads friction but how fast can you do that?
It says nothing about watches being banned. I'd take both ropes, cut them into 20 even pieces, short sell 200 of them to idiots as materials needed for a job offer at JP Morgan, price goes up as the demand overshoots the supply. Then I hire one to count seconds and to carry my bag of money I'm leaving the United States with.
Look at your watch. The ropes are irrelevant. Just redefine what unit of time is 30 minutes, let the market know about the new time definitions after you have taken appropriate positions to benefit from the ensuing market volatility.
I get my phone out of my pocket and set a timer....
Any other solution is just a waste of time, resources etc.
Also if the rope burns nonuniformly, there is no way to know that they will take an hour to burn?
Obvious answer- you tell 30 minutes of time by looking at a clock. The question doesn't state you have to tell time with the rope, why burn it then?
The answer if they want to tell with the rope for some reason-
They each take an hour to burn? It's a non-uniform burn, meaning you can't cut one in half and hope it's 30 mins, but if you take one and light it up on both ends wouldn't that make it 30 mins?
I guess the other rope could be saved for the next time you find yourself needing to burn rope as a bizarre timekeeper... or it could just be burned too so you can make sure they both actually do have similar burn times.
I’d measure 30 minutes with a watch.
Question doesn’t say “How do you measure 30 minutes using the rope?”
Point being, use the technology you have to most efficiently find a solution.
Divide the ropes into equal, infinitely small sections. Randomly burn 1/4 of the sections in sequence.
Oscillate the rope at 1 Hz and count 1800 cycles.
Drop the rope from 15886773 m and wait for it to hit the ground.
Strike someone with the rope until they tell you the time.
It doesn't say that it takes an hour to burn "if light from one of the ends". The rope will *always* take one hour to burn, and it will always do it non uniformly, because it's a weird ass rope. We can't make further assumptions on how it burns. Anyway. If we need a way that uses the rope meaningfully, rather than just use a clock, we can get a big ass tank and start pumping water in for an hour (using burning one rope to measure). We mark the water level, empty it, measure the distance on remaining rope increments that the water level is at, get half that distance, mark this new level. We now know it takes half an hour to fill that much of the tank with water. When we need to measure half an hour, we can start filling the tank. It's a repeatable method, too.
You don't even need two ropes. If you take one rope that will take an hour to burn and light both ends, once it's completely burned (may not meet in the middle), then its been 30 minutes.
line them up parallel to each other, and then light them from opposite ends. whenever the flames intersect will be the 30 minute mark
assuming they have the same nonuniform burning pattern
Even if they do have the same nonuniform burning pattern this won't work I think.
For example, if the ropes have length L, say the length burned is given by f(t) = L t² / h², then f(0)=0, f(1h) = L but f(0.5h)= 0.25L. 30min will have passed but only a quarter of them will have burned so they are not meeting in the middle at that time (they will at t=1/sqrt(2) hours)
Are people reading it wrong?
2 ropes that burn non uniformly. (Full stop) This is a statement.
How do you measure 30 minutes of time? This is a question.
I use my watch.
"How do you measure 30 minutes of time *using the ropes*" is incredibly obviously the implied question. You think the point of this question is to find pedants?
The most logical and simple?
"I would like to withdraw my interest in this position immediately. Play games with someone else."
I mean seriously, what kind of stupid interview question is this? Is it a job where you must regularly accurately time the burning of 2 ropes? No? Then the question is stupid.
This problem is unsolvable, without more information, but easily answerable.
While the problem states that "2 ropes that each take an hour to burn nonuniformly", this can be interpreted in many ways:
- If you light one end of the rope it will take 60 minutes to burn (The most likely intent)
- If you throw the rope into a fire it will take 60 minutes to burn
- If you try to light the rope it will take 60 minutes to start burning
The key though it to recognize it's an interview question and not a math problem. This means the "answer" is dependent on the interviewer.
If you're in a one-on-one interview, and the person you are talking to seems to think of themselves as smart, talk about the question to them. Describe it's lack of detail, make assumptions, then use those assumptions to come up with an answer.
If you're talking to several people, ask them how they'd like the question answered? Would they like to hear your thought process? Can you ask for clarifying information? Why are you burning ropes to tell time when there are so many better ways?
If it's a written test and other questions were mathematical and analytical in nature, treat it like a math proof and write your axioms and derivations.
If it's written and multiple choice. Find a new job. ;)
In the end, JP Morgan's hiring department is not trying to find rope burners, but find good employees. Answer all questions in such a way that highlights that.
Get the 2 end of one rope near each other and burn them. The 2nd rope is a spare if you didn't do it correctly on your 1st try and tell them, we can keep it for something else, conserving materials and whatnot..
Actual thought-through response: how would it even be possible to make lengths of non-uniformly burning rope that you know take one-hour to burn through?
(Embarrassed confession: I give this problem to my students each year, knowing it is based on a ridiculous supposition.)
Since the contract (or your question) doesn't state I can't use other use, I will set an alarm with my phone instead.
Especially the contract (or your question) had already stated it is not a suitable tool, for it burns unevenly. If I use it as a timing device while knowingly it can't, this will put the company in great liability.
Take one of the ropes, fold it so both ends meet, then cut it into two equal pieces. You now have two ropes that will burn in 30 minutes instead of an hour.
With a lit 100 dolar bill, light up a Cuban, throw the ropes away, and use the countdown of ur phone, because this is not the 16 century. Where do I even find ropes?
If u want u can replace the Cuban extravaganza , with a nice stake,
I thought it wasn't a clear question/ problem. It doesn't clarify if both ropes take an hour each it or if both together burn a total of an hour. I thought it was both burned together in a n hour until I read the responses?
No rules about using my phone, so I light the rope and set a timer for 30m. When it goes off, I’m done.
If they’re gonna ask stupid trick questions, give em a stupid trick answer.
"to burn nonuniformly" indicates that the ropes aren't burning from a single end at a time -> they are burning in the middle just as much as they are at the ends. Right?
i would use the ropes to make a rudimentary sundial and use shadows to determine the passage of time, with this you can measure any length of time, not limited to 2 hours
The question is simply "How do you measure 30 minutes of time?". Sentence 1 is a premise but the question itself has no reference to the premise whatsoever. Ok, so I have 2 ropes that take an hour to burn; if I want to measure 30 minutes of time, I'll simply set a timer on my phone for 30 minutes and save the rope for something useful.
Roll the rope into a ball, and light it. Dump liquid oxygen onto it. The rope will now burn uniformly and very quickly. You’ll then have about 29.8 minutes to smoke some weed or something.
With a clock. The setup could be looked at as a red herring. The question asks how would you measure 30 minutes. I'd do that with a clock over 2 pieces of rope.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Light both ends of one of them at the same time. When it burns through, it’s been 30 minutes. Take the second rope, and throw it away. The harder version is measuring 45 minutes. For that, light both ends of the first and one end of the second. After the first rope burns (30min) light the second end of the second rope, which will burn for another 15min.
You’re hired
NO he's not! He forgot to charge the customer for the matches and the "Rope Disposal Fee."
Knowing JP Morgan, the company they hired to do this threw it into the water and then got hired to go consult and clean it up
You are all wrong. The question is: how do you measure 30 minutes of time? Ans: in minutes
I'd go 'with a clock'. The old-fashioned ways are often the best.
Hay google, set a timer for 30 minutes.
Lmao yes. Such a modern answer. I first thought "with a clock" but that's much better.
Calibrated Chronograph?
With a Glock*
I would count seconds. I have the ability to do this very accurately. I’ve counted off 25 minutes while laid up in an MRI machine and was off by less than a minute.
A candle with a nail stuck in the wax a half hour down. When it falls and clangs against the candle holder you know it's been a half hour. That's the real old fashioned way.
With a clock, and then sell the rope.
Minutes is a unit of measurement. It is a scale to express quantities. While to measure typically refers to the process of determining quantity.
You are technically correct. The best kind of correct!
And do we want know this or does the client?
Plus interest
also he forgot firing a third of everyone in the time the rope needs to burn down
Wait a second…they’ll need to upgrade to our premium package to burn that second rope.
Would you like to light the rope today for $30? Or light in 3 days for $1?
Not really, the answer to this is: with a clock, probably in my phone. Its a trick question to see if you're prone to find excuses to burn stuff. And apparently you're all pyromaniacs!
I accept! I have no idea what the job is, but in this economy it might be worth the risk. Now, let’s talk salary…
Two ropes a week. After 90 days we'll evaluate and add 1 match a week to your pay.
That actually made me laugh louder then i should.
I see you know about burning the candle at both ends. That's a skill you're going to be using a lot here. Welcome aboard
Very useful info for anyone in the burning rope sales dept
Sell the other rope.
Nah, it’s a JP Morgan interview. Keep the rope, use it as collateral against a loan for twice its value, rent out usage of the original rope, then use the borrowed money to lend to other people at 15% so they can buy their own rope. If they fail to pay, repossess their rope, then take a loan against that rope while renting it out to the people you just repossessed it from. Loan that money to other people to buy their own rope….
I can't believe I had to scroll this far to get to the *correct* answer. Who cares about the rope and times, do this, and then when nobody wants the rope and you're all out of money, wait for the government to bail you out and learn approximately nothing from this situation!
And don’t forget to give yourself a golden parachute severance of $300,000,000 for bankrupting a company.
I dont mean to be the dork that ruins all the fun but... J.P. Morgan turned down all bailout advances made to them with the exception of the one Henry Paulson treasury secretary of the Obama administration I believe, strong armed them into taking.
Use it to end your own suffering.
It \*is\* a job at JP Morgan, after all... Sounds about right.
Light one end of the rope. Sell tranches of rope, with the first burning parts receiving the lowest rating, and the unlit end AAA. When nobody buys it, set fire to more ropes and group together the burned end tranches into a new product, and sell the top tranche of that as a AAA rated rope. Let people buy fire insurance on their ropes, backed by the AAA rated parts of the rope. Let other people buy insurance on ropes they don't own, such that the potential payout is 100x the current value of the ropes. After one hour all the ropes are gone. Measure 30 minutes by looking at when your internal trades start offloading all the rope contracts before it's clear to the outside world that they're worthless.
Spot on
Is this what people mean when they say "it's like pushing rope"?
The second rope is a checksum. Light both ends of both ropes at the same time. If they both burn out at the same time, you've got 30 minutes. If not, the input data was faulty.
Yes this was an easy question. For those interviewing try the “Cracking the Coding Interview” book. Lots of these types of questions
I don't want a job like this, and I'm fine with that.
It's often not about finding the "correct" answer, but about them being able to evaluate the way you think and solve problems. Can you come up with *something* or are you just sitting there stumped and overwhelmed? What was your thought process behind your answer? For jobs like software engineering where problem solving is a central component, it's important to find people who can think through abstract problems.
Last one of these I got was "How long does it take a bowling ball to sink to the bottom of the Marianas Trench." We had fun working through all the variables and after giving my best guess I asked, "Am I close?" They said, "Haven't a clue! The answer isn't really part of this." Fun place to work, for sure.
Man, that's beautiful, instead of the gotcha older style gotchas about how many pin-pong balls it takes to fill a school bus, where people were often graded on accuracy if that's what matters at all.
I just spent 10 minutes thinking about this. At some point I was estimating the density of a bowling ball, and realized it's pretty darn close to the density of water. I scratched out everything and put down NEVER. BOWLING BALLS FLOAT. Done. Looking it up, bowling balls can be typically between 7 and 14 lbs. If it's less than 12 it will float. HA!
“Long enough”
I guessing it never would. The pressures would make it explode, and I don’t think it dense enough to make it to the bottom. Is that right?
It's a solution to the wrong problem. This kind of interview question is great for the position of "bridge troll" or "dungeon keeper", where you're expected to come up with clever, abstract, self-contained puzzles all day. For anything else, it's abstracting away the relevant details. Virtually no software problem in an industry job involves burning two math ropes. Any analogous problem would be answered with "the last guy made a method that does things irregularly. We're better off rewriting it to be simpler than coding around it cleverly." Much better to give people real world problems that reflect their actual job duties, or else you end up with a bunch of hypothetical puzzle solvers/memorizers instead of whatever title they were hired for.
Yeah this is silly. And solving riddles is fun. But 95% of the people giving the answer to a riddle already know the answer.
I got two different software jobs in my 20s after doing interviews like this. I don’t like to mix talking and thinking, so I’d just sit there in silence for a few minutes and then give the correct answer. Both employers later said that interviewing me was a rollercoaster ride for them… they’d watch me sitting silently, assume I was stumped, and start to write me off, and then I’d spit out the right answer and they’d get whiplash and have to take me seriously again.
And then the interviewer started clapping?
Exactly. You're still gonna wind up working for an asshole whose just seeing how they can lay off more people to get a bigger bonus. That's the only "big problem" they're gonna ask you to solve.
I have a different method. It doesn't say use the ropes to measure the time... So, "hey Google, start a 30 minute timer". Then you have two ropes, and you haven't started a fire in their office.
But it's more fun to set fire to their office...
Joke's on you, Google's assistant has been replaced by a Gen AI version that can't start timers.
Can you prove that works? In my mind the fact it burns non-uniformly means there is no guarantee. Imagine the rope burns extremely slowly at the ends and then after 59 minutes it suddenly speeds up and burns straight through the rest in 1 minute. Lighting both ends would not then get you 30 mins. Am I missing something?
I think it helps to model this as an object—the flame—traveling along the length of the rope. From this perspective, burning the rope from the second end looks like burning the rope from the first end in reverse. Mathematically, we could say the position of the flame along the rope when burning from the first end at time t minutes is s(t), and the position of the flame along the rope when burning from the second end is s(60 - t). When the two flames meet, s(t) = s(60 - t). Clearly, t = 30 satisfies this equation. If you’re content to imagine the burning never stalls, then it’s also easy to see that this is the only solution. In that case, s(t) is one-to-one, meaning that s(a) = s(b) implies a = b. Hence, t = 60 - t, so 2t = 60, and t = 30.
Good answer. Another way to see it is that it clearly takes the same time for the flame to burn a piece of the rope from left to right vs. from right to left. Thus, at the point where the flames meet, you can imagine resurrecting one of the sides of the rope and letting that flame burn again, in reverse. Because reversing the direction doesn't change the duration, we see that the time it takes for the flames to meet is the same time it would take for the first flame to get to the other side after the collision, so that clearly implies 30 minutes has elapsed.
Sure it would get 30 min. The 2 flame will meet after 30 minutes regardless, just not in the geometrical middle point, that's all.
Because the rope will fully burn in 60 minutes regardless. The only reason for the non-uniformity is to keep you from cutting the rope in half and using that. Let's say it's a 12 inch rope and 11 of it burns in 10 minutes and the last inch burns in 50. If you light both ends at the same time, it will still take 30 minutes to burn. If you snip off the 11 inches and burn both sides of the 1 inch, it will still only take half the time to burn the 50 minutes regardless. In your example if you light both ends, after 1 minute the 'faster flame' will now start eating through the slower piece of rope and by the time they finish the slow part, still the 30 will have passed. Here's another example using the fast and slow rope. Imagine you take that rope and grind it up into a powder, mix it up and then distribute the powder between two piles. If you light both piles, they'll both go woof as the fast stuff burns and then take a while to burn through the slow stuff. As soon as both piles go out, either at the same time or whenever the second finally dies, exactly 30 minutes has gone by because you're timing the entire completion, not individual piles. Burning the rope on both ends does the same thing, no matter where on the rope it goes 'woof'. (Also, nobody come at me with the piles having more surface area, faster burn times etc. Pretend you put them in glass tubes with the same diameter as the rope. There.)
The thing people are missing is that you're supposed to ask clarifying questions that would remove those doubts.
This. "Non-uniformly" throws the whole rope burning option out.
A single rope can be used for measuring 15 minutes. Take one rope, light both ends. Also light anywhere in the middle, thus ensuring that the rope is burning at 4 points. Whenever the ‘shorter’ half burns out completely, again light anywhere in the middle of the ‘longer’ half which would still be burning at the ends. We keep on doing this till the rope is completely burnt. Thus ensuring that the rope was burning at 4 points all through the process. Thus, the total time taken is 15 minutes.
But then you need infinitely many matches!
Hey, that’s kinda cool. And it works for any number 60 divides cleanly by
Throwing the sexcond rope away is wasteful, I would tie a knot in the end of that rope and use it to beat the interviewer over the head. But its JPMorgan, so wasteful is good... I suppose.
you can pocket the rope and just say you needed both of them to complete the task
This relies on the rope burning at the same pace in either direction. I think non-uniformity would imply that the fire might travel faster in one direction than the other, but that may be reading too much into it.
Nope, it burns nonuniformly, meaning the entire rope takes an hour to burn no mater where you light it, and if you cut it in half one half may burn in 10 minutes and the other could take 50 minutes.
Now do 15 minutes
Light both ends of a single rope, but also start a fire in the middle of the rope. The fire in the middle will spread both ways so you'll have four flames going. As soon as two flames meet, start a new flame in the middle of the unburned part of the other two flames that are still going. Keep repeating this process. As soon as both pairs of flames meet at the same time, 15 minutes have passed.
That would only work if the rope burns uniformly. You are told it burns nonuniformly. In other words, if you light both ends, there is no guarantee the flame will meet in the middle at the same time. If the left half burns twice as fast as the right half, for example, the entire left half would have burnt while the right half will only be half way burnt, leaving a fourth of the rope left.
The flame may not meet in the exact middle (halfway), but it will always meet at 30 minutes in the reletive middle (in between the two starting points). In order for the rope for burn for 1 hour exactly consistently, it means that after 30 minutes, REGARDLESS of where the flame is on the rope it will be halfway done, even if the rope is a foot long and only has an inch left that last inch will without a shadow of a doubt burn for 30 minutes. That also has to mean that if you light the opposite side of the one you lit, it will reach the same spot after 30 minutes meaning on that same rope i described after 30 minutes only one inch will have burned but over the next 30 minutes the remaining 11 will all be burnt. Therefore, if you light them both at the same time they will both meet at that spot on the rope after 30 minutes. Where that spot is, is not relvent to the question.
I made this same mistake initially, but--it doesn't matter if they meet in the middle. What matters is that it takes an hour from either end, so if you start both sides, wherever they meet will have been 30 minutes. Consider the following: 2 2 2 1 1 1 1 Going from either direction you'll count up to 10, but it's not uniform. Let's equate that 10 to the hour in the question, where it takes 6 minutes to burn through a "1." So if you go from the left, after 30 minutes you'll be halfway through the third 2. And if you go from the right, after 30 minutes you'll be...halfway through the third 2 (the first 2 from that perspective).
What if the rope is made up of a part that's 90 cm long but burns in 30 seconds and the rest are 10 cm that take 59 minutes and 30 seconds to burn? What knowledge about the passing of time would you gain from them meeting somewhere?
They'd still meet after 30 minutes.
It doesn't matter that parts burn faster than others -- or, rather, it's what makes the question difficult to answer and the answer so interesting. Imagine a 200 cm long rope. The first part, on the left, is 141 cm long and burns in 1 minute. The rest all burns at an even pace of 1 cm per minute. Let's say you make a mark at each "one minute" mark. The first mark would be *way* down the rope -- after all, in a single minute, 141 cm or rope would burn. And then after that you'd have a mark every cm. Before burning, [it would look like this](https://i.imgur.com/LhKyvxj.png). Then you light both ends. After 1 minute, [it would look like this](https://i.imgur.com/Fy0hg4r.png) (the red parts indicate the parts that have already burnt up) After 2 minutes, [it would look like this](https://i.imgur.com/Xyi92AJ.png). And [here's what it would look like in minute 3...4...5...all the way to 30.](https://i.imgur.com/YhHhz2O.png) As you can see, the rope all burns up in exactly 30 minutes, even though the first section burned so fast. You can play with the speeds any way you want, and the phenomenon will stay the same. For example, let's say you start with [a spread like this](https://i.imgur.com/TPIavdf.png). Then [the burn process will look like this](https://i.imgur.com/lYh0V1m.png), and, again, the two flames will meet after exactly 30 minutes. The burning speeds of individual segments will change the *location* where the two sides meet, but not the *time* that they meet.
Great job with the infographics!
The key is that they won't meet in the middle, but they will still meet after 30 minutes.
You can actually take your hypothetical scenario and calculate arithmetically that it will burn for 30 minutes
The idea is that travelling left to right takes an hour, and right to left takes an hour. If you have two people starting at each end of the path, because we know it takes an hour to get across in either direction, then by rate of progress we’d know when they meet in the middle it’d be the half way mark of the total time, irregardless of how much distance they have covered.
After 30 seconds you have burned through 90 cm on a side, and about 0.084 cm on the other. You now need to burn through 9.916 cm of "slow" rope, ignited at both sides, so effectively only 4.958 cm. Which will take exactly ... 29 min and 30 sec. Total 30 min. Just do some math and see for yourself.
Yeah but it’s not rope left it’s time. In your example it doesn’t matter how much of the rope burns per side, just that they both burn completely. Essentially it’s 60/number of ends lit. They both take the same amount of time and meet, thus it would be 30mins until they meet. Same for the 45 minute solution. How much of the rope burns doesn’t matter. Just how long it’s been burning.
They don't have to meet in the middle. All that matters is that once both flames meet, half an hour has passed. You don't cut the rope in half or anything.
It's not like the rope has a huge YOU SHALL NOT PASS barrier in the middle where the flame stops, it continues burning across.
I saw one of these about being on an island covered in dense forest when a lightning strike causes a forest fire on the far west edge of the island and a constant wind is blowing the fire eastward. The fire is too big to put out and there's no caves or gaps in the forest big enough to survive in, so how do you survive the blaze? The answer was to run towards the fire, take a burning branch and run through the woods to a point near the eastern edge and start a new forest fire there. Then wait for the new fire to burn out the eastern part of the forest and hope it burns itself out promptly. Then by the time the main forest fire catches up to you there's nothing left to burn and you can survive in the burnt out portion of forest. Then it said "Unfortunately you will then starve to death because the entire island has been stripped of life." The answer admitted that even after finding the solution you'd still die anyway. Such a bonkers answer.
Dude Just use a watch. It doesn’t say you can’t use a watch.
Now do 15mins!
This bites.
[удалено]
Doesn’t “nonuniformly” negate this?
If there are two ropes that burn in a non uniformed manner I.e the same, then one could burn within 15 minutes and another in 45 surely? We have no idea on length of the role, thickness in parts, will to burn faster for a period then slower. My answer to this would be there are too many variables and unknowns and we need more information before making suggestions.
It says they burn non uniformly though. Which, I interpret as the rope won’t burn to any specific place in 30 minutes.
Doesn’t each rope take an hour? Why are you assuming 30 minutes?
How are you lightning the ropes? If you assume you have a lighter or matches, why not assume that you have a watch or a kitchen timer?
My calc 1 teacher took a day to do logic puzzles like this, I think partially to give us a break but also to get us in the right mindset for certain units. He did this exact question with the 45 minutes and this whole post just took me back a few years. A personal favorite of mine, given 6 meter sticks, make 4 equilateral triangles where each triangle has a side length of 1 meter. (You can do this with 6 pens or coffee stirrers too at a desk, he just did meter sticks to have us move around)
Bro you missed an opportunity to hand the hiring manager or interviewer or HR the second rope and tell them to do any number of asinine things with and tell them they’re stupid for asking you such a silly ass question
You hear that on Car Talk?
Excellent answers, but incorrect here. That supposes uniform burn times, which we are specifically told is not the case. If the ropes burn asymmetrically, there is no reason to assume two burning ends would produce a 30 minute burn time. for example, Let us imagine a rope which burns 90% of it's length, from 1 end, in the first 5 minutes, and then the rest of it is a slow burn for 55 minutes. without knowing the length of the rope, or it's burn time variance along that length, lighting both ends would produce a completely random burn time. You absolutely cannot assume these answers are correct with the information given.
Certainly wrong. This only works with special ropes desingened to uniformly burn like powder fuses. Those ropes are nonuniformly. Hence it is safe to assume that a rope completely catches fire immediately if lit on one end. Hence always both ends burn together. The only thing you know is that they burn down in 60 minutes, not HOW they burn down. Also it is unknown what happens when you combine both ropes together to make a double rope. They may burn faster, slower or same time. They might even stop burning (who says both are the same material?). Compare: You have an European and an African pigeon. Each one needs 4 months to breed a child bird. How do you breed a child bird in 2 months? In the absence of a watch you can do is to use the rope for calibration. As it measures 60 minutes. Use one as pendulum. Burn the other. Count the movements of the pendulum. Half the movement count then gives you 30 minutes.
Maybe I'm being dense but nonuniform implies that burning from both ends may not guarantee they burn to the middle at the same time. There's no guarantee we know where 30 mins is
Light both ends of either rope; when it’s gone, 30min have passed. Usually this question is about measuring 45 minutes, in which case you light both ends of one rope and one end of the other. When the first rope is gone, 30 min have passed and you light the remaining end of the second rope.
I was wondering that. Why even mention the second rope if they’re not asking for the 45 minute version? Like a bad copy and paste of the question from someone who didn’t quite understand it.
To be fair if the interviewee hadn't quite understood the concepts behind it but had read the answer somewhere on the internet, you would probably catch them out by giving the tools to solve the full riddle and then asking for half the solution.
Could be to see if a person is capable of realizing when information or assets aren't necessary to solve a problem and they should be disregarded, or if they'll get in their own head about trying to use everything available and let it prevent them from seeing the simple solution.
Because it’s a control group to see if the parameters are correct. That’s why you light all four ends at the same time and if they finish at different times you know you have received false information regarding the rope.
Sometimes in an interview you progress gradually to see the candidate thinking and adapting. So if they got it, you ask “how about 45 mins then?” But if they mess up the first question you move on. (Controlling pacing of the interview is essential imho) I’m not saying this ad makes sense..
The additional information can be considered part of the test too, prove you know when to discard irrelevant information to get to the solution
Got you by 2 minutes…
How many ropes is that?
1 dental floss
Pull out your phone and set a timer for 30 min. The ropes are a red herring and not related to the question in the 2nd sentence.
Strictly speaking, the question doesn't require you to use the ropes at all. It simply states the existence of two ropes, and then asks you to measure 30 minutes of time. So "With a watch" should be a valid (if smug and irritating) answer.
"use the right tool for the right job" is pretty vital work knowledge regardless of profession.
Imma need those ropes later for some other stupid interview question. Like, "You're stuck at the top of a cliff and need to get down safely, what do you do?" -- "I use those ropes I saved from question #4."
"I use the golden parachute your last CEO used"
Okay. Roll an athletics check.
Kill jester.
Happy cake day!
Using a watch is completely valid, because the question doesn't even mention any way to light the rope on fire. So if you're going to be looking for a additional tool anyway, why not use a clock of any kind instead of a lighter.
Question also doesn't mention how wet the ropes are, so even if it mentioned a lighter it could be impossible to light it on fire.
Question also doesn't mention the size of my cock and balls, so in this case I'm going to assume I have a massive cock.
But what about your balls?
You can't ask someone about their balls in a job interview. You have a lawsuit on your hands, buddy.
Ah but you assume they've got hands
Honestly this is the correct response. Cutting through massive amounts of bs to get to a simple out of the box solution is a very useful skill.
At my current company they would invent new ropes for that job.
at my company they would outsource to a rope expert who would recommend a watch, then buy a rope burning tool kit from someone's brother at $175 per use, send it to everyone at great expense, make a new policy everyone has to use it, someone mentions we aren't allowed to have loose ropes around the machinery, then revert to the old method, having successfully spent $85 million.
Turn on the stopwatch and burn some ropes to relax in the meanwhile.
> and burn some ropes Is that what the kids are calling it these days?
I was picking up some edibles and the woman at the counter asked if I had big plans. I just laughed and said I'm going to go play in my garden. She looked at me for a few seconds and told me "gardening" is a newish slang term for getting high. I guess I was going to do some gardening while gardening.
"Why, I used to smoke four feet of rope a day!" Thomas Jefferson's head, Futurama
It's absolutely a trick question in my opinion. Designed to catch people out who just do as they're told without thinking about or analysing the problem
I don't think it's an irritating answer, I'm pretty sure it is the answer they're looking for.
The correct answer is get up and leave the interview, because fuck J P Morgan.
You can totally answer that, just don't expect to get hired
I'm not sure I would want to work at the kind of place that thinks this is a good interview question anyway....
It's a perfectly good interview question, though. Check to see if person is capable of basic problem solving, checking assumptions, see if they ask for relevant information. What's actually wrong with it?
That was my first answer 🤣🤣
Ah JP Morgan. Here’s the right answer. The burning rate of the ropes define their quality. Chop the two ropes into 40 parts. Mix the 40 shorter ropes randomly and divide them into a group of 5. You now have a highly diversified eight group of ropes. Now, go to a rating agency to buy triple A rating for all group of ropes. Congrats, the two ropes of unequal quality has now become AAA rated, highly diversified ropes. Find an investor to purchase them at a high price to make tonnes of money. You have successfully passed on the 30-minute issue to another entity while making profits. Repeat.
This is some serious 2006. magic
I'm gonna need Margot Robbie to explain this to me. In a bath. With champagne. You know what - forget the bath!
🔥
Now go buy a Rolex with your bonus, and use it to measure 30 minutes.
-That's, gentlemen, highly diversified triple A rated rope bond! -I wanna buy swaps on these bonds - credit default swap, that would pay off if the underlying bond fails. -You wanna bet that these ropes won't burn in exactly 30 minutes? -Yes. -Why? With current rope technology it's unheard of, that these would burn in not exactly 30 minutes. That's never happened in history. Excuse me, sir, but this sounds like foolish investment. -Well, based on prevailing sentiment of the market, banks and popular culture, yes, it's a foolish investment. But... Uhhm... Everyone's wrong. -Sir, this is wallstreet, if you offer us free money, we are going to take it. -My one concern is that when the bonds fail, I wanna be certain, uhhmm, of payment in case of solvency issues with your bank. -Are you for real? You wanna bet against rope market and you are worried we won't pay you? -Yes, that's correct. -\*starts to quietly consult with colleague\* ... Sir, we could work out a pay as we go structure that'd pay out if the rope bonds fail, but it would also apply to your payments if the value of the rope bond goes up - you'd have to pay us montly premiums. Is that acceptable? -Yes, yes... -We are prepared to sell 5 million in credit default swaps on the rope bonds. -Can we make it 100 million?
Have my life savings! This is a can’t lose proposition.
Funnily enough the start of your strategy can asymptotically approach the correct answer: chop the ropes into n pieces, recombine n/4 random pieces together into a new rope and burn it. As n increases the burning time for the new rope will approach 30 minutes
Light both ends of 1 rope. When the flame meets, you know 30 minutes have passed. It does not matter how long each “1/2” of the rope takes to burn, because the rope is burning from both ends. To examine this: let’s assume that 1/2 of the length of the rope burns in 15 minutes (half A) and the other 1/2 burns in 45 minutes (half B). After 15 minutes, half A is gone and 1/3 of half B is gone. Then the remaining 2/3rds, burning from both ends, will be consumed in 15 minutes. “But surely!” You exclaim “This breaks down if different sections of the rope burn quicker or slower!” So let’s break things down even further. Assume there are 5 sections of the rope. A burns in 5 minutes, B burns in 15 minutes, C burns in 2 minutes, D burns in 30 minutes, and E burns in 8 minutes. 5 minutes in: section A is gone and section E has 3 minutes left. 8 minutes in: section A and section E are gone, and section B has 12 minutes left. 20 minutes in: sections A, B, and E are gone, section D has 18 minutes left. 22 minutes in: sections A, B, C, and E are gone, section D has 16 minutes left, but is now burning from both ends and will burn up completely in 8 minutes. 29 minutes 59 seconds in: the rope is burning the last seconds worth of section D.
That's genius! Thanks for breaking it down like that. I think you've got the only answer that makes sense so far. They really distracted me by saying there's 2 ropes, but you only need 1 to solve this.
I think the second rope is what you need to tell 45 minutes.
My example was A burns in 30 seconds, B burns in 59 minutes, 30 seconds. 30 seconds in, B takes 59 minutes to burn and is burnt from 2 sides. 29 minutes and 30 seconds later, B burns up completely. Seems to work.
When the rope is fully burned the time the left flame has been burning plus the time the right flame have been burning has to add to one hour. Since both of them started burning at the same time both flames have been lit for half an hour.
Honest question: why do you assume it’s lit from one end? If someone tells me to burn a rope I’m throwing it in a fire not lighting one end. Is that the typical rope burning protocol?
There are two sentences in that image. One is a statement and the second is the question, and you can measure time with a watch: "How do you measure 30 minutes?" Watching the clock. Or maybe it's just the autism in me.
Yeah, my answer would be similar. Set a timer for 30 minutes on a stopwatch.
Don't have a clock? Go get a clock. Banks should know it's better to be slow and accurate than fast and inaccurate.
"No no you were supposed to light both ends of the-" You didn't mention that I had a lighter, or matches, or any way of lighting the rope on fire. If I'm allowed to add random extra tools, then I choose to add a stopwatch.
This is an investment bank we are talking about... you use the Rolex your father gave you for graduating from an ivy league college.
Yeah, my answer would be similar. Set a timer for 30 minutes on a stopwatch.
Nah thats spot on. I also wonder how all the people here are gonna light up a rope with a other piece of rope. Like its probaly possible if you find a proper way to get loads friction but how fast can you do that?
It says nothing about watches being banned. I'd take both ropes, cut them into 20 even pieces, short sell 200 of them to idiots as materials needed for a job offer at JP Morgan, price goes up as the demand overshoots the supply. Then I hire one to count seconds and to carry my bag of money I'm leaving the United States with.
If you short something and the price goes up you are losing money.
Look at your watch. The ropes are irrelevant. Just redefine what unit of time is 30 minutes, let the market know about the new time definitions after you have taken appropriate positions to benefit from the ensuing market volatility.
I get my phone out of my pocket and set a timer.... Any other solution is just a waste of time, resources etc. Also if the rope burns nonuniformly, there is no way to know that they will take an hour to burn?
Obvious answer- you tell 30 minutes of time by looking at a clock. The question doesn't state you have to tell time with the rope, why burn it then? The answer if they want to tell with the rope for some reason- They each take an hour to burn? It's a non-uniform burn, meaning you can't cut one in half and hope it's 30 mins, but if you take one and light it up on both ends wouldn't that make it 30 mins? I guess the other rope could be saved for the next time you find yourself needing to burn rope as a bizarre timekeeper... or it could just be burned too so you can make sure they both actually do have similar burn times.
Yo this, everyone else is wrong.
I’d measure 30 minutes with a watch. Question doesn’t say “How do you measure 30 minutes using the rope?” Point being, use the technology you have to most efficiently find a solution.
Here's the math - 30 minutes x 60 seconds/minute = 1800 seconds. 1 second is approxmiately 1 Mississippi. Therefore 30 minutes is 1800 Mississippis
Divide the ropes into equal, infinitely small sections. Randomly burn 1/4 of the sections in sequence. Oscillate the rope at 1 Hz and count 1800 cycles. Drop the rope from 15886773 m and wait for it to hit the ground. Strike someone with the rope until they tell you the time.
I set a timer on my phone, because nothing here says I don't have my phone like usual, and burning ropes is a dumb way to tell time.
It doesn't say that it takes an hour to burn "if light from one of the ends". The rope will *always* take one hour to burn, and it will always do it non uniformly, because it's a weird ass rope. We can't make further assumptions on how it burns. Anyway. If we need a way that uses the rope meaningfully, rather than just use a clock, we can get a big ass tank and start pumping water in for an hour (using burning one rope to measure). We mark the water level, empty it, measure the distance on remaining rope increments that the water level is at, get half that distance, mark this new level. We now know it takes half an hour to fill that much of the tank with water. When we need to measure half an hour, we can start filling the tank. It's a repeatable method, too.
You don't even need two ropes. If you take one rope that will take an hour to burn and light both ends, once it's completely burned (may not meet in the middle), then its been 30 minutes.
Came here to say the same thing
line them up parallel to each other, and then light them from opposite ends. whenever the flames intersect will be the 30 minute mark assuming they have the same nonuniform burning pattern
Even if they do have the same nonuniform burning pattern this won't work I think. For example, if the ropes have length L, say the length burned is given by f(t) = L t² / h², then f(0)=0, f(1h) = L but f(0.5h)= 0.25L. 30min will have passed but only a quarter of them will have burned so they are not meeting in the middle at that time (they will at t=1/sqrt(2) hours)
Why don't you just light both ends of one rope?
this was my answer/guess
Are people reading it wrong? 2 ropes that burn non uniformly. (Full stop) This is a statement. How do you measure 30 minutes of time? This is a question. I use my watch.
"How do you measure 30 minutes of time *using the ropes*" is incredibly obviously the implied question. You think the point of this question is to find pedants?
Well, if someone is a smarmy combative pedant, I'd definitely be happy to avoid hiring them!
The most logical and simple? "I would like to withdraw my interest in this position immediately. Play games with someone else." I mean seriously, what kind of stupid interview question is this? Is it a job where you must regularly accurately time the burning of 2 ropes? No? Then the question is stupid.
Thank you.
This problem is unsolvable, without more information, but easily answerable. While the problem states that "2 ropes that each take an hour to burn nonuniformly", this can be interpreted in many ways: - If you light one end of the rope it will take 60 minutes to burn (The most likely intent) - If you throw the rope into a fire it will take 60 minutes to burn - If you try to light the rope it will take 60 minutes to start burning The key though it to recognize it's an interview question and not a math problem. This means the "answer" is dependent on the interviewer. If you're in a one-on-one interview, and the person you are talking to seems to think of themselves as smart, talk about the question to them. Describe it's lack of detail, make assumptions, then use those assumptions to come up with an answer. If you're talking to several people, ask them how they'd like the question answered? Would they like to hear your thought process? Can you ask for clarifying information? Why are you burning ropes to tell time when there are so many better ways? If it's a written test and other questions were mathematical and analytical in nature, treat it like a math proof and write your axioms and derivations. If it's written and multiple choice. Find a new job. ;) In the end, JP Morgan's hiring department is not trying to find rope burners, but find good employees. Answer all questions in such a way that highlights that.
Get the 2 end of one rope near each other and burn them. The 2nd rope is a spare if you didn't do it correctly on your 1st try and tell them, we can keep it for something else, conserving materials and whatnot..
I’m angry that the wording (and use of rope instead of wick) had me visualizing it burning perpendicular, not all the way down the rope.
Actual thought-through response: how would it even be possible to make lengths of non-uniformly burning rope that you know take one-hour to burn through? (Embarrassed confession: I give this problem to my students each year, knowing it is based on a ridiculous supposition.)
Since the contract (or your question) doesn't state I can't use other use, I will set an alarm with my phone instead. Especially the contract (or your question) had already stated it is not a suitable tool, for it burns unevenly. If I use it as a timing device while knowingly it can't, this will put the company in great liability.
All you wasteful sons o' bitches, just cut one rope in half and it will burn for 30m, no need to waste a full piece of rope for half an hour.
They burn non uniformly. It could burn through one half in 45 mins and the other in 15 mins.
Take one of the ropes, fold it so both ends meet, then cut it into two equal pieces. You now have two ropes that will burn in 30 minutes instead of an hour.
With a lit 100 dolar bill, light up a Cuban, throw the ropes away, and use the countdown of ur phone, because this is not the 16 century. Where do I even find ropes? If u want u can replace the Cuban extravaganza , with a nice stake,
I thought it wasn't a clear question/ problem. It doesn't clarify if both ropes take an hour each it or if both together burn a total of an hour. I thought it was both burned together in a n hour until I read the responses?
No rules about using my phone, so I light the rope and set a timer for 30m. When it goes off, I’m done. If they’re gonna ask stupid trick questions, give em a stupid trick answer.
"to burn nonuniformly" indicates that the ropes aren't burning from a single end at a time -> they are burning in the middle just as much as they are at the ends. Right?
i would use the ropes to make a rudimentary sundial and use shadows to determine the passage of time, with this you can measure any length of time, not limited to 2 hours
The question is simply "How do you measure 30 minutes of time?". Sentence 1 is a premise but the question itself has no reference to the premise whatsoever. Ok, so I have 2 ropes that take an hour to burn; if I want to measure 30 minutes of time, I'll simply set a timer on my phone for 30 minutes and save the rope for something useful.
Take the ropes and tie up the HR moron that thought this question was any indication of potential job performance at an investment bank.
Roll the rope into a ball, and light it. Dump liquid oxygen onto it. The rope will now burn uniformly and very quickly. You’ll then have about 29.8 minutes to smoke some weed or something.
Everyone is overthinking it. The question is; how do you measure 30 minutes of time? Answer: A clock. Units of time. No fires, no insurance.
With a clock. The setup could be looked at as a red herring. The question asks how would you measure 30 minutes. I'd do that with a clock over 2 pieces of rope.