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I had this question worded differently asked to me when I interviewed to do an undergrad at Cambridge. If you have a rope that is wrapped around earth and you l
by kovek 9y ago
I had this question worded differently asked to me when I interviewed to do an undergrad at Cambridge. If you have a rope that is wrapped around earth and you lift it off the ground as much as possible, and you see that it is 10km above the ground, then how long is the rope?
I was not able to answer that question right away, and their hint to draw it helped a lot. I did not end up getting accepted.
- seanmcdirmid 9y agoIt seems like one of those stupid brain teasers tech companies used to ask that are not very correlated with success but act as arbitrary filters.
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- anyfoo 9y agoIn this case the "arbitrary filter" was filtering applicants to a university for very basic math knowledge, so I think assuming that it's correlated with success at that university is not very far fetched.
- seanmcdirmid 9y agoEuclidean geometry games are hardly what people do in the real world, but if it floats your boat: https://www.euclidea.xyz https://www.euclidea.xyz I don't think after playing 20 or so levels I was much smarter for it. It turned out to be a bunch of rules that were extremely limited. You do begin to appreciate trig much more. If you are being given a geometry subject test and are prepared for it, this is fair game. If the question is just given out of the blue as a brain teaser, then no, the university is not mining useful signals at all.
- rishabhsagar 9y agoThank you. Here goes the 2 or so hours of me doodling away.. :)
- BurningFrog 9y agoSure, but it also filters for people like me, who have seen this problem at least a dozen times.
- seanmcdirmid 9y agoYa, these also can totally be gamed with the right amount of prep.
- chrisseaton 9y agoSo why doesn't everyone pass the interview? Either they can't be gamed, or they select for people who can at least be bothered to do the work to game them.
- seanmcdirmid 9y agoDepends on your resources for prep. Poor kids have less resources for that than rich kids, so they ultimately select for richer candidates.
- deleted 9y ago[deleted]
- pm215 9y agoWhen I did my university entrance interview (for maths, at Cambridge) the interviewers were clear that they expected that some subset of candidates would have seen the problem before, and some wouldn't -- for those in the first set they'd get them to quickly go through the problem and move onto the later parts which would be new to them; for those in the second set they'd provide sufficient guidance to let the candidate walk through the problem. The point was to get any particular candidate to a point in the problem sequence where this was something new to them, and then see how they tackled things. The idea that some applicants (usually from public schools) would have been very highly prepped for interview and others (usually from state schools) would not was clearly something they were well aware of and setting their interview design up to handle.
- coldtea 9y agoYes, because they don't want to measure "success" but knowledge of basic math. Which is par for the course for an educational institution (and a business one could argue).
- logfromblammo 9y agoIt also seems to be a less coherent version of the chicken from Minsk puzzle. Perhaps it's multiple choice. A. Dreadfully sorry, but I'm afraid I haven't memorized the circumference of Earth. B. What do you mean? Over the poles or 'round the equator? C. Is that 10 km above at all points on the rope, or just one? D. What's the rope made of? Jute? Sisal? Nylon? How far apart are the supports? Young's modulus... E. I don't know about that, but I have inherited a rather large quantity of string in 3-inch lengths...
- SamReidHughes 9y agoThat's a very straightforward math problem.
- seanmcdirmid 9y agoThere is a lot more than the Pythagorean theorem in that question. It would require remember a lot of middle school theorems from a long time ago; frankly calculus would be better.
- SamReidHughes 9y agoNo. You just need to know circumference = pi times diameter.
- SamReidHughes 9y agoOr no, I misunderstood the problem. Either way it's a simple problem that entering math majors should be able to solve.
- Dove 9y agoI don't see anything tricky about that problem. It requires some junior high geometry and high school trig, and yes, I suppose you need to know the radius of the earth offhand. Still. That strikes me a lot more as a math fizzbuzz than as a brain teaser. A college applicant can be reasonably expected to know this stuff.
- PhantomGremlin 9y agoI suppose you need to know the radius of the earth offhand. Or you can easily derive the radius if you remember that a meter was initially defined as 1/10,000,000 of the distance from the equator to the North Pole. So you can easily calculate the Earth's circumference, and from there the radius: 10,000,000 * 4 / 1000 / 3.1416 / 2 = 6366 km. Wikipedia gives 6371 km as the mean radius.
- YZF 9y agoThe version I got, in a tech company interview, was how much longer would you need to make the rope to allow a cat to go under it. They were basically just look for 2 x Pi x Cat in this case.
- kijin 9y agoThat question is ambiguous. If you only need a single cat to go under the rope at some point, you just add a small arch for the cat to walk through. This requires a length of rope somewhat less than twice the height of the cat. 2 x Pi x Cat would levitate the rope by the height of the cat along the entire circumference of the Earth, allowing a billion cats to go under it simultaneously. You could even make do with no additional rope if you're allowed to take advantage of terrain.
- liuhenry 9y agoThe answer to the first interpretation is considerably less than twice the height of the cat, and I think it's an interesting result as well: Assuming a 0.3 meter high cat, you only need ~0.12mm of extra rope (about the width of two sheets of paper) to be able to pull it up at a point and let the cat through.
- davidmanescu 9y agoFollow-up question - after extending the rope by 0.12mm and pulling it up to allow the cat to pass under it, how far away are each of the two points where the rope lifts off the ground?
- mamon 9y agoHaven't done any calculations but I would guess half of the Earth circumference? because if you want to minimize the length of the rope then you have to maximize distance between those two points.
- tromp 9y agoAs the article explains, these points are about sqrt(2Rh) = sqrt(2 x 6400km x 0.3m) = sqrt(3840000m^2) ~ 1.96km away from the cat.
- jnbiche 9y agoTo be clear, they gave you the radius of the earth here, if you didn't already know it by heart? Otherwise, I'm not getting how you could solve this problem (assuming they didn't give you the angle that the arch formed, for example).
- ivanbakel 9y agoYou don't need to know the radius of the earth unless you're asked for a numeric answer. The rope is 2 * pi * 10km longer than the Earth's circumference, since its radius is 10km more.
- jamesmaniscalco 9y agoI think this is the wrong interpretation; your answer would be correct if the rope were hovering at a height of 10 km along the full length. My interpretation is that the rope is pulled taut to a height of 10 km at a single point, so that it runs in a straight line to the horizon in either direction and lays on the ground the rest of the way; this is also relevant to the question of longest line of sight from a given height.
- jnbiche 9y agoActually, it's a different question. Check out the second diagram linked to below: https://news.ycombinator.com/item?id=14863949 https://news.ycombinator.com/item?id=14863949 So yes, you could supply the answer in terms of r radius, but you do need to know the radius unless I'm missing something obvious.