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Veritasium: The SAT Question Everyone Got Wrong [video]
- krackers 3y agoThis was also the infamous amc 2015 "clockblock" question https://artofproblemsolving.com/wiki/index.php/2015_AMC_10A_Problems/Problem_14 https://artofproblemsolving.com/wiki/index.php/2015_AMC_10A_...
- CrazyStat 3y agoI remember having the same question (probably with different sized circles) in our local high school math team competition ca. 2002. I got it wrong.
- genocidicbunny 3y agoI distinctly recall having to solve a version of this in my 2nd grade math class. Only about half the class got it right.
- lostmsu 3y agoThe title sort of spoils it as it becomes obvious you need to look for some issue with the trivial number solution.
- anamexis 3y agoI think any video about it would spoil it, because you wouldn't make a video about a trivial number problem.
- orenlindsey 3y agoThe guy who figured this out (who Veritasium interviewed) is crazy smart. Also, a lot of kids math problems (middle school and below) are super vague. I get that they're designed to teach a concept, but they could do it in a more exact/precise (idk what the word is) way.
- dudeinjapan 3y agoI think you are looking for the word “cromulent”.
- plibither8 3y agoDid you just learn this word too from another recent thread on HN? I did, haha!
- dudeinjapan 3y agoHa no I'm a Simpsons fan from waaaay back!
- mewpmewp2 3y agoConsidering how little educators are paid, I'm amazed as to how much they have been able to come up with and do already, though.
- makeitdouble 3y agoThe vagueness is seen as a feature, not a bug. The kid is supposed to read between the lines and find out what the problems are really about. That's straight how my teachers would explain it to us, and you see that line of thinking in the "problem solving" bits where the text is intentionally made harder to decrypt. Reading skills and shared background assessments are baked into most math tests, even if that's not the focus of it.
- junofan 3y agoI’m thankful I was doing competition math by that age and had access to more rigorous materials than these “readiness” assessments.
- whoopdedo 3y agoWhich is a big problem I have with these sort of tests. A problem that exists in most I.Q.-like assessments. Rather than evaluating how well the student is able to use their brain it's instead filtering those who were coached to think the same way as the test writers. That creates homogenity which is why I believe there are cultural divides in test results. Like the Cold War era stories where spies use seemingly innocuous or nonsensical code phrases to identify each other. "The sparrow flies at midnight. Calculate the velocity it would need to reach Berlin in 7 days."
- mlcrypto 3y agoThe perspective from inside the circle was mind blowing. Can that be an analogy to relativity & time?
- emmet 3y agoSuch a clever way of showing the mechanic! Tried to picture it in my head first and then he just did it for me
- aaron695 3y ago[dead]
- pmayrgundter 3y agoNone of the explanations gave me an intuition for it except the circle rolling down a straight line with the same length as its circumference. A roll down the line will rotate the circle once. Coming back the same. But rolling around one corner will add half a circumference, and another half for rolling around the other. So you get 2 * 0.5 extra circumferences, and so + 1 C. Somehow that helps with the other polynomials for me too. Super cool.
- KMag 3y agoDo you mean polygon, or did I miss something relating to a polynomial solution?
- jeffbee 3y agoTo me the intuitive explanation is that if they were gears, with shafts fixed in a block, the small wheel would turn 3 times per turn of the big wheel, but in the given scenario the small gear also has to go around the big one, hence the R/r+1 solution.
- Aeolun 3y agoYeah. I think that’s the intuition I have about this too. It rotates once by virtue of going around, and three times by virtue of the size of the big circle. If you imagine a very tiny circle it’d still rotate a full time.
- HarHarVeryFunny 3y agoYes, but that line of thought doesn't really help when the small disk is rolling around the inside of the large disk, not the outside.
- krackers 3y agoTriangle is probably easier to see (120 deg rotation when you turn the corner). Then you can see that the key is the sum of exterior angles, and this holds as you increase num sides. In the limit, you get a circle.
- drc500free 3y agoWhat makes sense to me is to think about something that DOESN'T roll. Suppose I start in Greenwich, walk - without rolling - down the prime meridian to the south pole, up the international date line to the north pole, and back down the prime meridian to Greenwich. How many rotations do I go through? One. I get a full rotation because I've followed the earth's curvature all the way around the globe once, even though I'm walking straight without rolling. So the answer is "how many rotations due to rolling" plus "one bonus rotation for passing around the curvature of the circle."
- jagthebeetle 3y agoThat intuition makes a lot of sense to me, especially if I picture the person's frame of reference. Kind of reminds me (a layman) of winding numbers. I suppose there are topologically inspired variations of this problem that might be even more "paradoxical" (or perhaps just silly). If you moonwalk the second half, you undo your rotation? Or if you follow specially designed subterranean tunnels, you can end up doing 0 or negative rotations!
- lordnacho 3y agoThe way I thought about it was to ask what happens if you just have a coin going around a point, which would be the natural end point of reducing the size of the second coin. That of course would give you 1, so a good first hypothesis is that the total is just however many spins the two coins go, plus 1.
- arketyp 3y agoThe video demonstrates the 1:1 coin size case and speaks about the curvature of the line it rolls on, but your thought experiment makes it a lot clearer. As the size of the other coin goes to 0, the amount "gnawed off" of the rolling coin will also go to 0 while obviously still rotating a full revolution.
- deleted 3y ago[deleted]
- jodrellblank 3y ago
- bobby_table 3y agoThe way I think of this is: If instead of having a small circle rolling around a larger one, think of a circle with ANY non-zero radius rolling around one with a zero (or really really small) radius. You’ll always end up with at least one rotation, regardless of how small the other circle is. So +1 makes sense.
- saberdancer 3y agoThe way I thought about it, you have to roll around the larger one and you have to roll around yourself (+1). So if they are two same size circles, it's 1 for the other and 1 for yourself. If the other one has 3 times bigger radius, it is 3 for the bigger one and 1 for yourself. Etc. Not sure if it is mathematically accurate but it seemed to make sense to me.
- jncfhnb 3y agoI think the explanation is kind of messy tbh. People are going to have one of two interpretations. If a coin rolls around another coin, is the distance traveled equal to the edge along the the static coin? Or is it the distance traveled by the center of the rotating coin? If it’s defined by the former, the answer is 3 because the circumference is 3x as long as that of the traveling coin. If it’s defined by the latter then it’s 4 because the circumference of the base coin buffered out by the radius of the traveling coin is 4x as long that of the traveling coin. I vote 3 personally
- orenlindsey 3y agoThe point is that the question is vague and is open to multiple different "correct" answers. SAT questions should only have one correct answer, with no possibility of any others.
- jncfhnb 3y agoThe point is that the question is sort of interesting and the history is just fluff for YouTube clicks and video length. The context is irrelevant.
- HarHarVeryFunny 3y agoIt's not just that it was poorly worded, but rather poorly conceived/analyzed. Apparently they had wanted the right answer to be "3", and therefore basically asked the wrong question (which would been a bit awkward to word!).
- medler 3y agoIt depends on the viewer’s perspective. From the coin’s point of view it rotates three times, but to an outside viewer it rotates four times. I think the outside viewer’s perspective is far more intuitive, so four is really the “most” correct answer to me.
- jncfhnb 3y agoPerhaps. But I think the most intuitive is noting that a coin’s perimeter should touch the other coin exactly one full time during a rotation.
- xorcist 3y agoDoes the video spoil the solution too or is it only the question?
- orenlindsey 3y agoWell, there's not really one solution. Watch the video to see what I mean.
- fsckboy 3y agothe video starts out with the question and then says you can pause if you want to work on it. Then it the next thing it says is something about the answer.
- medler 3y agoThe application to sidereal time is where this really gets interesting. It’s far from a trivial question of semantics or a mathematical trick. It’s something astronomers have known about for ages, since the amount of time it takes for the Earth to make one rotation is different from the perspective of distant stars than from the perspective of the sun.
- whartung 3y agoIndeed. This was my favorite part of the video. The discussion of the problem and SAT part are interesting, but when it delves into the sidereal time aspect, it just flies off into a direction where never saw coming and presented some fascinating aspects I’d never had need to consider.
- fsckboy 3y agowhat is perplexing to me is that I've been thinking about the sidereal problem for the last or so ...(because I heard on a podcast that the earliest sunset occurs more than a week before the solstice and the latest sunrise occurs after the solstice, but still the solstice is the shortest day, and they said something about the tilt of the earth and I was thinking that was not explanatory, so I've been idly noodling about it)... and I just got this problem wrong! didn't even occur to me :) in my defense, the thumbnail for this video does not state the question so I wasn't sure what I was supposed to do, but guided by the multiple choice I selected 3 but talk about having my brain primed for the question... doh!
- TarasBob 3y agoThe way I think about it is imagine the circle in the middle is very tiny compared to the circle that rolls.
- medler 3y agoI like this perspective as well. If the coin is rotating around a point (radius 0), the point on the coin edge touching the point will not move at all, yet the coin will make one rotation before returning to its original position.
- sillysaurusx 3y agoThere is an intuitive way to see why this is true. Picture a circle rolling around the outside of another. Easy to picture, right? Even if it’s not clear how many times it rotates, you can still visualize it. Now imagine the outer circle has to spin around the inside of the first circle. Stack two quarters, and try to spin the top quarter around the inside of the bottom quarter. You can’t do it. There’s no room. If they’re identical size, the top quarter can’t spin "around" the inner edge of the bottom quarter. Now put a penny on top of a quarter. Spin that around. Not along the outside, but along the inside of the quarter. You’ll see the penny is tracing a very tight circle. There’s not much room. Now put the penny next to the quarter and spin it around the outer edge of the quarter. It goes easily. Plenty of room. If you do the naive calculation, you’d get the same answer for both cases. But clearly there’s a difference. The difference is more apparent if you imagine the coins had little teeth, like gears. If you go around the outside, it’ll go just fine. But if you hollow out the quarter and put teeth along the inside, and try to spin the penny around in that, you’ll find that it doesn’t make anywhere close to a full rotation each time you go around.
- whoopdedo 3y agoThis becomes even more apparent when you turn the circumference of the fixed circle into a straight line. (As the video suggested but didn't show in the same way.) The center of the rolling circle will trace a line parallel and equal length to the fixed line, whether above or below it. If you reform the circle the outer line will be too short to form a complete circle, and the inner line will overlap itself.
- js2 3y agoThis is an 18 minute video about an SAT problem from 1982. If you're not sure you want to commit to it, here's a contemporaneous NYT article: https://www.nytimes.com/1982/05/25/us/error-found-in-sat-question.html?unlocked_article_code=1.JE0.bxTM._IG_RekctyzU&smid=url-share https://www.nytimes.com/1982/05/25/us/error-found-in-sat-que... (Gift link.) And a recent Scientific American article: https://www.scientificamerican.com/article/the-sat-problem-that-everybody-got-wrong/ https://www.scientificamerican.com/article/the-sat-problem-t... (Both of these are linked from the video description itself.) I'll bet Marilyn vos Savant wouldn't have got this one wrong[1]. :-) [1]: https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos...
- hightrix 3y agoThank you so very much. Reading this article was so much more valuable to me as I would have never watched an 18 min video to show a single question that needed 1 paragraph to discuss.
- jjnoakes 3y agoThe video does go further - it contains some interesting content around how this concept relates to the earth's orbit around the sun, the discrepancy between the duration of an earth day and a 360 degree rotation about the earth's axis, and why astronomy days are not the same length as earth days.
- jraph 3y agoYeah, the SAT question is almost an excuse to speak about this things, and you also get to see an interview with one of the concerned candidates. Very enjoyable video.
- 2muchcoffeeman 3y agoThere’s also an interesting note about when the specified answers in the question would have been right, the point of view of the centre circle.
- elbasti 3y agoQuestion: the outside circle is a tire made of rubber, which wears down at a known rate. Which tire wears down more: A tire that rolls around a circle of circumference D. A tire that rolls down a flat surface, total distance D?
- johnfn 3y agoWell, surely these are the same. Right? Haha of course they are. This is silly. Right? RIGHT?!?
- Aeolun 3y agoJust because it’s spinning more does not mean it wears out faster though. Maybe tires are more resistant to rolling on curvatures?
- scotty79 3y agoI'd say they are less resistant to going on positive curvatures. It's like a bum that goes deeper into the tire, deforming tire more which should result in more wear than driving on even surface.
- elwell 3y agoWhat if the large circle rotates at the same rate that the small circle 'orbits' it?
- jhncls 3y agoThe coin around coin problem has its own wikipedia page, although some people want to delete it: https://en.wikipedia.org/wiki/Coin_rotation_paradox https://en.wikipedia.org/wiki/Coin_rotation_paradox
- jhncls 3y agoThe same paradox is also featured prominently as part of a Mathologer video [0] and an article in Scientific American [1]. [0]: https://youtu.be/oEN0o9ZGmOM?t=523s https://youtu.be/oEN0o9ZGmOM?t=523s [1]: https://www.scientificamerican.com/article/the-sat-problem-that-everybody-got-wrong/ https://www.scientificamerican.com/article/the-sat-problem-t...
- alister 3y agoI love the Wikipedia animations -- they are usually extremely helpful -- but when I'm trying to read the article, I find them distracting. I usually move another window on top to obscure the animations so I can concentrate on the article. But there must be a better way. Is there a hotkey to stop animations? For Firefox in particular? EDIT: I don't want to stop animations permanently with about:config; I just want to pause and un-pause.
- wlonkly 3y agoThis extension lets you toggle the global setting, but it also optionally lets you toggle individual GIFs: https://addons.mozilla.org/en-US/firefox/addon/toggleanigif/ https://addons.mozilla.org/en-US/firefox/addon/toggleanigif/
- caditinpiscinam 3y ago> although some people want to delete it I hope they don't. The argument for removing it is basically that if you understand geometry, then the conclusion is obvious; but since this is an area where most people's understanding of geometry is incorrect (myself included, before today), the article is valuable. I don't see how it's different from articles on other mathematical paradoxes (Simpson's paradox, for example).
- ecshafer 3y agoMy answer to this after reading the question was 1, because by definition it is one revolution. So I thought that was trick, and the answer essentially is none of the above. But there is a lot more nuance here than just that with multiple definitions of revolution versus rotations, and sidereal time is where this answer can get weird.
- HarHarVeryFunny 3y agoThe only ambiguity there would be revolution/rotation about what center - the small disk's own center or the center of the large one. It seems pretty obvious they are expecting you to calculate something, so assuming this is a trick question and the answer is 1 would seem a risky interpretation, and anyways wasn't one of the answer options.
- matt-attack 3y agoBut isn’t that precisely the distinction between rotation and revolution already provides? When I first read it I thought, well they used the word revolution so clearly the answer is 1. If they had stated “rotations” then the answer is obviously 4. It’s pretty ridiculous they couldn’t use the right word when the distinction was taught back it elementary school during the discussion of the motion of the earth.
- HarHarVeryFunny 3y agoBut why is it obviously 4 ? Is it equally obvious that if the small disk was rolling around the inside of the large disk then the answer would be 2 ? If you already know the relationship between distance traveled by the center of the small circle and number of rotations, then of course both answers (for outside of circle, or inside) are obvious, but the inside case doesn't seem intuitive. btw, it seems they were intending "3" to be the right answer, but the wording isn't even close to what it'd have to be for that to be the right answer!
- matt-attack 3y ago
- gumby 3y agoInteresting: I took the SAT in 1982 and don’t remember this problem. They don’t give you your % right, just percentile and a mysterious score between 200 and 800 for some reason. Does 800 mean 100%?
- hatthew 3y agoanecdata from years ago: 100% is 800, and leaving one question blank is 780.
- zdw 3y agoI got an 800 on the Math portion of the SAT, but the results also said I missed a question (this was mid-90's), so maybe that one was thrown out? (1480 combined, did a prep class but didn't pay much attention to the language bits)
- gumby 3y agoBack in 1982 our school’s entire SAT prep was: “bring only #2 pencils. Sharpen them before you come. Fill the bubble completely and don’t leave any other marks. If you can eliminate one answer, it’s worth picking one randomly, else skip the question.” I don’t remember that there was any SAT prep culture like there is these days. Nobody had heard of ACT — perhaps it didn’t exist yet. There were apparently about 50 of us in my year at MIT who had 800/800, and apparently that was pretty standard. I don’t think I was the only one in my HS class of 39.
- calfuris 3y agoThe scaled scores are intended to be directly comparable, so the mapping from raw score to scaled score depends on the difficulty of the questions on the particular test that you took. On a sufficiently hard section, you can miss a question and still get an 800.
- gnicholas 3y agoWhen I took the SAT a couple decades later, there were multiple sittings per year. Is it possible you took it at a different time? You should be able to check the news coverage and see which sitting it refers to.
- ad404b8a372f2b9 3y agoIt's odd to me that anyone would come up with 3, to me it was immediately very apparent from the diagram that the closest answer was 9/2.
- HarHarVeryFunny 3y agoI guess if you're smart enough to realize that 4 is the right answer, but isn't one of the choices, then the next question is "what were they thinking?", which is why 3 would be the smart guess to get your answer marked as correct.
- deleted 3y ago[deleted]
- pbj1968 3y agoI’m no genius, but I used to score well on such tests as a youngster. I was handed an IQ test circa ~1996 and got about two thirds through it before I found a question where none of the responses were correct. I brought it to the teacher’s attention. “There is no way you could possibly be right, this test was reviewed first!” Anyway, blame it on photocopy errors or whatever, but the answers were wrong. Still mad about it. I took another one ~2007 when I was looking to be a marketing person for a construction equipment rental company. This one was about 30 questions over 60 minutes. I got to question 26, which was some extraordinarily complicated question about how many cuts would it take to chop down a large board into the pieces you needed. After I wasted several minutes methodically writing this out, I realized the true test was realizing it was a time waster question one should skip. 27-30 were far simpler and then the buzzer ran out on me.
- pedrosorio 3y ago> Still mad about it. Why?
- fsckboy 3y agothey told him it was an IQ test but it was actually a psychological profile to diagnose his anger issues
- mrfox321 3y agoFor the same reason why he brought up his iq tests in the first place. Because he self-identifies with some definition of iq.
- pbj1968 3y agoNot at all. The authority figure simply could not live in a world where the question was wrong. A better response, in his role as a school teacher, would have been to tackle the question in depth as a class or otherwise show me how I was mistaken. But given as I was immediately dismissed I’ll never know for sure.
- az226 3y ago
- daguava 3y ago[dead]
- chunsj 3y agoWhy should we take the meaning of revolution in this problem not as the contacting point to meet the circle again, but just as the pointing the same direction? I think this is the source of confusion here. I'm not the native speaker of English and I might take the meaning of "revolution" very absurdly here. Just curious and I have to ask this. :-)
- scotty79 3y agoHe mentions that the word revolution has specific meaning in astronomy which doesn't make any sense in the context of this problem.
- vood 3y agoI'm surprised that only 3 people reported the error. While problem is not trivial, my initial reaction was "it can't be 3, it's too obvious". And it seems that a lot of people in the comments here do get to the right answer on their own. So, why not hundreds of reports?
- crazygringo 3y ago> my initial reaction was "it can't be 3, it's too obvious". The SAT has math questions ranging from easy to hard-ish. Plenty of the questions have very obvious answers. Unlike the AP Physics 2 exam, for example.
- deleted 3y ago[deleted]
- belltaco 3y agoI did a eyeball ball park estimate and figured the closest answer was 9/2 and was right.
- goodpoint 3y agoYes, it's pretty easy to just imagine the rotation and guess it's somewhere around 4. The last part of the rotation is more difficult to imagine.
- scotty79 3y agoSecond part of the video is way more interesting, where he discusses how this toy problem actually relates to how we define what a year is depending on whether we look at the stars or at what's on Earth.
- stormdennis 3y agoI don't revolve once every 24 hrs, the earth does.
- less_less 3y agoOne interesting thing that's not in the video: there is a real application beyond the astronomy one, a scenario where you would want to roll one object around another object, and care about how many rotations it makes. https://en.wikipedia.org/wiki/Epicyclic_gearing https://en.wikipedia.org/wiki/Epicyclic_gearing These are used for car differentials, bicycle gear hubs, pencil sharpeners, and many other applications.
- freediver 3y agoExplaination that works for me is that if you were rolling it around a spot (zero diameter) you would need one full revolution.
- tim333 3y agoTldr it was a four choice multi choice question but the all the options were wrong because the people setting the test got it wrong. So I'm not sure everyone got it wrong, just that they weren't confident enough in a rushed test to cross out A,B,C and D and write in the correct answer!