As time goes by and thinking about giving up Chinese and math studies. It's time for me to admit that you are better than me and I should probably keep on just pretending to be good a school
Math questions like these are usually super easy when you know the trick. It doesnt make you smarter than someone else to know a trick that they do not. The students who understood the trick could do so without trouble in less than a minute, everyone else takes time to discover the trick for themselves.
Yeah, it's like asking an adult to cite a poem 5thgraders have just learned. Ofcourse I can't do that... That being said, we don't know how much the students had worked on the subject beforehand. I mean "a few" 5thgraders solved it? With what level of prior knowledge and of how many? There are some "gifted" children and if out of like 1 million 5thgraders a few find the trick on their own within a minute, I'd call that "gifted".
Well pattern recognition is absolutely a measure of intelligence. You are right of course, that the circumstances of the task is important, but that does not take away from the sophistication of mathematical knowledge required, nor the brilliance needed to recognize the answer right away.
Yes I agree with you. Knowing the trick anyone can do this as long as they understand basic geometry. If you gave a different question (still about geometry) to the same Chinese kid. He wouldn't get it in 1 minute. However, it's still fun to see if you can find the answer yourself. I'm not proud but it took me a little over 15 minutes to understand this.
The thing about these "less than a minute" problems is that it all comes down to how quickly you see how to solve the problem. I'd bet that the kids who solved this problem in under a minute had been working with geometry of shapes and were very familiar with this sort of problem.
I'm willing to bet that they might've solved it but not rigorously. You can see two sets of horizontal triangles both adding up to half the parallelogram horizontally, and then ignore the fact that only some areas are labeled yellow, and come up with the same equation for x. I "solved" it that way, but it's by no means rigorous. They could've also gotten the right answer of 9 by simply playing with the given numbers and choosing a result that "seems" correct. Since they're familiar with addition more than anything, you can add/subtract the two numbers in two different ways to get x=9 or x=11 and then choose between the two (50% of students with this method would've guessed correctly)
It's very possible that the ones who can solve it in less than a minute have already been taught how to solve this type of problems beforehand. In China it's very common for kids to get lessons for math olympiads and they study problem sets like this. They could be simply performing learned routines like "place the shapes on a checkerboard pattern, add up the ones at odd positions and subtract the ones at even positions".
OH WOW SO EASY HAHAHAHA I TOTALLY KNEW IT (aka spending 5 hours trying to figure it out, giving up, waiting a year and a half until finding this video)
Your channel remind me the days I studied math in China. And I really appreciate the teachers always show us how to solve questions with flexibility and creativity. Moreover, we are not born to be good at math, but most of us have been taking tons of practice questions ever since the elementary school. Everything comes with a cost I guess. If you want to do better in something, you have to keep practice on it.
Yo, remember, the smartest 25% of China is equal to the entire USA population... seeing that they have a such a large population it is not surprising they have a large amount of geniuses they must teach
Dear TH-cam, I am currently reviewing for my math exam tomorrow. I was so deeply focused and felt like I could finally ace the exam. How horrible of your algorithm to show me this. Me, a high schooler cannot cope with rational algebraic expressions yet you recommend a video of Chinese fifth graders solving a hard problem in just a minute. I will be reporting you, TH-cam for lowering my self esteem.
Basics? I'm sure I was never taught about the relationships between triangles in a parallelogram like this... Simple enough to understand, but wasn't taught it in school.
@@MultiChrisjb 'Simple enough to understand, but wasn't taught it in school.' Exactly this. I highly suspect the 5th graders who solved it were simply already exposed to the idea of solving in this manner. You could tell just looking at all the overlap and similar and partial triangles the 'easy' answer was going to be some partial arrangement trick like this. Realize something like this is very poor as an IQ test question, it is really a measurement of specific knowledge, not general IQ.
@ModelLights agree, iq tests don't measure your intelligence either. I have gotten scores from 100 in 1 test to over 140 in other tests, but most in 120 to 135. Maybe after a lot of iq tests you can calculate your average, but idk , it still seems silly to me. I don't believe my iq to be 100 but I don't believe it to be 140 either so I will stick with 120ish. But in the end it just is a score about your ability in solving puzzles imo. You cannot measure your iq like that.
I read this comment many times before I realized the genius of this. This is the best thing I have read today. Thank you for this blessed comment. It is comedy gold.
Im asian. Took me 10 minutes to admit defeat... couldn't open up my mind enough to different possible methods... i tried doing what he did except i didnt think of substituting the white for letters and put em in an equation... sigh
It doesn't matter how old you are. It matters if you are taught to solve right or not. Chinese math teachers go through everything in detail so the students have no gaps in their knowledge. I remember being 9th grade and I hardly understood basic math, when I changed school my new math teacher explained math very well and she also gave plenty of examples. Now I'm one of the top mathematicians in my state currently studying mathematicians in uni.
This is a great problem, and if you are thinking there is no way many American students would be able to solve this, as a middle school math teacher I can tell you why many students can't. In my math class I never give a formula and instead show what's happening and then the students derive the equation. This way when they forget to do something, I ask them questions related to what is actually happening. For example, we recently finished up our geometry section and I was talking to the other math teachers. They were like, "I don't know why my students can't remember simple things like radius is half the diameter or when doing area of a triangle, you divide by 2 after doing base times height. These equations are so easy!" Then I ask if they showed where the equation comes from and they said, "Yeah, it's base times height divided by two".... So basically, they just gave the equation and that was it. In my classes, I first show what it means to find the area of a rectangle and then go on to show how a triangle is literally half of a rectangle. I then show different triangles and show how no matter what, it's always half. Then, when they forget to divide by two I ask how many triangles are in a rectangle and they immediately say, "Oh crap, there's two, I was supposed to divide by two!" Once the students have the meaning, they can actually make sense of what's happening and they drastically improve. Anyway, why am I bringing this up? Well, I asked why they don't show the meaning behind the math and I got replied with, "Students don't care about the meaning, they just want to know how to do it so they can pass." This was coming from math teachers that have been teaching for 8+ years (I'm a first year teacher). With this sentiment, it's no wonder many students here in the US would have almost no chance of figuring out a problem like this.
Exactly! Too many teachers fail to develop their student's intuition. Mathematics is about "seeing" the answer, not just arriving at it blindly through rote and formulas. It is really bad in the UK, especially in your equivalent of public schools. Many teachers themselves lack the intuition, and so do not know the importance of attracting people with those skills into the teaching of mathematics. Instead, the try to teach by repetition, and wonder why it eventually hits a limit.
Americans are less competitive than their Asian counterparts, research suggests... A group of American students and a group of Japanese students were given a problem way beyond their level by a naughty researcher. The Americans gave up in less than a minute while the Japanese kept trying for an hour.
JP Mathieu I am a math teacher myself. I did exactly what you did. But that is basic teaching in danish schools where I teach. Examine a problem and find the solution yourself so you will know why the formula works. No need of endless repetition. But you still have to solve problems using the formula. Conceptualization then consolidation are the keywords here..
JP, keep up the good work! As a retired middle school math teacher, I had the fun of witnessing so many aha moments because my students had been taught in their lower grades by teachers who did not understand the concepts they were teaching the kids. By allowing students to experiment and discover things like how many times a diameter-lengthed string goes around the circumference of a circle, you are serving up a banquet every day!
JP Mathieu the fact that the other teachers are right to an extent is a result of more broad problems. i think in 200 years, modern schooling will be seen as medieval (spelling?) tortute compared to our then better ability to grasp psychology, development, and the will to break culture and beuracracy.
Took me 40s lol this question sucks, now I realise that avg American students (mostly) suck at maths Also I'm 15 a 9th grader Also I don't like maths as much as I do phy/bio Also my account name sucks
It took me a an hour to solve. I don’t care how quickly someone else can solve a problem; I have always been a slow and methodical thinker. I found it fun and challenging and solving it for myself was satisfying- what more could one want from a math puzzle? The important thing is personal growth and the joy that brings. Comparing oneself to others is unproductive and leads often to either arrogance or discouragement- neither are life enhancing. Thank you Presh Talwalkar for all these fun and challenging puzzles; I really enjoy your TH-cam channel. You have a great voice for narration; it is clear, friendly and enthusiastic.
I think it is the n triangle thingy. You can zig zag as many times as you want. All the spikes from one base will be half the parallelogram. All the spikes with a base from the other side will be the other half of the area of the parallelogram.
The trick is they have the same height, so all we are really saying is that the sum of the bases of the two triangles is the same as the base of the one triangle.
exactly my point! it's all memorization. Ever since high school and most of my undergrad in engineering, the chinese visa students did exceedingly well on written tests, but would always fail to explain WHY things were a certain way. they admitted to just memorizing things and not knowing why it's done. this is very common, i mean it's not a bad thing, but application problems turned out to be hard for them since they wouldn't be comfortable with elaborating a memorized concept.
Hanyue Li or if that was the case then why didn't most of them solve in under 1 minutes? What about bill he solved it in 10. It's about perspective. There are simply more Chinese with a better education system then the US
Btd Pro you don’t see exact same problem, they are similar. It just builds up the experience on what direction to think in order solve this type of problems. 100 is little too much, but still quite a lot, spending several hours a day.
jim halpert application problems probably aren’t hard to them, more likely they aren’t used to solve them. Chinese students aren’t encouraged to ask questions. They learn how to do things but not so great at figuring out what happened, and they don’t care much, they just need to get to the end, the good grades.
Lovely video! I'm disappointed in myself for not being able to solve this one. Didn't know about the 2 triangles using the full base still have the same area as half of the parallelogram.
I also didn't know about the '2 triangles on the full base' before I solved the puzzle, (I didn't even 'know' (or remember, if I ever did know) the rule about one triangle on the base being half the area, but that seemed fairly obvious once you consider a triangle formed on the parallelogram's diagonal) then it occurred to me that if the triangles whose bases spanned the parallelogram's base shared a side they would combine to make one triangle - with an area of half the area of the parallelogram. Now if you split the triangles apart again, sliding their 'summits' along the opposite edge of the parallelogram, you're not changing the vertical height of either triangle, and since their bases remain the same, their areas don't change either. They will still have a combined area of half the parallelogram's area. And by that logic, you could have any number of non-overlapping triangles (not just two) whose bases span an entire edge of the parallelogram and whose vertices opposite their bases touch the opposite edge of the parallelogram, and they would have a combined area of half the parallelogram's area!
LoL - SPOILERS! After puzzling for 10 mins I noticed your comment at the top of the list and then immediately solved it. As is very often the case, it's knowing (or at least finding) the trick that's the key. In hindsight any number of triangles with bases spanning any side would have half the area.
It took me somewhere between 10 and 15 minutes to solve. I suspect that maybe the 5th graders who solved it in under a minute might have seen examples which use similar techniques. In any event, it is a beautiful problem. Exactly the sort of problem I love to see on this channel. Not too easy, but not too hard to solve.
Classic. Unfortunately, Chinese children who do that are pointed just the same at the nearest rice field with the same words and then they can't change their fate for 60 years. So they are motivated to joke less. =P
There you go. The people who solve this in less than a minute were considered gifted, people who answered like you were deemed as geniuses for thinking out of the box.
@@anshsharma1357 To all mind blowing solvers here, I'd like to share the most difficult Geometry (and overall Math) problem (for me) I've solved so far in my life. It's TetraSpheres from contestcen.com/geom.htm I took about 15 days with 5 attempts to finally arrive at the correct answer to TetraSpheres problem. I'd like to know how much time you take to crack this one. Also if interested, do solve the following on same page contestcen.com/geom.htm • Circles in a square • 4 Tangents • 5 Spheres Submit your answer explanation to contestcen@aol.com and check out the correctness accordingly. Thank you so much.
TH-cam is a source of entertainment. if his challenges were impossible, not many people would find it appealing. which in my opinion, makes him smart, in a way that he has an audience.
or they had just had a lesson on this sort of problem, or it's an apocryphal back story, and I'm sure there are math prodigies out there that really could do the problem that fast... China is a very big country. So who know, in the end it doesn't matter. It's fun to work these problems and learn something new. The satisfaction is in the journey not being "right".
Wow, that’s pretty wicked. I was aware of this relationship with a triangle and a square, but it didn’t occur to me that it would work with all parallelograms. I also didn’t realize that you could have two separate triangles with collinear bases. Nice problem! The properties and relationships of Geometry are endlessly fascinating to me.
I'm a gifted student from Spain. I'm from second grade in secondary school, and it barely took me 35 seconds to solve it. But it was great fun! Thank you MindYourDecisions for your math puzzles!
@@ravager12 Estee... te agradezco el esfuerzo, pero ni se ve nada (entre la calidad de la imagen y que ademas pasas la pagina en dos segundos...) ni ver un cuaderno lleno de garabatos demuestra un carajo acerca de que lo hayas resuelto a la velocidad cómica que aseveras Un consejo: no te tomes tan en serio los comentarios de YT, resulta vagamente grimoso que te hayas tomado todo este esfuerzo en convencer a un extraño, y ademas no consiguiendolo... Que tengas un buen dia... al menos cortes has sido, que menos que corresponder
As a hardened math freak, I thought this one was hard… It turns out it's easy, evident and immediate, even for a child, if you know a simple property of parallelograms. A property that most of us don't know (or have forgotten ?). Now I can see why a (good) elementary schooler can solve it in a minute, provided s/he knows the half area property. The more you know…
Once you see it it's simple. Got hopelessly entangled in trying to find similar triangles and maybe some angle. Doh! Thanks, you made me smile the first time today!
I don't know why people think it can't be solved by the kids under a minute. First , those are competition for gifted kids . Second , at least in my country these theorems are taught to 7th graders , so anyone preparing for Olympiad stuff could naturally get the solution fast enough . And no , it's not like there is a pattern that add the even ones and subtract the odd ones or something, after considerable practice of general , difficult geometry problems , you can come up with the solution real quick.
Solved it in 2 minutes, pretty easy for someone who participated in math olympiads. A lot of geometry problems in 5th grade involve counting areas of triangles and solving basic equations.
It was such a treat to solve the problem using this relationship which has been staring at me in every geometry problem involving parallelograms and remained unacknowledged until now. Thank you!
Exactly. "actually, the younger you are to around 4 to 6 grader, the more likely you are able to solve this types of basic questions. If you are a high schooler, you most likely had forgotten some of the rules of basic maths. Just familiarise with them again and you'll get it in record time. "
@@Marnige Moreover, these types of problems are recurrent. The reason most of these guys got it so fast was because they have already done this type of exercise 100 times over. It's like a rubix cube. Impossible to solve on the fly but if you know the method to solve it then a fifth grader will solve it and not you.
@@bourdiergustave1506 Exactly, I am graduate and remember such problems but wasn't sure how to do them. I automatically did 79+10-72-8 without even knowing why and voila
Those are rookie numbers. I knew the answer was 9 before opening the video. It took me that long because I was solving Fermat's Last Theorem for the fifth time.
More than 20 years ago these things came easy for me. I even used triangles to solve physics math problems that I didn’t necessarily know how to solve otherwise, for as I was lazy and didn’t always attend classes. Probably would have done it in my head back then, now I definitely would have needed pen and paper and put some real effort into it. Mathematics is like a muscle when used a lot it’s strong, not using it it will become sloppy. This is my view of why young kids can solve these problems quickly, they have a talent and that tallent is put to work. Geometry was always my strongest field.
as someone who is significantly stronger than algebra, and using it to hack my way through physics wihtou paying attention, I find it fascinating that you were able to do the same with geometry.
Finally, a MindYourDecisions problem that I solved "accidentally"! I am no genius, but when I got it in 2 mins, I was amazed at myself! This is one of those moments where you don't have to "overthink" and you'll reach the final answer.
I did figure it out but I am shocked that in China 5th graders are taught such geometric principles. That's great. I did this with 4 equations and then substituted. Didn't take much time. Thanks Presh for making such videos and providing us with great math questions. It's just fun.
I solved it thinking differently. The parallelogram can be thought of as 6 identical separate triangles. Area of 1 of these triangles is 0.5x + 36 + 4 Area of 2 of these triangles is x + 72 + 8 Area of 3 of these triangles is 1.5x + 108 + 12 There area of 3 of these triangles equals half of the total area of the parallelogram. Therefore 1.5x + 108 + 12 = y + 79 + x + 10. y = 0.5x + 31. y is the area adjacent north to unknown (?) The area of y + ? equals the area of 1 of the separate triangles of the parallelogram. Therefore y + ? = 0.5x + 36 + 4 We already calculated y previously and we substitute it in. 0.5x + 31 + ? = 0.5x + 36 + 4 31 + ? = 40 ? = 9
There are 10 types of internet mathematicians, those who understand binary, and those who don't... ...And those who didn't expect this joke to be in base 3! XD
I got 98% in grade 8 Math and a M.Sc. in Mechanical Engineering. It took me longer than a minute. Computers make you forget how to solve a lot of problems. I've got a real expensive CAD/CAM Program to solve problems for me. I've been out of school for 30 years too; it's still good to put the calculator away and exercise the brain. I enjoy solving these problems.
I was so excited once you showed the method that I had to pause the video, grab a pencil and paper and solve it myself! Absolutely delightful! I can totally see how it could be solved in 2 minutes, (dang those are some sharp 5th graders though, I'm a pre-grad school college student, and I couldn't get it until you told me the trick!)
Dang. I was close before I gave up. I actually guessed that the answer was 9, although I couldn't prove it to myself. I was looking at triangles sharing a side with the paralellogram, and mentally sliding the opposite point along the opposite side of the parallogram, knowing that the triangle's area wouldn't change by doing that. But it didn't help. Very clever puzzle! Thanks for sharing.
The key in this problem is to be aware of the fact that one set of triangles are exactly to equal another set. It is difficult to realize that without being familiar with the nuances of the parallelogram area. Until then, you are uncertain whether they are exactly equal or not although you suspect they might be equal.
Hey! I actually figured this one out! I'd say it took me about 10 to 15 minutes of 'fiddling' then when I realized you could make triangles with areas equal to exactly half the area of the parallelogram it was a pretty quick calculation. I wonder about the 5th graders who solved it in under a minute. It's certainly not impossible but very impressive. I wonder if they had seen similar problems before? I mean, if I ever see a similar problem, I'd be able to solve it now pretty quickly.
I suspect it is one of those "killer problems" where the solution depends on seeing a (non obvious) pattern, like the other one on the "non existing triangle" sides. If one has been taught/shown the pattern before, it becomes obvious when it is/it can be repeated. And of course on a population of 1.5 billion individuals there are bound to be a few fifth graders that are enormously talented.
I remember this question in an International exam and I'm pretty sure I got it right, when the results came back I was in the top 1% worldwide and I also know with certainty that I am not Chinese (I am Australian)
When you can beat the puzzle: you're about same as 5th grader When you can't beat the puzzle: you're worst than 5th grader Either way, it's still hurting you
There's over 10 million 5th graders in China. Not being smarter than all of them is something I learned to accept long ago. Not a lot would be able to solve this problem.
Wow, I've tried to solve this many times and only now figured it out. In the end I solved it pretty much the same way as in this video. It took me probably an hour altogether but I made it. :)
I watched this vedio till 3:05 then it came into my mind that the problem was really tricky but at the same time very simple. :) But this was a very good problem. Thanks for sharing this one.
I figured it out, but slowly, by writing down the area of the parallelogram in terms of h1 and h2, substituting h2*AD with h1*DC, and solving multiple equations until I was left with x. Seeing that two triangles that use the whole base (and height) of the parallelogram have the same area as one is a genius idea.
Well, I did it in the same way(used triangles cuz the test was for kids and the way this problem was provided gave me an idea that one would need to get hold of the correct intersecting figures that would provide the area without any effort. It didn't take any more than 5 seconds to be able to see the triangles). This doesn't require any genius but I'm feeling great today, lol. You just need to have experience.
Took me about three minutes. One minute to recognize the way the upwards and downwards triangle sums equal each other as do the leftwards and rightwards triangles, one minute to assign letters to the blank spaces and solve it algebraically with two equations, and another minute to realize that I don't need two equations because each part is HALF the parallelogram, so they're all equal and I can just subtract it visually without algebra. Then I skimmed through the video just to see how well explained it was, to see if anyone would be able to make sense of my comment. :) Nice puzzle.
This is a very recognisable pattern. Once you know how to do it with one set of numbers, it's easy to see how to apply it to any comparable alternating pattern inscribed in a parallelogram. Chances are, the children who solved this were drilled in the method. The quick, accurate ones were just average at arithmetic.
Came here from the video you teased this in. I found the answer in a similar way, but it feels more intuitive to me. I used both the horizontal and the vertical triangles to make two equations: (a+x)+(72+b+8) = (c+e+79)+(f+10+d) and (a+b+79+10) = (e+f+8)+(x+c+d+72) Only the numbers and the x switch, so the x makes the difference.
Took me about two minutes, basically you have to be able to observe and find the two equivalent half parallelograms and it's pretty easy from then on. I definitely remember doing these kinds of problems in fifth and sixth grade when I was in China about a decade ago. I was really good at these being the maths kid of the class lmao.
@igidrau So you mean to tell me that knowing half of the area of the parallelogram is equal to the area of any triangle within it with a base that is the side of said parallelogram didn't help at all, all anyone would ever need is how to calculate the areas of the triangle and the parallelogram? Yeah im pretty sure every geometry textbook ever would beg to differ. Also by that logic, why do those even exist? All we should need is a leaflet with the formulas for the areas and perimeters of all basic geometric shapes, we should be able to figure out the rest on the fly....
@@Leo40214 No, if you say that all you need is to know how to calculate the area of a parallelogram, that's all you 're supposed to need. If a surgeon said all you need to know to perform heart surgery is the basic anatomy of the heart, he'd be wrong. The exact same principle applies here. It's just that a surgeon wouldnt have anything to gain from saying that while this guy gains watch time and ad revenue from saying what he said at the start of the video.
actually you don't need to know how to calculate the area of a parallelogram and the only property you need to know about a parallelogram is that opposite sides are parallel (that is only the definition)
but he literally proved the property in the video using nothing but the area formulas. even if you don’t aren’t familiar with it *before* you start the problem, it’s a completely logical progression to go from those formulas to seeing how the areas can be equal. it isn’t introducing new information, it’s just taking what’s already known/given and applying it in a different way
after 12 years I finally realised why 'A' level math was so easy. in primary school, we were tested on creativity but as we learned more techniques, we were tested on our mastery at using them. the former is what we are born with while the latter comes with practice.
I'll be honst here. I can definitely solve this, but It'll take me a minute to remember what math functions I need. Another minute to write it down and then quadruple time to work it through and then go back because I made a human math error when solving.
The answer is 9, I solved this almost instantly, because this problem uses a trick that I teach my students in geometry problems. I write this before watching the video, but I'm pretty sure every simple solution must use this method. The idea is that of comparing areas of shapes by comparing their heights and bases separately. If we denote the area of the quadrilateral in the middle as S, and as X the area of the triangle to the left of the 79 triangle, we have a large triangle who's area is 10+S+79+X. This triangle has the same base and height as the parallelogram so it has half of its area. Similarly, we can count the area of the two triangles resting on the parallelogram's upper edge, their combined area is 8+S+72+X+RED, where RED denotes the red area we're looking for. The sum of these two areas is also half the parallelogram, since they have the same height and their bases add up to that of the parallelogram. Equating these two expressions yields RED=9.
At 4:34 ish, I when back and figured out how they solved it in around 5 minutes Used a combo of both methods, could not put how I did it into words, no algebra, just the stuff I was given
They don't teach first about the 2 triangle thing at all. They understand simply how the area of a triangle is derived, and applied the understanding to the parallelogram and solved it as well. How about you, do you know how to derive 0.5 * base length * height? Or do you simply remember and regurgitate it?
I dont regard them as tricks. I would rather say it as a viewpoint of observation to start the problem itself. What you regard as trick for this prob may not be used for other prob in the same way. We can rather take that initial bit of time to think abt it, before even starting it. That would reduce a lot of time req for solving
You couldn't really "learn" these tricks. The truth is, there are SO many tricks you can use that even if you learned 100 tricks a day from the day you're born thoroughly, you'd still not be able to learn all the tricks even if you lived for 100 years. In fact, mathematicians are still looking for tricks to solve some of the most difficult math problems, such as Riemann's Hypothesis. If all we did at school in math class was learn math tricks, math would not advance. These tricks are simply not learnt, but achieved through perseverance and practice, mainly through noticing patterns and relating unknown concepts with more familiar ones. I used to think the way you do around 3 years ago, when I was learning calculus as an 8th grader. I was obviously extremely good at math to be able to learn so far ahead from my grade level, however, the way I learned math back then was memorizing formulas, which is the most common way of learning math. After taking the AMC 8 and 10, I checked out the solutions to the problems that I thought I "had never learned", and realized I understood everything in the solution, it was a matter of "learning" these tricks. So I searched the internet for these tricks, went to a website with a list of "top 100 most used math theorems", and began studying them. I quickly realized that NONE of these theorems ever appeared on the AMC 8/10, and neither have I even learned the field they were in (topology, advanced euclidean geometry, multivariable calculus, etc). After years of research and practice, I've learned that learning these tricks will not help you improve in math, unless you consider improving as being able to solve a "complicated" problem over and over again, each time changing a value. The only way you could be good at solving problems like these is to develop your problem solving skills. If you're interested, I recommend trying problems on the alcumus section of aops.com under resources. Try doing 5 problems a day, and you'll quickly start to develop this skill. If you want more practice and communication, try brilliant.org. Hope this helps!
Useful for what ? Carpet-laying ? Building a wooden boat ? Planning your vegetable garden ? Building a bridge between the two peaks ? Useful for nothing.
Meh, found this! name points between AB: M, BC: K, CD: N 1) square of AKD is half of paralellogram square 2) sum of squares ADM and BNM is also half of parallelogram square. this two areas has common areas x and y. red area is z. And so: (z+x)+(72+y+8)=x+79+y+10 So, z is 9.
Useful hack for finding solution - you can change task conditions, if it not affect result. it may help see you what was hidden because of complexity. For example, parallelogram is projection of rect, and projection not change areas ratio. Also scaling doesnt. And now you have simple square instead of parallelogram.
Wow it was an awesome problem I knew that area of the triangle with one of its sides same as the base or width of a parallelogram and the other vertex rests on the opposite side has half the area of the parallelogram. But I didn't knew that the sums of area of 2 triangle will be same too. Nice learning...
I remember this one, and hate it. When I was a kid my father used to get his relatives to mail him cram school books from Taiwan. He'd make me do problems every night, from elementary school to early high school. I wanted to go play with the other kids..... Angry, headache inducing times.
The problem as given is insolvable due to not knowing if the internal lines are straight all the way through. For all we know the lines could bend at the internal intersections or even be curved lines. The moment you state that a figure is not to scale, you are told you can not make ANY assumptions based on the diagram alone.
That’s what I was thinking! I think the true answer should be undetermined due to insufficient information. Too many times people assume information in diagrams and it drives me nuts!
Agreed. If the drawing is not to scale how tf the solution is based on drawing on top of it Solution should also be not to scale Serms to me that their idea is to make this problem unsolvable in every way except that one, saying that the drawing was correct, but the area values were just chosen randomly
I respectfully disagree. In my experience, virtually all math problems have "unstated givens". A necessary part of solving virtually any math problem is trying to figure out what is implied but not stated. The more you know about math, the more ways you can find to think outside whatever box that the creator of the math problem was assuming. It seems to me that in any math problem, whether any particular "unstated given" really should have been stated is often a matter of opinion. Here is how I looked at this problem. I saw it as a geometry problem. Most geometry problems are not drawn to scale, but the straight lines still denote straight lines. So to me, that was the "box" that the problem creator was assuming. I hardly considered the idea that the straight lines might really be bent or curved, because I could see instantly that if we allowed that, then clearly there was insufficient information to solve the problem. So clearly we couldn't allow that. I enjoyed the problem, and solved it (but not in anything like a minute). I'm sorry that your mileage differed.
If you want to pick the words and fool yourself, keep thinking that way and you never improve. Anyone who is trying to argue the words "not to scale" doesn't actually understand what it means. "Not to scale" means the given areas are not in measurable ratios. This gives a clear indication to students not to use scale paper to measure and estimate the value from another triangle, the area needs to be calculated. This term never indicates a straight line can be bent.
Thanks!
Twelve minus 8 is ..
@@Justsaying-.12 - 8 = 8
I always thought I was smart and really good at math and logic problems
Until I started watching this channel
I still am , even after watching these.
Hear, hear
Eriola Allmetaj
I never considered myself smart or good at math and logic problems.
Finding this channel just reinforced that fact.
Eriola Allmetaj same
Same 😂😂
I am a chinese person, and now I am thinking am I really Chinese?
dy an 不知道，你真的是中国人吗？-
你问我，我问谁？
@@texas2957 你问你自己呗 XD
＂我＂说你是中国人
As time goes by and thinking about giving up Chinese and math studies. It's time for me to admit that you are better than me and I should probably keep on just pretending to be good a school
Mayosski ok?
Math questions like these are usually super easy when you know the trick. It doesnt make you smarter than someone else to know a trick that they do not. The students who understood the trick could do so without trouble in less than a minute, everyone else takes time to discover the trick for themselves.
That's right, and that's why youtube will kill teacher's job. In this quarantine my son is advancing more here at home than at school...
Yeah, it's like asking an adult to cite a poem 5thgraders have just learned. Ofcourse I can't do that...
That being said, we don't know how much the students had worked on the subject beforehand. I mean "a few" 5thgraders solved it? With what level of prior knowledge and of how many? There are some "gifted" children and if out of like 1 million 5thgraders a few find the trick on their own within a minute, I'd call that "gifted".
Well pattern recognition is absolutely a measure of intelligence. You are right of course, that the circumstances of the task is important, but that does not take away from the sophistication of mathematical knowledge required, nor the brilliance needed to recognize the answer right away.
Yes I agree with you. Knowing the trick anyone can do this as long as they understand basic geometry. If you gave a different question (still about geometry) to the same Chinese kid. He wouldn't get it in 1 minute. However, it's still fun to see if you can find the answer yourself. I'm not proud but it took me a little over 15 minutes to understand this.
@@evastronomy8048
That's normal lmao
The thing about these "less than a minute" problems is that it all comes down to how quickly you see how to solve the problem. I'd bet that the kids who solved this problem in under a minute had been working with geometry of shapes and were very familiar with this sort of problem.
Right, I doubt they were coming at it cold, as we were.
I'm willing to bet that they might've solved it but not rigorously. You can see two sets of horizontal triangles both adding up to half the parallelogram horizontally, and then ignore the fact that only some areas are labeled yellow, and come up with the same equation for x. I "solved" it that way, but it's by no means rigorous.
They could've also gotten the right answer of 9 by simply playing with the given numbers and choosing a result that "seems" correct.
Since they're familiar with addition more than anything, you can add/subtract the two numbers in two different ways to get x=9 or x=11 and then choose between the two (50% of students with this method would've guessed correctly)
It's very possible that the ones who can solve it in less than a minute have already been taught how to solve this type of problems beforehand. In China it's very common for kids to get lessons for math olympiads and they study problem sets like this. They could be simply performing learned routines like "place the shapes on a checkerboard pattern, add up the ones at odd positions and subtract the ones at even positions".
I agree with you. It's very true
i could take the same person 1 or 20 minutes to solve, you need a bit of luck to see it
OH WOW SO EASY HAHAHAHA I TOTALLY KNEW IT (aka spending 5 hours trying to figure it out, giving up, waiting a year and a half until finding this video)
Don't worry, you're still amazing at arranging and performing music :)
Nobody is born equal. Sad reality.
Wait Lionel why are _you_ here?
Why tf are you here? Go compose something!!
@@k10-s7q music is math
Your channel remind me the days I studied math in China. And I really appreciate the teachers always show us how to solve questions with flexibility and creativity. Moreover, we are not born to be good at math, but most of us have been taking tons of practice questions ever since the elementary school. Everything comes with a cost I guess. If you want to do better in something, you have to keep practice on it.
Practice makes a man perfect.
This is why I think people with tallent are really people with strong interest
intresting fun fact: th-cam.com/video/YIs3th01NV0/w-d-xo.html
amazing .....th-cam.com/video/wbQmH1jDKUA/w-d-xo.html
Well said.
A 5th grader in China is solving under a minute.... But in US grown adult are still arguing that the earth is FLAT.... RIP America.... lol
it's laurel
Or are they a boy or girl.
Yo, remember, the smartest 25% of China is equal to the entire USA population... seeing that they have a such a large population it is not surprising they have a large amount of geniuses they must teach
William Lewis
No you mean the dumbest 25% is equal to America
William Lewis it's to scale meaning it is not surprising because lthay doesn't matter, it should be harder to be smart with so much ppl
Dear TH-cam,
I am currently reviewing for my math exam tomorrow. I was so deeply focused and felt like I could finally ace the exam. How horrible of your algorithm to show me this. Me, a high schooler cannot cope with rational algebraic expressions yet you recommend a video of Chinese fifth graders solving a hard problem in just a minute. I will be reporting you, TH-cam for lowering my self esteem.
thanks for ruining the joke at the end
Instead of commenting, you could have studied!
The prerequisites for the problem was to know how to solve these types of problems already
@@ajety no he was saying it to the other guy
kat pxinshu How’d the exam go?
This is one of the most beautiful solutions on this channel. No trig, no calculus - just the very basics.
Basics? I'm sure I was never taught about the relationships between triangles in a parallelogram like this... Simple enough to understand, but wasn't taught it in school.
It is called Genius
@@MultiChrisjb 'Simple enough to understand, but wasn't taught it in school.' Exactly this. I highly suspect the 5th graders who solved it were simply already exposed to the idea of solving in this manner.
You could tell just looking at all the overlap and similar and partial triangles the 'easy' answer was going to be some partial arrangement trick like this.
Realize something like this is very poor as an IQ test question, it is really a measurement of specific knowledge, not general IQ.
@ModelLights agree, iq tests don't measure your intelligence either. I have gotten scores from 100 in 1 test to over 140 in other tests, but most in 120 to 135. Maybe after a lot of iq tests you can calculate your average, but idk , it still seems silly to me. I don't believe my iq to be 100 but I don't believe it to be 140 either so I will stick with 120ish. But in the end it just is a score about your ability in solving puzzles imo. You cannot measure your iq like that.
@@MultiChrisjb You can figure out their relationship!
"Can You Solve A 5th Grade Math Problem From China?"
can't i just try and solve it from my living room instead?
I read this comment many times before I realized the genius of this. This is the best thing I have read today. Thank you for this blessed comment. It is comedy gold.
BlankTom Amazing comment
Lol
The English language is so buggy
loooooooool
Difficulty: ASIAN.
I"m not asian and I solved it in 10 sec.
Najdorf sicilian aha...
That's racist.
Mike :] im an asian myself
Najdorf sicilian i know, im kidding. You're all so smart.
Got you going though, huh? :]
Im asian. Took me 10 minutes to admit defeat... couldn't open up my mind enough to different possible methods... i tried doing what he did except i didnt think of substituting the white for letters and put em in an equation... sigh
It doesn't matter how old you are. It matters if you are taught to solve right or not. Chinese math teachers go through everything in detail so the students have no gaps in their knowledge. I remember being 9th grade and I hardly understood basic math, when I changed school my new math teacher explained math very well and she also gave plenty of examples. Now I'm one of the top mathematicians in my state currently studying mathematicians in uni.
This is a great problem, and if you are thinking there is no way many American students would be able to solve this, as a middle school math teacher I can tell you why many students can't.
In my math class I never give a formula and instead show what's happening and then the students derive the equation. This way when they forget to do something, I ask them questions related to what is actually happening. For example, we recently finished up our geometry section and I was talking to the other math teachers. They were like, "I don't know why my students can't remember simple things like radius is half the diameter or when doing area of a triangle, you divide by 2 after doing base times height. These equations are so easy!" Then I ask if they showed where the equation comes from and they said, "Yeah, it's base times height divided by two"....
So basically, they just gave the equation and that was it.
In my classes, I first show what it means to find the area of a rectangle and then go on to show how a triangle is literally half of a rectangle. I then show different triangles and show how no matter what, it's always half. Then, when they forget to divide by two I ask how many triangles are in a rectangle and they immediately say, "Oh crap, there's two, I was supposed to divide by two!" Once the students have the meaning, they can actually make sense of what's happening and they drastically improve.
Anyway, why am I bringing this up? Well, I asked why they don't show the meaning behind the math and I got replied with, "Students don't care about the meaning, they just want to know how to do it so they can pass." This was coming from math teachers that have been teaching for 8+ years (I'm a first year teacher). With this sentiment, it's no wonder many students here in the US would have almost no chance of figuring out a problem like this.
Exactly! Too many teachers fail to develop their student's intuition. Mathematics is about "seeing" the answer, not just arriving at it blindly through rote and formulas. It is really bad in the UK, especially in your equivalent of public schools. Many teachers themselves lack the intuition, and so do not know the importance of attracting people with those skills into the teaching of mathematics. Instead, the try to teach by repetition, and wonder why it eventually hits a limit.
Americans are less competitive than their Asian counterparts, research suggests...
A group of American students and a group of Japanese students were given a problem way beyond their level by a naughty researcher. The Americans gave up in less than a minute while the Japanese kept trying for an hour.
JP Mathieu I am a math teacher myself. I did exactly what you did. But that is basic teaching in danish schools where I teach. Examine a problem and find the solution yourself so you will know why the formula works. No need of endless repetition. But you still have to solve problems using the formula. Conceptualization then consolidation are the keywords here..
JP, keep up the good work! As a retired middle school math teacher, I had the fun of witnessing so many aha moments because my students had been taught in their lower grades by teachers who did not understand the concepts they were teaching the kids. By allowing students to experiment and discover things like how many times a diameter-lengthed string goes around the circumference of a circle, you are serving up a banquet every day!
JP Mathieu the fact that the other teachers are right to an extent is a result of more broad problems. i think in 200 years, modern schooling will be seen as medieval (spelling?) tortute compared to our then better ability to grasp psychology, development, and the will to break culture and beuracracy.
The red triangle looks a little bit bigger than the triangle with an 8. I guessed 9.
Muffin Button same but i guessed based on the 10 being bigger
yeah but the question said not drawn to scale
nice logic dude
Same, thats what i said aswell
“Not to scale”
I am Chinese but usually these questions are just for fun.
I’m Asian too and this question is a joke it isn’t hard to find triangles
@@chocowell_ I'm not asian I'm albanian but we just have these questions as little games
Took me 40s lol this question sucks, now I realise that avg American students (mostly) suck at maths
Also I'm 15 a 9th grader
Also I don't like maths as much as I do phy/bio
Also my account name sucks
ahah ahah
ProNoobGamer h “maths”
It took me a an hour to solve. I don’t care how quickly someone else can solve a problem; I have always been a slow and methodical thinker. I found it fun and challenging and solving it for myself was satisfying- what more could one want from a math puzzle? The important thing is personal growth and the joy that brings. Comparing oneself to others is unproductive and leads often to either arrogance or discouragement- neither are life enhancing.
Thank you Presh Talwalkar for all these fun and challenging puzzles; I really enjoy your TH-cam channel. You have a great voice for narration; it is clear, friendly and enthusiastic.
I'm happy for you buddy, but...
Bruhhh
Never realized the 2 triangles thingy, once you explained that and I saw the problem again I instantly saw the solution too
I think it is the n triangle thingy. You can zig zag as many times as you want. All the spikes from one base will be half the parallelogram. All the spikes with a base from the other side will be the other half of the area of the parallelogram.
The trick is they have the same height, so all we are really saying is that the sum of the bases of the two triangles is the same as the base of the one triangle.
The Chinese students can solve it in less than one minute because they literally encountered 100’s of problems like this one EVERY SINGLE DAY.
exactly my point! it's all memorization. Ever since high school and most of my undergrad in engineering, the chinese visa students did exceedingly well on written tests, but would always fail to explain WHY things were a certain way. they admitted to just memorizing things and not knowing why it's done. this is very common, i mean it's not a bad thing, but application problems turned out to be hard for them since they wouldn't be comfortable with elaborating a memorized concept.
Hanyue Li or if that was the case then why didn't most of them solve in under 1 minutes? What about bill he solved it in 10. It's about perspective. There are simply more Chinese with a better education system then the US
Btd Pro you don’t see exact same problem, they are similar. It just builds up the experience on what direction to think in order solve this type of problems. 100 is little too much, but still quite a lot, spending several hours a day.
jim halpert application problems probably aren’t hard to them, more likely they aren’t used to solve them. Chinese students aren’t encouraged to ask questions. They learn how to do things but not so great at figuring out what happened, and they don’t care much, they just need to get to the end, the good grades.
yeah you're right
Lovely video! I'm disappointed in myself for not being able to solve this one. Didn't know about the 2 triangles using the full base still have the same area as half of the parallelogram.
Well now you know
Shrey Rupani That’s certainly the key insight I was missing. I think I was on the right track, but I was weak and watched the answer.
Yeahh me too. I figured out the half triangle(79+10) but thats it.
I also didn't know about the '2 triangles on the full base' before I solved the puzzle, (I didn't even 'know' (or remember, if I ever did know) the rule about one triangle on the base being half the area, but that seemed fairly obvious once you consider a triangle formed on the parallelogram's diagonal) then it occurred to me that if the triangles whose bases spanned the parallelogram's base shared a side they would combine to make one triangle - with an area of half the area of the parallelogram. Now if you split the triangles apart again, sliding their 'summits' along the opposite edge of the parallelogram, you're not changing the vertical height of either triangle, and since their bases remain the same, their areas don't change either. They will still have a combined area of half the parallelogram's area.
And by that logic, you could have any number of non-overlapping triangles (not just two) whose bases span an entire edge of the parallelogram and whose vertices opposite their bases touch the opposite edge of the parallelogram, and they would have a combined area of half the parallelogram's area!
LoL - SPOILERS! After puzzling for 10 mins I noticed your comment at the top of the list and then immediately solved it. As is very often the case, it's knowing (or at least finding) the trick that's the key. In hindsight any number of triangles with bases spanning any side would have half the area.
I‘m taking my German Math finals two days from now... TH-cam suggests me this and now my hopes are completely down.
How did it go?
Did you do well?
Chinese gifted kids: You cant defeat me.
Me: I know, but he can.
The guy who guessed it right in 2 seconds:
The legend
Unknown
The MADLAD
legend27
Senpai
bruh das me lmfao
It took me somewhere between 10 and 15 minutes to solve. I suspect that maybe the 5th graders who solved it in under a minute might have seen examples which use similar techniques. In any event, it is a beautiful problem. Exactly the sort of problem I love to see on this channel. Not too easy, but not too hard to solve.
Find the area of the red triangle
Point the finger to the screen and say:
”that’s the area”
Classic. Unfortunately, Chinese children who do that are pointed just the same at the nearest rice field with the same words and then they can't change their fate for 60 years. So they are motivated to joke less. =P
If it was in a math test and I didn’t understand, I’d try to be smart and do that. It’s not technically wrong
There you go. The people who solve this in less than a minute were considered gifted, people who answered like you were deemed as geniuses for thinking out of the box.
Unfortunately the area is not to scale. The image is not equal to the actual area.
The parallelogram was a paid actor
How is parallelogram a paid actor?
@@michaelwinge3042 This would not have happened if the parallelogram had a gun
Weijian Lim it’s a joke
got this in about five minutes. you don't need to know any special theorems you just need good geometric intuition
yep, took me like a minute by just looking at the screen. was easy to spot the triangle areas that are half of the parallelogram
Nerd
@@anshsharma1357
To all mind blowing solvers here, I'd like to share the most difficult Geometry (and overall Math) problem (for me) I've solved so far in my life.
It's TetraSpheres from contestcen.com/geom.htm
I took about 15 days with 5 attempts to finally arrive at the correct answer to TetraSpheres problem. I'd like to know how much time you take to crack this one.
Also if interested, do solve the following on same page contestcen.com/geom.htm
• Circles in a square
• 4 Tangents
• 5 Spheres
Submit your answer explanation to contestcen@aol.com and check out the correctness accordingly.
Thank you so much.
Yeah, me too.
@@anandk9220 which one exactly is it?
"the diagram is not to scale" oh damn I was really going to take out my ruler
I remember a question on the SAT saying it wasn't to scale, then I solved it and it was perfectly to scale. I'm getting scammed here.
less than a minute? i've lost any will to compete in anything
Alex yeah sure. He got it in 1 minute, but someone who has a TH-cam channel devoted to problem solving can't solve it at all. Sounds fishy...
Max I.
MindYourDecisions is not a smart guy. There’s a reason very few of his puzzles are real challenging.
TH-cam is a source of entertainment. if his challenges were impossible, not many people would find it appealing. which in my opinion, makes him smart, in a way that he has an audience.
Alex maybe they just guessed
or they had just had a lesson on this sort of problem, or it's an apocryphal back story, and I'm sure there are math prodigies out there that really could do the problem that fast... China is a very big country. So who know, in the end it doesn't matter. It's fun to work these problems and learn something new. The satisfaction is in the journey not being "right".
Wow, that’s pretty wicked. I was aware of this relationship with a triangle and a square, but it didn’t occur to me that it would work with all parallelograms. I also didn’t realize that you could have two separate triangles with collinear bases. Nice problem! The properties and relationships of Geometry are endlessly fascinating to me.
The two separate triangles was new to me too and what broke open the problem. Really enjoyed learning that bit
I'm a gifted student from Spain. I'm from second grade in secondary school, and it barely took me 35 seconds to solve it. But it was great fun! Thank you MindYourDecisions for your math puzzles!
Nah, tu perfil absolutamente vacio y nuevo dice que las posibilidades de que estés mintiendo como un bellaco son altísimas
Pics or it didn't happen
@@TheChzoronzon Sí que lo hice y si quieres que te lo demuestre lo haré. Cómo quieres que te envie fotos que lo demuestren?
Ya está
@@ravager12 Estee... te agradezco el esfuerzo, pero ni se ve nada (entre la calidad de la imagen y que ademas pasas la pagina en dos segundos...) ni ver un cuaderno lleno de garabatos demuestra un carajo acerca de que lo hayas resuelto a la velocidad cómica que aseveras
Un consejo: no te tomes tan en serio los comentarios de YT, resulta vagamente grimoso que te hayas tomado todo este esfuerzo en convencer a un extraño, y ademas no consiguiendolo...
Que tengas un buen dia... al menos cortes has sido, que menos que corresponder
are you smarter than a fifth grader?
apparently not...
kkim5000 talented*
Becuz their teacher teach that to their student
Bro this is not about smartness. These were already taught to them. So they could solve it in under a minute.
I solved it in 20 secs so i guess i am
@@godbeerus2202 I know for example my school doesn t teach me to think that way so I would be able to solve this
As a hardened math freak, I thought this one was hard… It turns out it's easy, evident and immediate, even for a child, if you know a simple property of parallelograms. A property that most of us don't know (or have forgotten ?). Now I can see why a (good) elementary schooler can solve it in a minute, provided s/he knows the half area property. The more you know…
Risu0chan i thought the same, won't be forgetting it anymore tho lol
Risu0chan thanks, after watching this video I will take more steps to reinforce my knowledge about properties that I may have forgotten
The "even for a child" only counts if you are chinese
Once you see it it's simple. Got hopelessly entangled in trying to find similar triangles and maybe some angle. Doh!
Thanks, you made me smile the first time today!
OMG sameeee, I was trying also to find similar triangles but no triangle was similar as their areas are different lol
This really wasn’t that hard. You just need to know that specific theorem
Ye, its always easy when you know how its done
In no parallel universe would you and I be friends
@@Chief_Miles_OBrien xD..
by "specific theorem" you mean the area formula for a triangle? because that is literally everything used to derive the answer.
Android Sheldon LMAO
I don't know why people think it can't be solved by the kids under a minute.
First , those are competition for gifted kids . Second , at least in my country these theorems are taught to 7th graders , so anyone preparing for Olympiad stuff could naturally get the solution fast enough . And no , it's not like there is a pattern that add the even ones and subtract the odd ones or something, after considerable practice of general , difficult geometry problems , you can come up with the solution real quick.
Oh my, I made it in two minutes because I remembered about the triangles within a paralleogram rule!! Very nice one, it is simple but still fun!!!!
Solved it in 2 minutes, pretty easy for someone who participated in math olympiads. A lot of geometry problems in 5th grade involve counting areas of triangles and solving basic equations.
It was such a treat to solve the problem using this relationship which has been staring at me in every geometry problem involving parallelograms and remained unacknowledged until now. Thank you!
I solved it under 3 minutes but I am a 12th grader in India....and I was able to solve it because I was practicing geometry problem for a while.
Exactly. "actually, the younger you are to around 4 to 6 grader, the more likely you are able to solve this types of basic questions. If you are a high schooler, you most likely had forgotten some of the rules of basic maths. Just familiarise with them again and you'll get it in record time. "
@@Marnige Moreover, these types of problems are recurrent. The reason most of these guys got it so fast was because they have already done this type of exercise 100 times over. It's like a rubix cube. Impossible to solve on the fly but if you know the method to solve it then a fifth grader will solve it and not you.
@@bourdiergustave1506 Exactly. I bet they did it in a minute because for them, it's just a matter of addition and subtraction now.
@@will123134 Did it take more than a minute though?
@@bourdiergustave1506 Exactly, I am graduate and remember such problems but wasn't sure how to do them. I automatically did 79+10-72-8 without even knowing why and voila
I am a 3rd grade student, and I solved in 3 seconds. The reason I took that long is because I was in the middle of working on a Laplace Transform.
Shango Not impressive. I solved this under a second and I'm still in the second trimester.
Shango and the only reason it took that long was because i was trying to do a backflip.
LOL!
Those are rookie numbers. I knew the answer was 9 before opening the video. It took me that long because I was solving Fermat's Last Theorem for the fifth time.
Trolling like hell
I can't hit the like button more times. Can't stop appreciating the guy who made this problem. Thanks thanks thanks Presh.
Dad: you doctor yet?
Son: Im 12.
Dad: talk to me when you doctor.
Son: then we will never talk again, dad.
More than 20 years ago these things came easy for me. I even used triangles to solve physics math problems that I didn’t necessarily know how to solve otherwise, for as I was lazy and didn’t always attend classes.
Probably would have done it in my head back then, now I definitely would have needed pen and paper and put some real effort into it.
Mathematics is like a muscle when used a lot it’s strong, not using it it will become sloppy.
This is my view of why young kids can solve these problems quickly, they have a talent and that tallent is put to work. Geometry was always my strongest field.
as someone who is significantly stronger than algebra, and using it to hack my way through physics wihtou paying attention, I find it fascinating that you were able to do the same with geometry.
Finally, a MindYourDecisions problem that I solved "accidentally"! I am no genius, but when I got it in 2 mins, I was amazed at myself! This is one of those moments where you don't have to "overthink" and you'll reach the final answer.
I did figure it out but I am shocked that in China 5th graders are taught such geometric principles. That's great. I did this with 4 equations and then substituted. Didn't take much time. Thanks Presh for making such videos and providing us with great math questions. It's just fun.
Did you miss the 5th grade geometry problem from *Soviet Union* ?
th-cam.com/video/m5evLoL0xwg/w-d-xo.html
ParaLOLogram
Love your videos
BRAWLLL STARS
Hello
I solved it thinking differently. The parallelogram can be thought of as 6 identical separate triangles.
Area of 1 of these triangles is 0.5x + 36 + 4
Area of 2 of these triangles is x + 72 + 8
Area of 3 of these triangles is 1.5x + 108 + 12
There area of 3 of these triangles equals half of the total area of the parallelogram.
Therefore 1.5x + 108 + 12 = y + 79 + x + 10.
y = 0.5x + 31.
y is the area adjacent north to unknown (?)
The area of y + ? equals the area of 1 of the separate triangles of the parallelogram.
Therefore y + ? = 0.5x + 36 + 4
We already calculated y previously and we substitute it in.
0.5x + 31 + ? = 0.5x + 36 + 4
31 + ? = 40
? = 9
Hmm..every 3 out of 2 students struggle with maths.
I get it! XD
There are 10 types of internet mathematicians, those who understand binary, and those who don't...
...And those who didn't expect this joke to be in base 3!
XD
Finally I'm special at math's lol
2 out of 3 you mean. oh god.
use your brain.
@@user-yp2kp1mj2q that joke went right over your head
Knew the concept but never thought it can be used this way.
Thanks @MindYourDecisions
Me: "maybe what it between 8 and 10, so i guess its 9"
Answer : 9
Me : ftw?
lol same here and I still don't know why it's 9.
It's the average
8+10÷2=18÷2=9
Now you have passed the test!
Me too lol
SARV's guessing brain: mY gOaLs ArE bEyOnD yOuR uNdErStAnDiNg.
Does it count as right if i skipped the equasion part and just thought "9"
Sup3rN0va i hope so
The people liking your comment also thought of 9
maybe you are a savant
Same here
In term of result,yes.
In term of methodology,no.
I got 98% in grade 8 Math and a M.Sc. in Mechanical Engineering. It took me longer than a minute. Computers make you forget how to solve a lot of problems. I've got a real expensive CAD/CAM Program to solve problems for me.
I've been out of school for 30 years too; it's still good to put the calculator away and exercise the brain. I enjoy solving these problems.
I was so excited once you showed the method that I had to pause the video, grab a pencil and paper and solve it myself! Absolutely delightful! I can totally see how it could be solved in 2 minutes, (dang those are some sharp 5th graders though, I'm a pre-grad school college student, and I couldn't get it until you told me the trick!)
Dang. I was close before I gave up. I actually guessed that the answer was 9, although I couldn't prove it to myself. I was looking at triangles sharing a side with the paralellogram, and mentally sliding the opposite point along the opposite side of the parallogram, knowing that the triangle's area wouldn't change by doing that. But it didn't help.
Very clever puzzle! Thanks for sharing.
The key in this problem is to be aware of the fact that one set of triangles are exactly to equal another set. It is difficult to realize that without being familiar with the nuances of the parallelogram area. Until then, you are uncertain whether they are exactly equal or not although you suspect they might be equal.
Am 27 and solving this took me more than 10 minutes. I feel spastic now. Fantastic video.
6:26 was my OHHHH moment
A 5th grader didn't do this in their head in less than a minute.
@MKMW C lol
Hey! I actually figured this one out! I'd say it took me about 10 to 15 minutes of 'fiddling' then when I realized you could make triangles with areas equal to exactly half the area of the parallelogram it was a pretty quick calculation.
I wonder about the 5th graders who solved it in under a minute. It's certainly not impossible but very impressive. I wonder if they had seen similar problems before? I mean, if I ever see a similar problem, I'd be able to solve it now pretty quickly.
I suspect it is one of those "killer problems" where the solution depends on seeing a (non obvious) pattern, like the other one on the "non existing triangle" sides. If one has been taught/shown the pattern before, it becomes obvious when it is/it can be repeated. And of course on a population of 1.5 billion individuals there are bound to be a few fifth graders that are enormously talented.
I remember this question in an International exam and I'm pretty sure I got it right, when the results came back I was in the top 1% worldwide and I also know with certainty that I am not Chinese (I am Australian)
Great problem! I like problems with an aha moment. As opposed to tedious calculation.
Finally some quality content.
This just popped up on my suggestions but I'm amazed how that problem can be easily solved.
When you can beat the puzzle: you're about same as 5th grader
When you can't beat the puzzle: you're worst than 5th grader
Either way, it's still hurting you
There's over 10 million 5th graders in China. Not being smarter than all of them is something I learned to accept long ago. Not a lot would be able to solve this problem.
Don't be sad you applied all the theorems you knew, but kids knew only one, so they were quick
Wow, I've tried to solve this many times and only now figured it out. In the end I solved it pretty much the same way as in this video. It took me probably an hour altogether but I made it. :)
I watched this vedio till 3:05 then it came into my mind that the problem was really tricky but at the same time very simple. :)
But this was a very good problem. Thanks for sharing this one.
I figured it out, but slowly, by writing down the area of the parallelogram in terms of h1 and h2, substituting h2*AD with h1*DC, and solving multiple equations until I was left with x. Seeing that two triangles that use the whole base (and height) of the parallelogram have the same area as one is a genius idea.
Well, I did it in the same way(used triangles cuz the test was for kids and the way this problem was provided gave me an idea that one would need to get hold of the correct intersecting figures that would provide the area without any effort. It didn't take any more than 5 seconds to be able to see the triangles). This doesn't require any genius but I'm feeling great today, lol. You just need to have experience.
I didn’t knew what was a parallelogram in 5th grade…
Took me about three minutes. One minute to recognize the way the upwards and downwards triangle sums equal each other as do the leftwards and rightwards triangles, one minute to assign letters to the blank spaces and solve it algebraically with two equations, and another minute to realize that I don't need two equations because each part is HALF the parallelogram, so they're all equal and I can just subtract it visually without algebra.
Then I skimmed through the video just to see how well explained it was, to see if anyone would be able to make sense of my comment. :) Nice puzzle.
This is a very recognisable pattern. Once you know how to do it with one set of numbers, it's easy to see how to apply it to any comparable alternating pattern inscribed in a parallelogram. Chances are, the children who solved this were drilled in the method. The quick, accurate ones were just average at arithmetic.
I remember those days of dealing with these questions. I probably lost my talent after adulting. Haha.
Came here from the video you teased this in. I found the answer in a similar way, but it feels more intuitive to me. I used both the horizontal and the vertical triangles to make two equations:
(a+x)+(72+b+8) = (c+e+79)+(f+10+d) and
(a+b+79+10) = (e+f+8)+(x+c+d+72)
Only the numbers and the x switch, so the x makes the difference.
this question is so simple, still I didn't get for the first moment and I had to hear his explanation...
anyway I just need to practice for 40h/day
If you can do geometry slowly, you can do it quickly!
Mathematical intuitions are born not created!
Ling ling
another ling ling wanna be
I was actually on the right track, I guess that’s good
Okay, I admit. This one got me. Brilliant!
Took me about two minutes, basically you have to be able to observe and find the two equivalent half parallelograms and it's pretty easy from then on. I definitely remember doing these kinds of problems in fifth and sixth grade when I was in China about a decade ago. I was really good at these being the maths kid of the class lmao.
This is kinda misleading, you're required to know the properties of the parallelogram, not just how to calculate its area.
That’s like saying I need to learn what’s in the calculus textbook, not what the cover of the book looks like.
@igidrau So you mean to tell me that knowing half of the area of the parallelogram is equal to the area of any triangle within it with a base that is the side of said parallelogram didn't help at all, all anyone would ever need is how to calculate the areas of the triangle and the parallelogram? Yeah im pretty sure every geometry textbook ever would beg to differ. Also by that logic, why do those even exist? All we should need is a leaflet with the formulas for the areas and perimeters of all basic geometric shapes, we should be able to figure out the rest on the fly....
@@Leo40214 No, if you say that all you need is to know how to calculate the area of a parallelogram, that's all you 're supposed to need. If a surgeon said all you need to know to perform heart surgery is the basic anatomy of the heart, he'd be wrong. The exact same principle applies here. It's just that a surgeon wouldnt have anything to gain from saying that while this guy gains watch time and ad revenue from saying what he said at the start of the video.
actually you don't need to know how to calculate the area of a parallelogram and the only property you need to know about a parallelogram is that opposite sides are parallel (that is only the definition)
but he literally proved the property in the video using nothing but the area formulas. even if you don’t aren’t familiar with it *before* you start the problem, it’s a completely logical progression to go from those formulas to seeing how the areas can be equal. it isn’t introducing new information, it’s just taking what’s already known/given and applying it in a different way
I paused the video to solve it. I did get the right answer, but I took an exaggerated long time to do so; this video was very useful.
after 12 years I finally realised why 'A' level math was so easy. in primary school, we were tested on creativity but as we learned more techniques, we were tested on our mastery at using them. the former is what we are born with while the latter comes with practice.
I'll be honst here. I can definitely solve this, but It'll take me a minute to remember what math functions I need. Another minute to write it down and then quadruple time to work it through and then go back because I made a human math error when solving.
What a lovely question. Brilliantly done. Thank you.
Damn I was like there is 8 and 10 but no nine so I’m guessing nine and it was correct
Shady Directions Studios same! Haha
i like that out of the box thinking
You will go very far in life :)👌👌👌
sAME i saw it was less than 10 but more than 8 so i thought 9
I did 10 plus 8 divided by 2 to get 9
I solved it in 10 seconds by guessing 9 based on observation and extreme luck lmao
The answer is 9, I solved this almost instantly, because this problem uses a trick that I teach my students in geometry problems. I write this before watching the video, but I'm pretty sure every simple solution must use this method.
The idea is that of comparing areas of shapes by comparing their heights and bases separately. If we denote the area of the quadrilateral in the middle as S, and as X the area of the triangle to the left of the 79 triangle, we have a large triangle who's area is 10+S+79+X. This triangle has the same base and height as the parallelogram so it has half of its area.
Similarly, we can count the area of the two triangles resting on the parallelogram's upper edge, their combined area is 8+S+72+X+RED, where RED denotes the red area we're looking for.
The sum of these two areas is also half the parallelogram, since they have the same height and their bases add up to that of the parallelogram. Equating these two expressions yields RED=9.
At 4:34 ish, I when back and figured out how they solved it in around 5 minutes
Used a combo of both methods, could not put how I did it into words, no algebra, just the stuff I was given
"Can you figure out this problem?"
Haha. No.
You know I didn't know the answers BUT I learned , thank you sir.
well,i f in china they teach first about the 2 triangle thing, then is not big deal
Mariano Gaston ,right, try that in U.S.
They don't teach first about the 2 triangle thing at all. They understand simply how the area of a triangle is derived, and applied the understanding to the parallelogram and solved it as well. How about you, do you know how to derive 0.5 * base length * height? Or do you simply remember and regurgitate it?
It's sad that we don't learn these tricks in school. They can be so useful and are so simple.
I know right, I'm in 9th grade and I couldn't even solve this simple problem....
And I'm the best in my math class...
I dont regard them as tricks. I would rather say it as a viewpoint of observation to start the problem itself. What you regard as trick for this prob may not be used for other prob in the same way. We can rather take that initial bit of time to think abt it, before even starting it. That would reduce a lot of time req for solving
You couldn't really "learn" these tricks. The truth is, there are SO many tricks you can use that even if you learned 100 tricks a day from the day you're born thoroughly, you'd still not be able to learn all the tricks even if you lived for 100 years. In fact, mathematicians are still looking for tricks to solve some of the most difficult math problems, such as Riemann's Hypothesis.
If all we did at school in math class was learn math tricks, math would not advance. These tricks are simply not learnt, but achieved through perseverance and practice, mainly through noticing patterns and relating unknown concepts with more familiar ones.
I used to think the way you do around 3 years ago, when I was learning calculus as an 8th grader. I was obviously extremely good at math to be able to learn so far ahead from my grade level, however, the way I learned math back then was memorizing formulas, which is the most common way of learning math.
After taking the AMC 8 and 10, I checked out the solutions to the problems that I thought I "had never learned", and realized I understood everything in the solution, it was a matter of "learning" these tricks. So I searched the internet for these tricks, went to a website with a list of "top 100 most used math theorems", and began studying them. I quickly realized that NONE of these theorems ever appeared on the AMC 8/10, and neither have I even learned the field they were in (topology, advanced euclidean geometry, multivariable calculus, etc).
After years of research and practice, I've learned that learning these tricks will not help you improve in math, unless you consider improving as being able to solve a "complicated" problem over and over again, each time changing a value. The only way you could be good at solving problems like these is to develop your problem solving skills.
If you're interested, I recommend trying problems on the alcumus section of aops.com under resources. Try doing 5 problems a day, and you'll quickly start to develop this skill. If you want more practice and communication, try brilliant.org. Hope this helps!
Useful for what ? Carpet-laying ? Building a wooden boat ? Planning your vegetable garden ? Building a bridge between the two peaks ? Useful for nothing.
This is not a simple problem
Didn't know the whole 2 triangle = half of parallelogram area thing. But once i watched the trick part, i was able to solve it pretty easily
I feels like I almost forgot everything I learnt from school
Really you forgot everything because it will be I "feel" like I almost...... Not I feels 🤣🤣🤣🤣🤣🤣🤣
Meh, found this! name points between AB: M, BC: K, CD: N
1) square of AKD is half of paralellogram square
2) sum of squares ADM and BNM is also half of parallelogram square.
this two areas has common areas x and y. red area is z. And so:
(z+x)+(72+y+8)=x+79+y+10
So, z is 9.
Useful hack for finding solution - you can change task conditions, if it not affect result. it may help see you what was hidden because of complexity.
For example, parallelogram is projection of rect, and projection not change areas ratio. Also scaling doesnt. And now you have simple square instead of parallelogram.
gopher
I don't see why you have to square the areas. Actually, if you square them, your equations are not true.
Sergio Korochinsky he must have meant area where he wrote square.
Nice!
Wow it was an awesome problem
I knew that area of the triangle with one of its sides same as the base or width of a parallelogram and the other vertex rests on the opposite side has half the area of the parallelogram.
But I didn't knew that the sums of area of 2 triangle will be same too.
Nice learning...
I remember this one, and hate it. When I was a kid my father used to get his relatives to mail him cram school books from Taiwan. He'd make me do problems every night, from elementary school to early high school. I wanted to go play with the other kids..... Angry, headache inducing times.
did it pay off or not?
Is it only me, or can anyone else see an optical illusion where the two horizontal sides of the parallelogram don't look parallel?
Same here!
I had to look at the screen at a grazing angle to check that the lines were actually parallel!
same for me
these people really smart at making math questions...
well, i am from hong kong, so i think i can
after watching video: yeah if only i remember what i learnt from 5th grade
Stay safe tho
@@user-ck1zi8qf4i stay safe?
@@realperson9951 Hong Kong riots?
@@user-ck1zi8qf4i oh yea, thanks
@@user-ck1zi8qf4i theres chaos near my home today
i think i need your "stay safe tho" now
The problem as given is insolvable due to not knowing if the internal lines are straight all the way through. For all we know the lines could bend at the internal intersections or even be curved lines. The moment you state that a figure is not to scale, you are told you can not make ANY assumptions based on the diagram alone.
Mavoc It is safe to say there are no "bent" lines... only "bent" sexual orientation like yours
That’s what I was thinking! I think the true answer should be undetermined due to insufficient information. Too many times people assume information in diagrams and it drives me nuts!
Agreed. If the drawing is not to scale how tf the solution is based on drawing on top of it
Solution should also be not to scale
Serms to me that their idea is to make this problem unsolvable in every way except that one, saying that the drawing was correct, but the area values were just chosen randomly
I respectfully disagree.
In my experience, virtually all math problems have "unstated givens".
A necessary part of solving virtually any math problem is trying to figure out what is implied but not stated.
The more you know about math, the more ways you can find to think outside whatever box that the creator of the math problem was assuming.
It seems to me that in any math problem, whether any particular "unstated given" really should have been stated is often a matter of opinion.
Here is how I looked at this problem. I saw it as a geometry problem. Most geometry problems are not drawn to scale, but the straight lines still denote straight lines. So to me, that was the "box" that the problem creator was assuming. I hardly considered the idea that the straight lines might really be bent or curved, because I could see instantly that if we allowed that, then clearly there was insufficient information to solve the problem. So clearly we couldn't allow that.
I enjoyed the problem, and solved it (but not in anything like a minute). I'm sorry that your mileage differed.
If you want to pick the words and fool yourself, keep thinking that way and you never improve.
Anyone who is trying to argue the words "not to scale" doesn't actually understand what it means.
"Not to scale" means the given areas are not in measurable ratios.
This gives a clear indication to students not to use scale paper to measure and estimate the value from another triangle, the area needs to be calculated.
This term never indicates a straight line can be bent.
This was so simple and mind boggling!
Thankyou 🙏🏼
I solved it man ,yes!!. It took about 10 minutes for Me to do it
Good job 🤗👍👏
Easy one
After watching video😂