Genius student solved this in 1 minute - insanely hard geometry problem

Рет қаралды 1,869,726

Күн бұрын

Thanks to Bill from New York for this suggestion! Bill emailed me a problem asked in China to identify talented students. A few very talented students did solve it in less than one minute! I was not able to solve the problem at all. The question involves finding the area of a red triangle in a parallelogram, for a diagram you can see in the video. Even though I didn't solve it, I really enjoyed learning the solution.
My blog post for this video:
wp.me/p6aMk-5r6
If you like my videos, you can support me at Patreon:
/ mindyourdecisions
Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.
My Blog: mindyourdecisions.com/blog/
Twitter: / preshtalwalkar
Facebook: / 168446714965
Google+: plus.google.com/1083366085665...
Pinterest: / preshtalwalkar
Tumblr: / preshtalwalkar
Instagram: / preshtalwalkar
Patreon: / mindyourdecisions
Newsletter (sent only for big news, like a new book release): eepurl.com/KvS0r
If you buy from the links below I may receive a commission for sales. This has no effect on the price for you.
My Books
"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.8/5 stars on 31 reviews)
amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews)
amzn.to/1o3FaAg
"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews.
amzn.to/1GhUUSH
"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews)
amzn.to/1NKbyCs
"Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 4 reviews)
amzn.to/1NKbGlp
"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews)
amzn.to/1LOCI4U
"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews)
amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews)
amzn.to/XRm7M4

Пікірлер: 3 800

@utility73 Жыл бұрын

Thanks!

@Justsaying-. Жыл бұрын

Twelve minus 8 is ..

@bombastic_side_eye_007 10 ай бұрын

@@Justsaying-.12 - 8 = 8

@lennidarys892 4 жыл бұрын

I am a chinese person, and now I am thinking am I really Chinese?

@texas2957 4 жыл бұрын

dy an 不知道，你真的是中国人吗？- 你问我，我问谁？

@lennidarys892 4 жыл бұрын

@@texas2957 你问你自己呗 XD

@texas2957 4 жыл бұрын

＂我＂说你是中国人

@mayosski 4 жыл бұрын

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

@texas2957 4 жыл бұрын

Mayosski ok?

@oni_thefirst 6 жыл бұрын

I always thought I was smart and really good at math and logic problems Until I started watching this channel

@mohitha9230 6 жыл бұрын

I still am , even after watching these.

@askpatrick 6 жыл бұрын

Hear, hear

@philia9351 6 жыл бұрын

Eriola Allmetaj I never considered myself smart or good at math and logic problems. Finding this channel just reinforced that fact.

@edwingraca7708 6 жыл бұрын

Eriola Allmetaj same

@alanmarino404 6 жыл бұрын

Same 😂😂

@aWildKITsune 4 жыл бұрын

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.

@evastronomy8048 4 жыл бұрын

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...

@Shuizid 4 жыл бұрын

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".

@djefr 4 жыл бұрын

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.

@philipptruveller7829 4 жыл бұрын

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.

@egg9709 4 жыл бұрын

@@evastronomy8048 That's normal lmao

@jiachengxue913 4 жыл бұрын

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.

@elonmusk9814 2 жыл бұрын

Practice makes a man perfect.

@SomeAndrian 2 жыл бұрын

This is why I think people with tallent are really people with strong interest

@aayushpaswan2941 2 жыл бұрын

intresting fun fact: kzfaq.info/get/bejne/j6-jZteZlZeyhmQ.html

@cobokobo2115 2 жыл бұрын

amazing .....kzfaq.info/get/bejne/rciBoKtiz6qvhXU.html

@hamadeliterank 2 жыл бұрын

Well said.

@jamessarungbam3598 6 жыл бұрын

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

@add852 6 жыл бұрын

it's laurel

@mrp8488 5 жыл бұрын

Or are they a boy or girl.

@williamlewis2383 4 жыл бұрын

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

@jasonstarrising 4 жыл бұрын

William Lewis No you mean the dumbest 25% is equal to America

@withnovideos-wm8bf 4 жыл бұрын

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

@jamessmith2522 6 жыл бұрын

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.

@wwoods66 6 жыл бұрын

Right, I doubt they were coming at it cold, as we were.

@BigDBrian 6 жыл бұрын

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)

@letao12 6 жыл бұрын

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".

@bluefrog3622 6 жыл бұрын

I agree with you. It's very true

@henkbaas2381 6 жыл бұрын

i could take the same person 1 or 20 minutes to solve, you need a bit of luck to see it

@blaque5900 4 жыл бұрын

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.

@nakamakai5553 3 жыл бұрын

This is one of the most beautiful solutions on this channel. No trig, no calculus - just the very basics.

@MultiChrisjb 2 жыл бұрын

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.

@lukmanalvaro855 2 жыл бұрын

It is called Genius

@ModelLights 2 жыл бұрын

@@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.

@th3smurf692 Жыл бұрын

@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.

@holdthatlforluigi 7 ай бұрын

@@MultiChrisjb You can figure out their relationship!

@Nxn908xxx 6 жыл бұрын

I was born yesterday and I solved it in half a Planck time. Took me that long cuz I was working on Riemann zeta function and building a quantum computer at the same time.

@TheHadMatters 6 жыл бұрын

Only a day old and already making up excuses for your laggardness. I really hope you see a change in your behaviour soon, for your family's honour's sake.

@lutherschultz4725 6 жыл бұрын

you must be an average asian kid

@aleksinuutila2315 6 жыл бұрын

Nxn908xxx Well smart kid, Chuck Norris solved it ten days before he was conceived.

@thuhoang9924 6 жыл бұрын

Don't you mean plank instant? Also, no human could solve it in half a plank instant because nothing is shorter than a plank instant.

@user-iq5iu2tt2h 6 жыл бұрын

Pathetic. How can someone be that slow? What a pitiful situation.

@MusicalBasics 4 жыл бұрын

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)

@CalamityInAction 3 жыл бұрын

Don't worry, you're still amazing at arranging and performing music :)

@dijkstra4678 3 жыл бұрын

Nobody is born equal. Sad reality.

@zswu31416 3 жыл бұрын

Wait Lionel why are _you_ here?

@andrewcabile3015 3 жыл бұрын

Why tf are you here? Go compose something!!

@UzairKhan-qd3xu 3 жыл бұрын

@@andrewcabile3015 music is math

@thijsbeentjes4008 4 жыл бұрын

Never realized the 2 triangles thingy, once you explained that and I saw the problem again I instantly saw the solution too

@pooritech 2 жыл бұрын

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.

@jefflittle8913 2 жыл бұрын

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.

@timm.7988 4 жыл бұрын

I‘m taking my German Math finals two days from now... KZfaq suggests me this and now my hopes are completely down.

@abinashkumar3207 3 жыл бұрын

How did it go?

@rurall 2 жыл бұрын

Did you do well?

@rossszeto3830 4 жыл бұрын

I am Chinese but usually these questions are just for fun.

@chocowell_ 4 жыл бұрын

I’m Asian too and this question is a joke it isn’t hard to find triangles

@natalieiphone245 4 жыл бұрын

@@chocowell_ I'm not asian I'm albanian but we just have these questions as little games

@atulanand4646 4 жыл бұрын

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

@vermut27 4 жыл бұрын

ahah ahah

@psychsteeves4577 4 жыл бұрын

ProNoobGamer h “maths”

@pxinshu777 4 жыл бұрын

Dear KZfaq, 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, KZfaq for lowering my self esteem.

@Xanthopathy 4 жыл бұрын

thanks for ruining the joke at the end

@ekadanta.ganesh 4 жыл бұрын

Instead of commenting, you could have studied!

@Elyzeon. 4 жыл бұрын

The prerequisites for the problem was to know how to solve these types of problems already

@hyeyyul5944 4 жыл бұрын

@@ajety no he was saying it to the other guy

@cindyjiang1158 4 жыл бұрын

kat pxinshu How’d the exam go?

@adamgillespie3393 4 жыл бұрын

"the diagram is not to scale" oh damn I was really going to take out my ruler

@lebelgianwaffle13 4 жыл бұрын

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.

@markstahl1464 2 жыл бұрын

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.

@clarkX100 Жыл бұрын

The two separate triangles was new to me too and what broke open the problem. Really enjoyed learning that bit

@Thanos-hp1mw 6 жыл бұрын

Difficulty: ASIAN.

@noone3367 6 жыл бұрын

I"m not asian and I solved it in 10 sec.

@Mike-dr1hz 6 жыл бұрын

Najdorf sicilian aha... That's racist.

@Thanos-hp1mw 6 жыл бұрын

Mike :] im an asian myself

@Mike-dr1hz 6 жыл бұрын

Najdorf sicilian i know, im kidding. You're all so smart. Got you going though, huh? :]

@Hyoiza 6 жыл бұрын

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

@blanktom6049 6 жыл бұрын

"Can You Solve A 5th Grade Math Problem From China?" can't i just try and solve it from my living room instead?

@cartoonpower0 4 жыл бұрын

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.

@nightowl19god25 4 жыл бұрын

BlankTom Amazing comment

@shadowclones4669 4 жыл бұрын

Lol

@TLiu-1b 4 жыл бұрын

The English language is so buggy

@imperialblast 4 жыл бұрын

loooooooool

@spazzolino8990 4 жыл бұрын

Find the area of the red triangle Point the finger to the screen and say: ”that’s the area”

@RedGallardo 4 жыл бұрын

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

@insert8242 4 жыл бұрын

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

@AlexandreG 4 жыл бұрын

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.

@trentonrothan9724 3 жыл бұрын

Unfortunately the area is not to scale. The image is not equal to the actual area.

@ravager12 2 жыл бұрын

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!

@TheChzoronzon Жыл бұрын

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

@ravager12 Жыл бұрын

@@TheChzoronzon Sí que lo hice y si quieres que te lo demuestre lo haré. Cómo quieres que te envie fotos que lo demuestren?

@ravager12 Жыл бұрын

Ya está

@TheChzoronzon Жыл бұрын

@@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

@alexanderhorter1287 4 жыл бұрын

The red triangle looks a little bit bigger than the triangle with an 8. I guessed 9.

@roo9970 4 жыл бұрын

Muffin Button same but i guessed based on the 10 being bigger

@larryli7015 4 жыл бұрын

yeah but the question said not drawn to scale

@gazebochannel3828 4 жыл бұрын

nice logic dude

@chocoblocko9cb991 4 жыл бұрын

Same, thats what i said aswell

@alfredofettuccine2397 4 жыл бұрын

“Not to scale”

@john-paulmathieu7195 6 жыл бұрын

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.

@icystrangers5482 6 жыл бұрын

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.

@Anonymous-jo2no 6 жыл бұрын

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.

@maan1511 6 жыл бұрын

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..

@amjPeace 6 жыл бұрын

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!

@readjordan2257 6 жыл бұрын

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.

@unnameableuser Жыл бұрын

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!

@karoshi2 3 жыл бұрын

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!

@multipurpose7445 2 жыл бұрын

OMG sameeee, I was trying also to find similar triangles but no triangle was similar as their areas are different lol

@ShreyRupani 6 жыл бұрын

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.

@martin-rs2gf 6 жыл бұрын

Well now you know

@Kevin-S 6 жыл бұрын

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.

@Epiciouss 6 жыл бұрын

Yeahh me too. I figured out the half triangle(79+10) but thats it.

@stevethorpe 6 жыл бұрын

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!

@paulgrimshaw6301 6 жыл бұрын

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.

@LittleRadicalThinker 6 жыл бұрын

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.

@hans3331000 6 жыл бұрын

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.

@btdpro752 6 жыл бұрын

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

@LittleRadicalThinker 6 жыл бұрын

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.

@LittleRadicalThinker 6 жыл бұрын

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.

@goldbergsam1540 6 жыл бұрын

yeah you're right

@sar8046 4 жыл бұрын

Me: "maybe what it between 8 and 10, so i guess its 9" Answer : 9 Me : ftw?

@rich20010 4 жыл бұрын

lol same here and I still don't know why it's 9.

@imkevin1 4 жыл бұрын

It's the average 8+10÷2=18÷2=9

@user-dq9gz3sh1r 3 жыл бұрын

Now you have passed the test!

@Eggemeyers 3 жыл бұрын

Me too lol

@GDPlainA 3 жыл бұрын

SARV's guessing brain: mY gOaLs ArE bEyOnD yOuR uNdErStAnDiNg.

@aaryanmarcha1176 4 жыл бұрын

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.

@iamyoda7917 4 жыл бұрын

Did you miss the 5th grade geometry problem from *Soviet Union* ? kzfaq.info/get/bejne/o5uVqa-gsZbcp5s.html

@clieding 6 жыл бұрын

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 KZfaq channel. You have a great voice for narration; it is clear, friendly and enthusiastic.

@aca792. 5 жыл бұрын

I'm happy for you buddy, but...

@zuro181 4 жыл бұрын

Bruhhh

@youtubedislikebutton9599 4 жыл бұрын

Chinese gifted kids: You cant defeat me. Me: I know, but he can. The guy who guessed it right in 2 seconds:

@s1unknown577 4 жыл бұрын

The legend

@savitar2581 4 жыл бұрын

Unknown The MADLAD

@Sammy-bi9fj 4 жыл бұрын

legend27

@mysticdragonex815 4 жыл бұрын

Senpai

@juno2740 4 жыл бұрын

bruh das me lmfao

@workfromhomebuddy3683 4 жыл бұрын

This just popped up on my suggestions but I'm amazed how that problem can be easily solved.

@toddfarkman2177 4 жыл бұрын

I came back to this a few days after watching it. It still took me 5 minutes to do the math. But a lot of these problems are simple to someone just learning the concepts. If you were just practicing triangles in a parallelogram, this problem is really simple.

@arkering9574 4 жыл бұрын

The parallelogram was a paid actor

@weijianlim4431 4 жыл бұрын

How is parallelogram a paid actor?

@falsonaga 4 жыл бұрын

@@michaelwinge3042 This would not have happened if the parallelogram had a gun

@Ae0nMike 4 жыл бұрын

Weijian Lim it’s a joke

@twwc960 6 жыл бұрын

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.

@patriciaceli1536 11 ай бұрын

Me encantó! Ejercicios como este y los de tu canal amplían nuestra mente! Gracias! ❤

@DerivativeOfJungbluth 3 жыл бұрын

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!!!!

@caesarsalad44 6 жыл бұрын

less than a minute? i've lost any will to compete in anything

@maxi.229 6 жыл бұрын

Alex yeah sure. He got it in 1 minute, but someone who has a KZfaq channel devoted to problem solving can't solve it at all. Sounds fishy...

@anticorncob6 6 жыл бұрын

Max I. MindYourDecisions is not a smart guy. There’s a reason very few of his puzzles are real challenging.

@caesarsalad44 6 жыл бұрын

KZfaq 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.

@julianlohe7669 6 жыл бұрын

Alex maybe they just guessed

@pipertripp 6 жыл бұрын

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".

@drusna 4 жыл бұрын

got this in about five minutes. you don't need to know any special theorems you just need good geometric intuition

@efe563_ 3 жыл бұрын

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

@warriorclasheromega5258 3 жыл бұрын

Nerd

@anandk9220 3 жыл бұрын

@@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.

@sakibishraq221 3 жыл бұрын

Yeah, me too.

@angelhristov9870 3 жыл бұрын

@@anandk9220 which one exactly is it?

@yashphatak6260 Жыл бұрын

This was so simple and mind boggling! Thankyou 🙏🏼

@HassanLakiss 2 жыл бұрын

What a lovely question. Brilliantly done. Thank you.

@vedaryan334 4 жыл бұрын

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.

@Risu0chan 6 жыл бұрын

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…

@unthawedwater747 6 жыл бұрын

Risu0chan i thought the same, won't be forgetting it anymore tho lol

@btdpro752 6 жыл бұрын

Risu0chan thanks, after watching this video I will take more steps to reinforce my knowledge about properties that I may have forgotten

@0megazeero 4 жыл бұрын

The "even for a child" only counts if you are chinese

@winnewFirst 2 жыл бұрын

I can't hit the like button more times. Can't stop appreciating the guy who made this problem. Thanks thanks thanks Presh.

@blobfish1112 4 жыл бұрын

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. :)

@derekmaeshiro2291 4 жыл бұрын

This really wasn’t that hard. You just need to know that specific theorem

@peorakef 4 жыл бұрын

Ye, its always easy when you know how its done

@Chief_Miles_OBrien 4 жыл бұрын

In no parallel universe would you and I be friends

@IndyLaLune 4 жыл бұрын

@@Chief_Miles_OBrien xD..

@nasekiller 4 жыл бұрын

by "specific theorem" you mean the area formula for a triangle? because that is literally everything used to derive the answer.

@lackadaisicalperson3843 4 жыл бұрын

Android Sheldon LMAO

@bakainu3559 4 жыл бұрын

Asian kid : solves under 1 min Video: takes 10min

@tsukishimakei9689 4 жыл бұрын

Kya tumne solve kiya kya

@bakainu3559 4 жыл бұрын

@@tsukishimakei9689 Yes ✌

@marivictumanda5719 4 жыл бұрын

Yash Nayakawadi solved it in the first second. Look at 8 it’s similar to the red triangle now if theres a bit more to the red its 9.

@bakainu3559 4 жыл бұрын

@@marivictumanda5719 wow first second.. It's pretty good, took me 2 mins

@wanlitan7406 4 жыл бұрын

I mean he first introduced the problem, told you what is needed to solve it, explained what you need to solve, explained the answer very slowly, and still provided an alternate solution. All of that combined is less than 9 and a half minutes, not sure where 10 came from. Furthermore, just because somebody said they solved it that fast doesn't mean they necessarily did.

@Sarah-oj7bh 3 жыл бұрын

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.

@ObitoUchiha-de4oy 8 ай бұрын

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.

@AcademiaCS1 2 жыл бұрын

I love the problem and the solution. I'm sure you've presented a problem that uses the concept of the triangles that contains the half of the area of the parallelogram. Thanks for sharing, Presh

@dbtest117 5 жыл бұрын

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.

@En1gmaUnknown 2 жыл бұрын

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.

@sedfer411 6 жыл бұрын

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.

@japhethbelgira2603 2 жыл бұрын

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.

@rowdyprostate8247 2 жыл бұрын

i’m usually pretty good at these, i’d be embarrassed to say how long some of them take me, but i usually come to answer after a long pause. this one completely stumped me though, i was trying to find the side lengths from D to the top right corner of the triangle we were looking for the area of and the parallel side length from B to the bottom corner of the area 8 triangle. I knew i couldn’t find any side lengths from the given area triangles as they weren’t drawn to scale and didn’t have 90 degree angles but i thought by reflecting the area 10 triangle to the left of the line from B to the bottom corner of the area 8 triangle that i was getting somewhere. one of my longest pauses to date and none of the work i was doing was getting me anywhere, i could have had a year to work on this and i don’t think i’d have arrived at an answer. the 2 triangle within a parallelogram where the 2 of the sides make up the length/width of the parallelogram and they share a height/length being equal to half the parallelogram area part is crazy to me. after it was explained it seems so simple, but it’s far from intuitive as i’ve never seen something similar used in other problems. seems crazy that children can spot a way to set up equal equations from this to cancel like unknowns and solve.

@senoir. 4 жыл бұрын

6:26 was my OHHHH moment

@haxzaw8550 4 жыл бұрын

A 5th grader didn't do this in their head in less than a minute.

@sdadeveloper5223 3 жыл бұрын

@MKMW C lol

@jayantgupta7969 6 жыл бұрын

Hmm..every 3 out of 2 students struggle with maths.

@Thanos-hp1mw 6 жыл бұрын

I get it! XD

@pitadomu 5 жыл бұрын

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

@gabano1311 5 жыл бұрын

Finally I'm special at math's lol

@user-yp2kp1mj2q 5 жыл бұрын

2 out of 3 you mean. oh god. use your brain.

@doodelay 4 жыл бұрын

@@user-yp2kp1mj2q that joke went right over your head

@lenrussell2424 2 жыл бұрын

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!)

@kenhaley4 6 жыл бұрын

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.

@kishanshukla9583 4 жыл бұрын

Knew the concept but never thought it can be used this way. Thanks @MindYourDecisions

@saiphaneeshk.h.5482 4 жыл бұрын

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...

@SnowhitedSnowhited 4 жыл бұрын

Thats new to me. Very nice !

@kkim5000 6 жыл бұрын

are you smarter than a fifth grader? apparently not...

@TheTariqibnziyad 6 жыл бұрын

kkim5000 talented*

@goldbergsam1540 6 жыл бұрын

Becuz their teacher teach that to their student

@godbeerus2202 5 жыл бұрын

Bro this is not about smartness. These were already taught to them. So they could solve it in under a minute.

@myselfsfanboy8527 5 жыл бұрын

I solved it in 20 secs so i guess i am

@mrhatman675 5 жыл бұрын

@@godbeerus2202 I know for example my school doesn t teach me to think that way so I would be able to solve this

@shango6164 6 жыл бұрын

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.

@Diaryofaninja 6 жыл бұрын

Shango Not impressive. I solved this under a second and I'm still in the second trimester.

@Diaryofaninja 6 жыл бұрын

Shango and the only reason it took that long was because i was trying to do a backflip.

@anticorncob6 6 жыл бұрын

LOL!

@subinmdr 6 жыл бұрын

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.

@albertma1 6 жыл бұрын

Trolling like hell

@perryhiley6749 4 жыл бұрын

After you showed the principle about triangles and parallelogram area, it was easy. I didn't know (or I didn't remember it) before.

@paddock5733 4 жыл бұрын

Wow, thats so smart! I didnt Think of that when I tried it myself

@aryandas6403 5 жыл бұрын

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.

@Marnige 4 жыл бұрын

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. "

@bourdiergustave1506 4 жыл бұрын

@@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.

@flyingpenandpaper6119 4 жыл бұрын

@@bourdiergustave1506 Exactly. I bet they did it in a minute because for them, it's just a matter of addition and subtraction now.

@mollistuff 4 жыл бұрын

@@will123134 Did it take more than a minute though?

@akshanshchoudhary7397 4 жыл бұрын

@@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

@hunterkonrad 6 жыл бұрын

Great problem! I like problems with an aha moment. As opposed to tedious calculation.

@viniciusfernandes2303 3 жыл бұрын

Thanks for the video!!

@metinguden1943 2 жыл бұрын

You are incredible. Thanks for everything

@japeking1 5 жыл бұрын

Thanks for this.... it took me about the 10 minutes, so I can't match the kids but I'm fading in my 70's and have done nothing like this for 55 years.....so you have made me very happy and even reinvigorated my dull existence.

@HeartistMurali 5 жыл бұрын

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.

@stellaqian1645 4 жыл бұрын

I remember those days of dealing with these questions. I probably lost my talent after adulting. Haha.

@lenocis.sim-racing 4 жыл бұрын

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)

@sup3rn0va87 4 жыл бұрын

Does it count as right if i skipped the equasion part and just thought "9"

@roo9970 4 жыл бұрын

Sup3rN0va i hope so

@Elyzeon. 4 жыл бұрын

The people liking your comment also thought of 9

@neifoto 4 жыл бұрын

maybe you are a savant

@Raenaece 4 жыл бұрын

Same here

@Fenrir-sv7zt 4 жыл бұрын

In term of result,yes. In term of methodology,no.

@victorsixtythree 6 жыл бұрын

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.

@dlevi67 6 жыл бұрын

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.

@selmaardwinta2584 3 жыл бұрын

gosh, problems like this i love learning abt but could never solve it by myself. it makes me frustrated but at the same time highly respekt those who can actually do it

@ber2996 4 жыл бұрын

"Can you figure out this problem?" Haha. No.

@zoetropo1 4 жыл бұрын

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.

@CxC2007 6 жыл бұрын

Dad: you doctor yet? Son: Im 12. Dad: talk to me when you doctor.

@mrgoogle6968 4 жыл бұрын

Son: then we will never talk again, dad.

@janny844 Жыл бұрын

the hint of finding 1/2 of the parallelogram and really helps

@thetenrings Жыл бұрын

LETSSS GOOO I figured it out. Sadly took me 6 minutes but still good. This channel really made me more adaptable to math problems. Do you have any advice for math competitions for some reason I do perform not as well in them and my mind blanks out. Thanks

@lordtouchmesama8479 6 жыл бұрын

Damn I was like there is 8 and 10 but no nine so I’m guessing nine and it was correct

@raynnraynns7959 6 жыл бұрын

Shady Directions Studios same! Haha

@cyberpilot6512 6 жыл бұрын

i like that out of the box thinking

@wildchicken2049 5 жыл бұрын

You will go very far in life :)👌👌👌

@kiisbo 4 жыл бұрын

sAME i saw it was less than 10 but more than 8 so i thought 9

@sophiafritz1760 4 жыл бұрын

I did 10 plus 8 divided by 2 to get 9

@gooblio 5 жыл бұрын

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.

@fierzo9152 4 жыл бұрын

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.

@MexicanDre 4 жыл бұрын

You know I didn't know the answers BUT I learned , thank you sir.

@rwold8779 5 жыл бұрын

This is pretty easy but it requires you to know that property of parallelograms --- the fact that you can "slide" the end point of the triangle and still wind up with half the area of the parallelogram. I never learned that, as far as i can remember. I can imagine a world where that is taught to students, and they would inherently know how to do a problem like this. But we never learned to think about that.

@tolmt6736 4 жыл бұрын

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

@amanuelgaromsa3918 4 жыл бұрын

Thank you so much. well i hope more videos of u will impress me.

@dushyanthabandarapalipana5492 2 жыл бұрын

I am so greatful to you!

@TimTeemo 6 жыл бұрын

ParaLOLogram

@Av0nr 4 жыл бұрын

Love your videos

@bryanu1737 4 жыл бұрын

BRAWLLL STARS

@pranavborse2111 4 жыл бұрын

Hello

@2DarkHorizon 4 жыл бұрын

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

@Chillago 2 жыл бұрын

Big Brain

@ignacioguarachi8172 4 жыл бұрын

Am 27 and solving this took me more than 10 minutes. I feel spastic now. Fantastic video.

@samyak101 2 жыл бұрын

Great question, was able to solve it myself but took some time

@themasterblaze7563 4 жыл бұрын

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.

@darknight_12 4 жыл бұрын

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

@davidwillis7991 4 жыл бұрын

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.

@atul_singh4565 2 жыл бұрын

Don't be sad you applied all the theorems you knew, but kids knew only one, so they were quick

@marinauder 4 жыл бұрын

Gosh, I wish I watched it during leisure time, not at midnight!

@jo8dr 2 жыл бұрын

For me I saw the triangle ADE (where the point E is the point on the right, between B and C) and added the shaded parts, which was 89. It is half of the parallelogram, so the shaded area in the rest should also be 89? Maybe it only worked for this specific question, but that's probably how many of them got it so quickly

@IonKattTMCE 4 жыл бұрын

I solved it in 10 seconds by guessing 9 based on observation and extreme luck lmao

@Magali2088 4 жыл бұрын

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

@lezhilo772 4 жыл бұрын

If you can do geometry slowly, you can do it quickly! Mathematical intuitions are born not created!

@MrDamojak 4 жыл бұрын

Ling ling

@jessicazhao5417 4 жыл бұрын

another ling ling wanna be

@JMScibra Жыл бұрын

I managed this in about 3 minutes, but I feel like I was a bit lucky with this one. I don't specifically remember learning that two triangles are equal to half a parallelogram's area when their combined bases is equal to that of the parallelogram, and their altitude is also equal to the parallelogram's, but it made sense when I noticed it.