The hardest problem on the hardest test

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Natanel Sharabi : Please more awesome problem solving videos!

GameTass : Brain.exe has stopped working

Decidous : Oh shit it isn't multiple choice...

Jeff Lox : Just realized why this channel is called 3blue1brown

VDR : God take me please.. why do these things exist where I exist..

Taran Van Hemert : this video slowly blew my mind.

ElectricYoshiHD : Class: 2 + 5 = ? Homework: (y-1)2x-3y = 64 Exam: You have 5 apples, you give one away, calculate the mass of the sun.

PePe McDouble : I thought this was clickbait... I was right, it's a chinese guy trying to sell me something. I think

kulpreet Singh : How do you create such animations?

Raimonds Zakis : Instructions not clear, I accidentally went down into 4th dimension and I think my sphere just turned inside out.

EighteenCharacters : Wonderful.

Herr Hurbig : The biggest irony is that I’m watching this instead of studying for my math final. I’m doing math instead of math.

Clive Grant : Intriguing solution. Just goes to show that thinking outside the box can be very rewarding. But the initial 2D solution rang a few alarm bells for me. The solution averaged the arc length P1P2, say a, over 180 degrees (a = 0 ..0.5), and got the answer 0.25. If you average it over 360 degrees (a = 0 .. 1), the answer is 0.5 (wrong). The error is due to the fact that, for P3 to enclose the center, the required arc is a for 0 .. 180 degrees, and 1-a for 180 .. 360 degrees. Averaging over the the first 180 degrees just happens to give the right answer in this case.

Usman Khan : Wait this was a problem in a test in the anime, Assassination Classroom.

Catherine x : *In class:* 2 x 2 = 4 4 ÷ 2 = 2 *In test:* The circumference of a circle is 92cm, the radius of a circle is 83cm. What is in my back garden?

Paul Paulson : Now i expect 11 more videos 😉

TheMultiverse Plays : wrong

D Daley : I have work at 8 tomorrow and it's midnight... why tf am I watching this I'm not even in high school

Victor lopez : Now I more than my teacher. Thank you!

Student Vlogs - Dylan : Was this video in Chinese or Mandarin?

Ethan Hunter : I'm being 100% serious when I say that this video was more meaningful and interesting than everything I've experienced in the last week combined. Thank you.

GD Mil : i am only in 7th grade.

Stavi Enthusiast : I bet Will Hunting would score a 120.

Colin McCurdy : Are the coin flips needed in this question? Once we correctly divide the sphere into 8 portions can't we assume there is a 1/8 chance?

Anubhav Mahapatra : Always i come to realise how beautiful mathematics is...That point of fixing P3 and choosing two random lines passing through center was very ingenuine...Beauty

Kelvin Klein : Yass, new video

Anubhav Mahapatra : I LOVE MATHEMATICS...especially GEOMETRY...It's damn beautiful.

François-Xavier Hard : Great video, and nice problem. I found an even more elegant, easier, and faster way to solve it, by considering the probability (p) in dimension 0 and 1: - 0D: the universe is a point, the sphere is a point, the tetrahedron is point, so p = 1. - 1D: the universe is line, the sphere is 2 points (A, B), the tetrahedron is two points (C, D) randomly set on A and B. C and D can be both on A, both on B, or one on A and one on B. So p = 0.5. From this we can already extrapolate in dimension n, but we have two solutions: either p = 1/(2^n) or p = 1/(n + 1). Now we simply have to find which is the correct one. As I see it, every time you increase the dimension by 1, you split your object in 2 parts, so you divide the probability by 2. - From 0D to 1D: the line is split into two hemispheres by the point. - From 1D to 2D: the circle is split into two hemispheres by the line. - From 2D to 3D: the sphere is split into two hemispheres by the circle. - etc... So not only we have the solution in 2 minutes, but also in dimension n: p = 1/(2^n) = 1, 1/2, 1/4, 1/8... What do you guys think? I have to admit that the second part of my explanation is not very mathematical or rigorous, but I guess this is point of this video and exercise. Cheers!

Jerry Su : I mean, if the student can’t think from this perspective in 20 minutes, he won’t figure it out in 3 hours anyway😭

Sam Bishara : Is the answer of the sponsored bit 2?

X Blocky : Nice animation. What's software did he use?

Charbel Eid : each student has 1/4 chance of not being cheated on since there is 1/2 chance for each one of the guys sitting next to him to turn towards him. 1/4×8=2 so 2 students... Ok compared to the putnam problem this is childs play🙂

Conosis : *Oof*

Calum79 : Math is very fun

Ben Cornell : Hey man, Im only a junior in highschool and Im not amazing at math, but can’t you solve for the simplest version and then use the fact that the first dimension is to the power of one, the second to the power of two and the third to the power of three? Once you got to the part with 0.25 probability, I rooted it to move it to the first dimension then cubed that to move it to the third dimension. That provided 0.125 or 1/8. Let me know if this is incorrect or just lucky though, thanks!

Playonce : Maths in master degree level might be harder than "Can I go home questions?"

KHUMBELO BELE : You need to chill man.......... Nxaa 😡😡😡

Domination YT : I'm in middle school, why am I watching this?

COOPER #7 : that was interesting

SerjEpic : I hate math why am I 9 minutes in this video

Ehsan Qazi : You just earned a new subscriber 😉

marg trivedi : Brilliant. It grew on me. This is not just mathematical problem solving but understanding the art of geometry.

Viktor Dušek : I watched it like are you crazy or what? I don't understand any of the words he said...

Askejm : \/ That’s right That’s wrong /\ What’s right and what’s wrong

Cliff Worsfold : 0:23 is it just me or does A5 look deceptively easy?

YellowBunny : After you showed the first 2d solution intuition just told me in 3d it would have to be 1/8, but I couldn't say why.

Gui Seb : This is actually very interesting

aLazyFreak : I am by no means a mathematician, but doesn't it make sense to think of the circle in terms of the power used to find its area? For example, in a two-dimentional circle you use the power of 2 to find its area, so the probability is 1/4. Would it be a viable solution to first find the root of that probability (1/2), leaving us with a one-dimentional line and then calculating that probability to the power of 3 (the power used to find the area of a sphere), thus getting the correct answer of 1/8?

Amphestep : It’s pretty easy to visualize the 1/8th probability in 3 dimensions after you work out the problem in 2d, but most test takers didn’t get even close to that far.

TryHardz-MC : wow ur smart keep the good work up