The hardest problem on the hardest test

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Natanel Sharabi : Please more awesome problem solving videos!

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

GameTass : Brain.exe has stopped working

Josev : The link doesn't show the solution to the last problem, so in case anyone is wondering, the solution is 1/4.

kulpreet Singh : How do you create such animations?

EighteenCharacters : Wonderful.

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

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.

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

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

Paul Paulson : Now i expect 11 more videos 😉

Xi Le : *Where the center number from 0 to ∞ ?* or *What's the middle number from zero to infinity?*

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

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😭

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!

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.

El Camacheesy : I bet Will Hunting would score a 120.

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.

I Rage A Lot : Now I more than my teacher. Thank you!

TheMultiverse Plays : wrong

Taran Van Hemert : this video slowly blew my mind.

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

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

Lucas Pont : Yeah mate I first have to figure out what the question means lol.

8bitmagic : That was awesome

Kelvin Klein : Yass, new video

Conosis : *Oof*

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!

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🙂

Ronan Sullivan : I think I have a simpler solution to the problem. In order for the tetrahedron to have the center in it, the points must not be isolated to one hemisphere. If they are then it will not contain the center. The first point is the reference and from it you can set a random hemisphere. Since there is a 50/50 chance that a point will lie in one hemisphere or the other, then 1/2 ^3 = 1/8.

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

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

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

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

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?

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

konohaNinja : videos like this keeps me grounded

Josh Page : Idk even how but i guessed the right answer to both the 2d and 3d problem before the video 0_0

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

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

corç vaşington : 2 boyutluda birşeyin oranını 1/4 bulduk buraya kadar kolay sonrasında 3 boyutluya geçtiğimiz için şansımız 2 kat azalır istediğiniz işlemi veya yolu kullanın cevap 1/8 :)

Luiz Meier : Excellent.

stupidmonkeywing : the link didn't take me to the solution, what's the answer to your last puzzle?

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.

TheLenny27 : Is it maybe an idea to make a series explaining all questions from a putnam? One every video.

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?

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.