The hardest problem on the hardest test
The most difficult mathematical question on the most difficult mathematical test

Follow by Email
Facebook
Twitter
Instagram
A difficult geometry puzzle with an elegant solution. Home page: https://www.3blue1brown.com/ Brought to you by you: http://3b1b.co/putnam-thanks And by Brilliant: https://brilliant.org/3b1b Solution to the puzzle mentioned at the end: https://brilliant.org/3b1bindicator/ These videos exist thanks to Patreon: https://www.patreon.com/3blue1brown A different write-up of this solution: http://lsusmath.rickmabry.org/psisson/putnam/putnam-web.htm 1992 Putnam with this problem: http://kskedlaya.org/putnam-archive/1992.pdf A problem with a similar flavor came up on the 2005 Putnam A6. Give it a try! The solution for that problem, by the way, was written by Calvin Lin, a friend of mine who works at Brilliant. Small world! http://kskedlaya.org/putnam-archive/2005.pdf http://kskedlaya.org/putnam-archive/2005s.pdf ------------------ Animations largely made using manim, a scrappy open source python library. https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown

Comments

Kalpita Hatode : The horses name is friday

Mico Gomos : :*knows nothing about math :(Still watches video)

Andrea De Fanti : WOW That was soooo Easy im only 3 weeks old and i solved it no problem in 2 mins

Echo : To solve this, you need. 1. A full stack of paper. 2. 50 pencils 3. 200 IQ 4. Probably some more paper

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?

Dage6552 : *Starts Exam and turns first page over* Formula Sheet: OMAE WA MOU SHINDERU! Me: NANI!?

windows 97 ャ陰ぜ : There YouTube. I watched it. Happy? btw, nice vid bro

Shackhagen : Why am I watching a math video at 12:02 am on a Saturday

Anthony Youssef : Welcome to part 598 of "why is this in my recommended?"

Antonio Hernandez : Question: Probability that this tetrahedron contains the sphere's center? Me in the test: Yes

Davud Pivac : "how you might have stumbled across the solution yourself" Didn't know this was a comedy channel

Nick Harris : Somewhere between 0-100%. Looks like I got it right

Me Joel : Probability on circle is 1/2², probability of a sphere is 1/2³. I find the simplicity of the outcome rather beautiful

Eric Khaing : Ppffft...hard? I could do these questions in my sleep. Could you explain this one more time tho?

Diego Grigorescu : Idk why I'm watching this, I don't understand a single term lmao

GalaxyJuice TV : In an online test: 43/7 = Your incorrect answer: 6.14 Test answer: 6.142857142857143

pipe : meanwhile i have to do basic division in my calculator almost every time

HaztePolvo Perra : Math classes in high school: Find X / 3x=12 Math exams in high school: F I N D T H E P R O B A B I L I T Y of the C E N T E R of the S P H E R E being inside this pointy B O I

George Farah : Fastest 3 things in the universe: 1- light 2- universe expansion 3-me clicking on a 3blue1brown notification

EROL AĞÇAKAYA : The discomfort that this three-dimensional thinking can give is far more than the happiness it will give after solving it.

Ben Teague : 11:15 The only part I understood

Brown Pixel : Homework: 8x4 Test: John has 3 apples, the train leaves in two hours, calculate the mass of the sun.

So Tree : See you lost me at "math"

rushil kumar : I never thought I would be able to understand how to solve a putnam problem... i am completely overwhelmed with joy... your style of explaining the problem just blew my mind.... i have been a subscriber since last year or so, thank you for making me realise the elegance in math

thereal MCPM : Me: Not as probable as me failing this test... *walks outside and chain smokes an entire pack of cigarettes*

Richard Tran : The answer is 2

Dr. 1up : The real hardest question. Explain the entire storyline of Kingdom Hearts to some who doesn’t know the series

lil macncheese : easy 2+2 is 4 minus 1 that's 3 quick mafhs

Max Miesen : This guy is amazing at explanations. If he can teach the hardest problem this well, imagine what he would be like as a high school teacher.

Green Papajas : The probability of me understanding this explanation is 0.000002

NicklingLP : Me: uses calculator to find out what is 7+7 Also me: knows how to solve hard math problems easily

Sunny shah : In class: 1 + 1 = 2 2 + 2 = 4 In test: Given the implicit equation of a sphere, calculate the gradient vector and explain why the gradient vector points in the direction of maximum up slope.

iOwn Squidz : In class: 1-3= -2 -2+3=1 During the test: If (3,-2) is the center of a triangle why would the communist revolution in Guatemala have an impact on the American continent?

Will Britt : yo what language is this

Xannos P. : Well this is why I gave up on math lol

Niskis : Surface integral *traumatic flashbacks to Calculus III* *shivers*

ZmanVlog : Question: Probability that the tetrahedron contains the sphere's center? Me: 50% Either it does or doesn't.

Sage Brush : So seriously, solidworks would've helped me with the most difficult math EVER? Holy shit

David Rodríguez Grande : I just saw the problem, nothing else, and... Can I go home?

Bady89 : Fake, everybody know that Kobayashi-Maru Test is the hardest one.

Waseem Saada : the hardest problems require the strongest wills. (Thanos from avengers)

ء : Brain.exe has stopped working

I have to wait 90 days to change my name : Wait, they put numbers on the test?!?! Screw that

EmmettIsPro : I guessed 12% at the beginning lol I was so close with a random guess

Yeah you lose Harry : Alright smarty pants What falls faster a pound of bricks or a pound of dogs?

Pável Cotacallapa : Monte Carlo Simulation works very best.

Mono : Why am I watching this at 1 in the morning

eenin : Your voice is a mix between Mordecai from Regular Show and Fred from Scooby Doo

Amarrussell Amarusama : Math : solve this tehtraderon Me : nope