A Quick Cake Conundrum - Numberphile

  • Added:  6 days ago
  • A quick little problem from Cliff Stoll, who baked a birthday cake for Brady... More links & stuff in full description below ↓↓↓

    See more Cliff videos: http://bit.ly/Cliff_Videos

    The scientific way to cut a cake... https://youtu.be/wBU9N35ZHIw

    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile

    We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.

    Website: http://www.numberphile.com/
    Numberphile on Facebook: http://www.facebook.com/numberphile
    Numberphile tweets: https://twitter.com/numberphile
    Subscribe: http://bit.ly/Numberphile_Sub

    Videos by Brady Haran

    Patreon: http://www.patreon.com/numberphile

    Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/

    Brady's latest videos across all channels: http://www.bradyharanblog.com/

    Sign up for (occasional) emails: http://eepurl.com/YdjL9
  • Video CategoriesScience & Technology
  • Runtime: 3:38
  • Tags for this video:  numberphile  cake  cut  

Comments: 655

  • jawad mansoor
    jawad mansoor 2 hours ago

    I love real life Doc BRown

  • njack1994
    njack1994 4 hours ago

    How to divide it and make it still look like a slice of cake? Well you want one piece one third bigger then the rest and 4 pieces of equal size for a total of five pieces. So imagine a circle instead of a square one piece makes up 96 degrees of the circle and the others make up 66 degrees of the circle.

  • Ju Goopy
    Ju Goopy 17 hours ago

    The cake looks like a piece of bread in the thumbnail.

  • Ashish Upadhyay
    Ashish Upadhyay 21 hour ago

    Method 2: Cut the cake along the middle plane , and you get two identical parts. Now cut those two identical parts into two pieces. Bam! You got 4 equal pieces.

  • Phenanthroline
    Phenanthroline 22 hours ago

    This might be my favourite video on the internet :D

  • Uriel Fabregat
    Uriel Fabregat 22 hours ago

    You could also cut the cake in the corner of the L shape, there you have two pieces. Grab each one, turn it sideways and cut it again. You end up with 4 identical trapezoids

  • Anastasia Dunbar
    Anastasia Dunbar 1 day ago

    hoe abou' fievh?

  • salil pai
    salil pai 1 day ago

    you could have also cut it into 3 parts then cut each into 4 sub parts and give each person 3 pieces.

  • Rizon1985
    Rizon1985 1 day ago

    Before taking out a cake, poke a knife or a skewer into it. If there still sticks dough to it, it's not done yet. That's the first think you learn baking...

  • Midnightas - Programming Tutorials

    Sell it on eBay

  • M Jason
    M Jason 1 day ago

    Option B: Cut into two congruent trapezoids by making a 45 degree cut from the center to the corner. Then leverage the 3-dimensionality of the cake by making a second cut horizontally through the remaining cake. Voila, four equal pieces. (This solution hinges on the uniformity of the cake from top to bottom. Would not work well with frosting.)

  • Riddhiman Roy
    Riddhiman Roy 1 day ago

    Stuff like this, thats not scripted, is whats amazing about people. Going off script produces some real gems

  • Chilledfish
    Chilledfish 1 day ago

    It's really not that hard. Which number divided by 4 gives you 3? That's how many parts you have to distribute evenly. Then you give each of the 4 people, 3 parts out of the 12. It's not rocket science.
    The real conundrum is: Is the cake quick, or is the conundrum quick?

  • Overkillius
    Overkillius 2 days ago

    I love this guy

  • cezar t
    cezar t 2 days ago

    I'll skip the middle one, not crusty enough

  • White Razor
    White Razor 2 days ago

    I swear that's just a big sandwich in that baking dish.

  • Conway79
    Conway79 2 days ago

    In the thumbnail it looks like a mouldy piece of bread.

  • Yoav Lev
    Yoav Lev 2 days ago

    please do the Banach- tarski next!

  • Settwi
    Settwi 2 days ago

    3/4 / 4 = 3/16. think of the cake in 16th unit squares. divide equally. done.

  • Adam Bernstein
    Adam Bernstein 2 days ago

    I'm at 1:44. My solution: cut the remaining L shape into 3 even squares. Then cut each square twice along the diagonals. You now have 12 triangular shaped pieces. Each of the four family members gets 3 triangular shape bits. Seems easy enough to me. Now I watch the rest of the video for the solution. Hope my answer is right. :)

  • SkylersRants
    SkylersRants 2 days ago

    The conundrum isn't fair because the middle piece has no crust. :)

  • Radnor Roads
    Radnor Roads 2 days ago

    I remember this puzzle from a book in my childhood, but with pizza! What a blast from the past.

  • Mr. O'Connor: Science

    Make a 45 degree cut from the middle to the upper right corner, creating two identical trapezoids. Then remove them from the pan, and make a horizontal cut through each, creating in total 4 thinner trapezoids.

  • NnO0Worries
    NnO0Worries 2 days ago

    The cocoa is from Droste (from the effect): https://en.wikipedia.org/wiki/Droste_effect

  • Tristan Johnson
    Tristan Johnson 2 days ago

    Not to brag
    but just to help you inferior minds understand my greatness in maths, I got the answer in 0.00004295424 seconds by doing some post-graduate level Fourier analysis based vector calculus in my head at only the age of -0.75 years

    (i am a sperm).

  • B1GB1RDB4G3L
    B1GB1RDB4G3L 2 days ago

    Aw I love Cliff :)

  • Robert Van Bodegon
    Robert Van Bodegon 3 days ago

    Stick to numbers. Baking not so much.

  • theBraxil
    theBraxil 3 days ago

    Why do you have coco out? The cake isn't even chocolate?

  • Michael Murphy
    Michael Murphy 3 days ago

    I absolutely adore this man. Everyone needs a little Cliff Stoll in their life

  • John Thimakis
    John Thimakis 3 days ago

    Exploding coco. 🍫😃

  • Zac E
    Zac E 3 days ago

    or you could cut the cake in half (diagonally) and then cut in half vertically (creating two equally thin layers).

  • sahariel187
    sahariel187 3 days ago

    The right way to do it is to cut yourself a big piece, about 1/3 of the cake, then divide the rest amongst the other 3 people, 2/9ths each

  • O Cricles
    O Cricles 3 days ago

    The exploding cocoa thing is actually legit; a lot of fine powders, when the particles are in the air like dust, can explode pretty violently under the right conditions. They're called dust explosions, and it can happen with stuff like flour, coffee, sugar, grain and even some fine metal powder.

  • Thyeggman
    Thyeggman 3 days ago

    You could also cut the cake depth-wise (?) and then again along the 45-degree angle from the center corner to the opposite outside corner

  • Marcos Ramirez
    Marcos Ramirez 3 days ago

    If you cut the L in the middle you'll get 2 trapezoids and you can cut the trapezoids in the middle to get fourths i thought of that is the beggining

  • Kevin Johnson
    Kevin Johnson 3 days ago

    Four cuts. Center of top left square to center of bottom right square. Center of top left square to top center of pan. Middle of pan to right top corner of pan. Center of bottom right square to right middle of pan. Basically cutting into 12 equal triangles and each person gets 3 triangles. I read this as each person gets a one piece, so cutting it this way will satisfy that requirement.

  • Ian Flanagan
    Ian Flanagan 3 days ago


  • Bingo Base
    Bingo Base 3 days ago


  • Pradhyumn Jain
    Pradhyumn Jain 4 days ago

    wht if u cut the cake laterally....then we can divide it in a infinite no. of equal pieces

  • neodoc1976
    neodoc1976 4 days ago


  • D. C
    D. C 4 days ago

    Everybody's favourite Mathematician!! 😃😃😃

  • Sneha Iyengar
    Sneha Iyengar 4 days ago

    how do give a lecture on vectors and it's application

  • Devin Allen
    Devin Allen 4 days ago

    Rep-tiles ♥️♥️♥️

  • Ryan Roberson
    Ryan Roberson 4 days ago

    ive heard of this problem before, and if the cake be stiff enough you can make 4 identical pieces of 1/2 side length similar to the original

  • Michael Amos
    Michael Amos 4 days ago

    I'm definitely not a math person but couldn't he cut diagonally from opposite corners, like an X, and have 4 equal sized triangles?

  • John Galdino
    John Galdino 4 days ago

    Hello! Very entertaining and educational as always! When you find the solution for a mathematical problem, where do you submit it ? I've found two patterns between all primes, and I'm polishing up my formula.

  • Zain Al Ain
    Zain Al Ain 4 days ago

    I have imagined the solution before it was revealed...

  • Jaleb Jay
    Jaleb Jay 4 days ago

    I was looking at it in three cuts which I found looking at trapezoids. Cut the diagonal that the first square was part of and make them into two smaller figures. Then cut a line through the midpoints of the parallel lines. I didn't even think to look at the concept of this video.

  • palmomki
    palmomki 4 days ago

    I used the "mystical" power of 12 to solve this. I swear, it solves a lot of stuff. Everytime I hear something along the lines of "divide a group of three things in four" or viceversa, I just go "let's divide it in 12 instead and see what happens".

  • GNU/Bird
    GNU/Bird 4 days ago


  • Wiseass Skeleton
    Wiseass Skeleton 4 days ago

    I knew where this was going as soon as I saw that the 'problem' was 3/4 of a square.

  • Ralph Dratman
    Ralph Dratman 4 days ago

    Cliff Stoll is just a little bit eccentric. You know, just a tad off the beam. A smidge.

  • justin fwibber
    justin fwibber 4 days ago

    That was depressingly simple. I figured it out right away. I was expecting something hard. I usually never get these things.

  • Harry Michelson
    Harry Michelson 4 days ago

    The cake in the thumbnail looks moldy.

  • Rob McLear
    Rob McLear 4 days ago

    Cliff is amazing. When The Cuckoos Nest was published and I finished reading it, I sent him an email to tell him how much I loved the book and some other stuff, and he sent a very log, personal reply which must have taken a significant amount of his time to write. Very grateful for that still.

  • Michael Montgomery
    Michael Montgomery 4 days ago

    I love this guy

  • kazeman
    kazeman 4 days ago

    My solution was to cut the cake into 3 equal squares and then cut each one in 4 following their diagonals
    Et voila, 3 triangular pieces for 4 people ( no ruler needed)

  • skipjack91
    skipjack91 4 days ago

    A cake? Really? I would've baked you a Pi!

  • Mike S.
    Mike S. 4 days ago

    Math and humor. What more could a Youtube viewer ask for?

  • iñigo san jose
    iñigo san jose 4 days ago

    i love this guy, my fav of numberphile by far

  • Lester Squad
    Lester Squad 4 days ago

    *Sees thumbnail* it's Mr. Klein Bottle

  • logiclrd
    logiclrd 4 days ago

    Try tossing some cocoa onto an open fire, so that it puffs out into the air over the flames. You might be surprised :-) (Disclaimer: I haven't tried this with cocoa, but I have tried it with flour and sugar.)

  • Lucas Moeller
    Lucas Moeller 4 days ago

    i love this guy

  • LeeJn
    LeeJn 4 days ago

    kinda close to a powder bomb...stay safe

    EDIT: not the colorful fun-fun powder bomb lol

  • Tsavorite Prince
    Tsavorite Prince 4 days ago

    You could make a fractal out of this!

  • Agnes Ginardi
    Agnes Ginardi 4 days ago

    That wasn't the solution I thought of. Cut it into thirds as is easy. Cut two of the three squares in half, and the third square in quarters. Each person gets one half and one quarter. It works out the same way as his L's though.

  • Amin
    Amin 4 days ago

    HEY! I'ts mr klein bottle !!

  • charlievane
    charlievane 4 days ago

    you should've continued shooting, he was getting interesting

  • Rafael Trevisan Lisboa

    *Cocoa Explodes*

  • Rafael Trevisan Lisboa

    I love this man so much!!!!!!!!!!! Such energy

  • DutchDread
    DutchDread 4 days ago

    But they don't all get the same type, some get more crust, if you know kids, you know this solution is unaceptable

  • Erwin Lommer
    Erwin Lommer 4 days ago

    What if everybody likes the outer edge pieces? Then it is not the same for everybody because the one in the center has no outer edge parts! #unequality

  • NoriMori
    NoriMori 4 days ago

    This was a triumph…

  • Luis Manuel Castro Moreno

    Divide en 4 el pastel completo, retira 1/4, los 3/4 restantes divídelos individualmente en 4, es decir, toma un cuarto más y divídelo en 4, al finalizar podrás tomar solamente 3/4 de cada 1/4 que quedó. :p

  • mrBorkD
    mrBorkD 5 days ago

    Since the pattern is recursive, you could make an infinite pattern. It would look quite cool!
    Just keep repeating the cuts for the leftover square. Infinite cake!...pieces.

  • Nerobyrne
    Nerobyrne 5 days ago

    cut it into three pieces, then cut 1/3 out of each of them.
    Then cut one of those thirds into three pieces again.

    There you go! Well, now everyone has one big and one small piece, but it's fair!

  • forty-two
    forty-two 5 days ago

    figured this out in about 10s

  • rahul kumar
    rahul kumar 5 days ago

    please tell me if there's formula for calculating no of Latin cubes , I know there's one for latin squares , please reply

  • Harley Martin-Farrell

    Technically yes, the cocoa could explode. If it had been dispersed in the air, for instance if you tipped it out, the cocoa would ignite quicker, and in extreme cases could become a fireball.

  • needforsuv
    needforsuv 5 days ago

    WHO measures a cake
    also who gets the crumbs

  • Kori114
    Kori114 5 days ago

    That was pretty obvious.... I had figured out that solution before they got to it. I was expecting something more clever.

  • Hsterts Hertz
    Hsterts Hertz 5 days ago


  • theorganguy
    theorganguy 5 days ago

    my problem(s) with this is: one of the four isn't getting any of the yummy crust... and all four did not get any sprinkles... like... WTH? :-P

  • Christoffer Krab
    Christoffer Krab 5 days ago

    Divide it into a parker square

  • Jack Sainthill
    Jack Sainthill 5 days ago

    Or slice the cake into four horizontally.

  • Pythonesque
    Pythonesque 5 days ago

    1) Halve the remainding cake from center to top right
    2) Cut a diagonal square
    - For both equal halves, one will get a single piece and the other gets two triangle pieces.

  • Doppelpunkt Dedede
    Doppelpunkt Dedede 5 days ago

    Cliff has a very nice garden.

  • Darius Duesentrieb
    Darius Duesentrieb 5 days ago

    He reminds me of Doctor Brown.

  • Devang Liya
    Devang Liya 5 days ago

    If you make 10 Cliff videos in 10 hours, I would watch them immediately and complain you don't make enough of him.

  • Rule it All of it
    Rule it All of it 5 days ago

    happy birthday

  • Rosie Fay
    Rosie Fay 5 days ago

    Somehow it doesn't look like a cake to me.

    Oh, and let's divide that L-shape like this:
    (scroll past the spoiler space)

  • SECK
    SECK 5 days ago

    Darn you exploding cocoa! When will technology ever advanced far enough to defeat you!!!

  • Neoares
    Neoares 5 days ago

    1:52 :)

  • Jez
    Jez 5 days ago

    Exploding cocoa powder actually can be a problem in the factories! Where I work, they do dust explosion testing. If it's organic, small enough particles and gets suspended in the air... then with an ignition source--boom!

  • Staudinka
    Staudinka 5 days ago

    Cliff is the best!

    I guess Cocoa could explode if you fill the air with it and then set fire to it.

  • Jebus Gaming
    Jebus Gaming 5 days ago

    Or cut each of the 3 quarters into 4 pieces, giving you 12 tiny pieces, then each person gets 3 tiny pieces

  • GuanoLad
    GuanoLad 5 days ago

    Whatever you do, don't watch any ignited dairy creamer videos.

  • Ganaelin
    Ganaelin 5 days ago

    cut it in half set one upside down so the two cut parts match up then cut it in half then cut the two halves in half? would that work?

Analyse website