A Quick Cake Conundrum - Numberphile

  • Added:  Month 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: bit.ly/Cliff_Videos

    The scientific way to cut a cake... tvclip.org/video/wBU9N35ZHIw/

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  • Science & TechnologyScience & Technology
  • Runtime: 3:38
  • numberphile  cake  cut  

Comments: 726

  • Cliff Mohlomi Louw
    Cliff Mohlomi Louw 3 days ago

    please assist on the conjecture

    The set {2,3,A,B} contains all prime numbers in the natural set.

    A={6n-1: n is natural}/{36xy-6y+6x-1: (x,y) are natural}
    B={6n-5: n is natural}/[{1} U { 36xy-6y-6x+1} U { 36xy+6y+6x+1}: (x,y) are natural]

    MC. Makhetha

  • Daren Rhines
    Daren Rhines 8 days ago

    I wonder if he made the bong he used before this video

  • Tristan Hollink
    Tristan Hollink 9 days ago

    Does this guy voice Ernie on Sesame street

  • The Owner
    The Owner 9 days ago

    Easy. Create a circle of the remaining cake and slice it to four equal parts.
    I paused the video at 1:55 so I wouldn't see the solution before answering :)

  • Crumb Guzzler
    Crumb Guzzler 17 days ago

    I see where this is going if you have fractal umpa lumpa birthday guests.

  • Canaan Collier
    Canaan Collier 18 days ago

    Lol I thought just to take the remaining cake, cut it half, then to cut both of those pieces in half

  • xXMinniNinJaXx
    xXMinniNinJaXx 20 days ago

    Wooow I love cliff!

  • GrayEcho
    GrayEcho 22 days ago

    Take a super wide graduated cylinder and dip the whole cake in it and measure the change in water level as volume. Divide the volume by four. Take the cake out and slowly dip it back in until the change in water level is equal to that volume and cut the piece of the cake there. There you go: soggy cake.

  • Krimunk Morin
    Krimunk Morin 22 days ago

    well with the 2 traps route
    you know that the area of the right angle triangle up thrre equals half the area of the 1/4 square under it.

    eyball an imaginary line through the bottom 1/4squares half points on the y axis and that leaves you with a trap made up of 3 equal area shapes.
    one, triangle on top
    one, rectangle in the middle
    one, rectangle at the bottom
    place your cut through the middle rectangles mid points on the y axus.
    cut along the x axis.

    do the same for the other trapezoid.
    you now have 4 equal peices.

  • Omnihil777
    Omnihil777 23 days ago +1

    Exploding Coco - extinguish it with Ice T

  • Henry Dickinson
    Henry Dickinson 26 days ago

    Cliff's laugh sounds like he might secretly be Santa Claus

  • andrewxc1335
    andrewxc1335 28 days ago

    The problem with this method is that the outer-edge people get more edge and the middle person gets none... This might be okay in some households.

  • Dhananjay Dhole
    Dhananjay Dhole 28 days ago

    Cut half way along the height / depth to make 2 L and then diagonally from the inner corner of the L to the outer to get 4 equally pieces.

  • Gordon Whyte
    Gordon Whyte Month ago

    Cake is for women and children!!!! Voila.

  • Alexander Kalbach
    Alexander Kalbach Month ago +1

    Couldn't you just cut along the bend of the L so it's two equal pieces, and then cut the cake horizontally so you basically have two layers of each piece?

  • MC cashMax
    MC cashMax Month ago

    well a 3 piece cake into 4 pieces, 12 is a multiple of 4 and 3, so I guess I would cut it into the equal pieces, then cut them into 4 quarters so I have 12, then give three pieces to each person, Easy.

  • Blyt
    Blyt Month ago

    I find this guy's accent to be grating :(

  • Christian Farina
    Christian Farina Month ago

    cut the remaining cake into three parts, then cut the trhee parts into four smaller parts and give three of the little square to each.

  • Ashley Teece
    Ashley Teece Month ago

    I love how enthusiastic he is

  • Ryung
    Ryung Month ago

    Or you could just cut it diagonally from the center of the tin and then cut the 2 remainders diagonally into triangles... no too easy? well i guessssssss we could infinitely cut it down instead...

  • beam john
    beam john Month ago

    Makes sense because your are cutting squares in quads

  • Marcus Hellström
    Marcus Hellström Month ago

    Could you connect this to fibonacci numbers arising (as absolutes) along a diagonal of, absolutes of; complex numbers? Also crazily enough, I'd ask if fibonacci numbers with multiplikative, additive and subtractive(ordinary squareroots and squares of imaginary "units"=numbers) operations does span the field of integrals? ((we have two followers along the diagonal "possibly" creating a third follower on the diagonal))!!

  • Chrstphre Campbell
    Chrstphre Campbell Month ago

    that's a very clever and elegant solution, but if your less clever; you can cut the remaining L into 3 pieces, then cut them into 4 pieces each with an X cut, then give each person 3 of those pieces. ( ? ) ( Oops ! i just read down and this was already mentioned ! )

  • Jupiter Maroon
    Jupiter Maroon Month ago

    I would have said, cut the three remaining quarters,
    So you have three peices but you need to divide them between 4 people. Well cut them in half, then cut those pieces in half. You now have twelve pices and each person gets 3 of those.

  • TheTrogolizer
    TheTrogolizer Month ago

    Great. Now I want cake.

  • Analogy Accepted
    Analogy Accepted Month ago

    For once, I solved a problem within 2 seconds...

  • LiamE69
    LiamE69 Month ago

    Exploding custard HAS been this huge problem over the ages

  • Dara Groen
    Dara Groen Month ago

    I won a chocolate bar solving this in highschool

  • Gyro Zeppeli
    Gyro Zeppeli Month ago

    I'm a simple man
    I see Cliff Stoll
    I click

  • santiago gimenez
    santiago gimenez Month ago

    no general unlike population test favor spouse crash.

  • Malek Fantazi
    Malek Fantazi Month ago

    I kind of worked this out (incorrectly). I assumed by "equal parts" he just meant parts of equal area, so I subdivided the L into 12 equal right triangles, then cut 4 shapes which each were composed of 3 of these smaller triangles.

  • Billy Jones
    Billy Jones Month ago

    They are just going to eat it anyway so just break up the remaining cake and make 3 piles that look about the same. Or if you keep dividing it again and again i guess you will be more accurate, as in everyone get the same amount.

  • MBA2804
    MBA2804 Month ago

    bake me a cake. bake me a cake. bake, bake me a cake, bake me a cake, bake me

  • Jason Axford
    Jason Axford Month ago

    Invert cake tin and tap out cake onto a plate. Place cake next to a katana expert. Watch the katana expert make three slices horizontally through cake. Too bad if they all like icing.

  • RageMageD
    RageMageD Month ago

    one minute into this.... im thinking this is a pretty shitty looking cake to give as a gift

  • ShroudedPanda
    ShroudedPanda Month ago +1


  • Mojos Bigstick
    Mojos Bigstick Month ago

    Happy Birthday Brady!

  • Broken Wave
    Broken Wave Month ago

    yeah but 1 piece gets no edge/crust...

  • Aeroscience
    Aeroscience Month ago

    Where's the optics video from cliff?

  • Assist King Eriksen #Tottenham

    Measure three quarters of the two bits of the cake on the side and the remainder has to be equal to the other two

  • Patrick Bateman
    Patrick Bateman Month ago

    Cliff is a gift to the world

  • nick m
    nick m Month ago

    Easier to cut each third into quarters

  • Yua H
    Yua H Month ago

    Using the cakes 3 dimensions, first cut in half along the side, i.e. the cross section, and then cut from the top at the juncture of the L shape and voila you have four equal pieces.

  • The Game Support Giga

    do a video about the number 42(0)

  • jawad mansoor
    jawad mansoor Month ago

    I love real life Doc BRown

  • njack1994
    njack1994 Month 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.

  • Julia Garbe
    Julia Garbe Month ago

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

  • Ashish Upadhyay
    Ashish Upadhyay Month 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 Month ago

    This might be my favourite video on the internet :D

  • Uriel Fabregat
    Uriel Fabregat Month 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 Month ago

    hoe abou' fievh?

  • salil pai
    salil pai Month 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 Month 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 Month 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 Month ago +1

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

  • Chilledfish
    Chilledfish Month 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 Month ago

    I love this guy

  • cezar t
    cezar t Month ago

    I'll skip the middle one, not crusty enough

  • White Razor
    White Razor Month ago

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

  • Conway79
    Conway79 Month ago

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

  • Yoav Lev
    Yoav Lev Month ago

    please do the Banach- tarski next!

  • Settwi
    Settwi Month ago

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

  • Adam Bernstein
    Adam Bernstein Month 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 Month ago

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

  • Radnor Roads
    Radnor Roads Month 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 Month ago

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

  • Tristan Johnson
    Tristan Johnson Month 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 Month ago

    Aw I love Cliff :)

  • Robert Van Bodegon
    Robert Van Bodegon Month ago

    Stick to numbers. Baking not so much.

  • theBraxil
    theBraxil Month ago

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

  • Michael Murphy
    Michael Murphy Month ago

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

  • John Thimakis
    John Thimakis Month ago

    Exploding coco. 🍫😃

  • Zac E
    Zac E Month ago

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

  • sahariel187
    sahariel187 Month 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 Month 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 Month 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 Month 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 Month 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 Month ago


  • Bingo Base
    Bingo Base Month ago


  • Pradhyumn Jain
    Pradhyumn Jain Month ago

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

  • neodoc1976
    neodoc1976 Month ago


  • D. C
    D. C Month ago

    Everybody's favourite Mathematician!! 😃😃😃

  • Sneha Iyengar
    Sneha Iyengar Month ago

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

  • Devin Allen
    Devin Allen Month ago +1

    Rep-tiles ♥️♥️♥️

  • Ryan Roberson
    Ryan Roberson Month 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 Month 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 Month 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 Month ago

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

  • Jaleb Jay
    Jaleb Jay Month 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 Month 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 Month ago


  • Wiseass Skeleton
    Wiseass Skeleton Month 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 Month ago

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

  • justin fwibber
    justin fwibber Month 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 Month ago

    The cake in the thumbnail looks moldy.

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