# 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

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

## Comments: 655

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jawad mansoor2 hours agoI love real life Doc BRown

njack19944 hours agoHow 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 Goopy17 hours agoThe cake looks like a piece of bread in the thumbnail.

Ashish Upadhyay21 hour agoMethod 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.

Phenanthroline22 hours agoThis might be my favourite video on the internet :D

Uriel Fabregat22 hours agoYou 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 Dunbar1 day agohoe abou' fievh?

salil pai1 day agoyou could have also cut it into 3 parts then cut each into 4 sub parts and give each person 3 pieces.

Rizon19851 day agoBefore 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 Tutorials1 day agoSell it on eBay

M Jason1 day agoOption 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 Roy1 day agoStuff like this, thats not scripted, is whats amazing about people. Going off script produces some real gems

Chilledfish1 day agoIt'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?

Overkillius2 days agoI love this guy

cezar t2 days agoI'll skip the middle one, not crusty enough

White Razor2 days agoI swear that's just a big sandwich in that baking dish.

Conway792 days agoIn the thumbnail it looks like a mouldy piece of bread.

Yoav Lev2 days agoplease do the Banach- tarski next!

Settwi2 days ago3/4 / 4 = 3/16. think of the cake in 16th unit squares. divide equally. done.

Adam Bernstein2 days agoI'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. :)

SkylersRants2 days agoThe conundrum isn't fair because the middle piece has no crust. :)

Radnor Roads2 days agoI remember this puzzle from a book in my childhood, but with pizza! What a blast from the past.

Mr. O'Connor: Science2 days agoMake 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.

NnO0Worries2 days agoThe cocoa is from Droste (from the effect): https://en.wikipedia.org/wiki/Droste_effect

Tristan Johnson2 days agoNot 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).

B1GB1RDB4G3L2 days agoAw I love Cliff :)

Ur Dank Ass Boi Figment2 days agoe

Robert Van Bodegon3 days agoStick to numbers. Baking not so much.

theBraxil3 days agoWhy do you have coco out? The cake isn't even chocolate?

Michael Murphy3 days agoI absolutely adore this man. Everyone needs a little Cliff Stoll in their life

John Thimakis3 days agoExploding coco. 🍫😃

Zac E3 days agoor you could cut the cake in half (diagonally) and then cut in half vertically (creating two equally thin layers).

sahariel1873 days agoThe 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 Cricles3 days agoThe 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.

Thyeggman3 days agoYou 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 Ramirez3 days agoIf 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 Johnson3 days agoFour 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 Flanagan3 days agoREPTILES...

Bingo Base3 days agoTHIS MAN IS A GENIUS

Pradhyumn Jain4 days agowht if u cut the cake laterally....then we can divide it in a infinite no. of equal pieces

neodoc19764 days agoCAKE IS A LIE.

D. C4 days agoEverybody's favourite Mathematician!! 😃😃😃

Sneha Iyengar4 days agohow do give a lecture on vectors and it's application

Devin Allen4 days agoRep-tiles ♥️♥️♥️

Ryan Roberson4 days agoive 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 Amos4 days agoI'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 Galdino4 days agoHello! 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 Ain4 days agoI have imagined the solution before it was revealed...

Jaleb Jay4 days agoI 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.

palmomki4 days agoI 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/Bird4 days agoHE DID IT THE ABSOLUTE MADMAN

Wiseass Skeleton4 days agoI knew where this was going as soon as I saw that the 'problem' was 3/4 of a square.

Ralph Dratman4 days agoCliff Stoll is just a little bit eccentric. You know, just a tad off the beam. A smidge.

justin fwibber4 days agoThat was depressingly simple. I figured it out right away. I was expecting something hard. I usually never get these things.

Harry Michelson4 days agoThe cake in the thumbnail looks moldy.

Rob McLear4 days agoCliff 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 Montgomery4 days agoI love this guy

kazeman4 days agoMy 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)

skipjack914 days agoA cake? Really? I would've baked you a Pi!

Mike S.4 days agoMath and humor. What more could a Youtube viewer ask for?

iñigo san jose4 days agoi love this guy, my fav of numberphile by far

Lester Squad4 days ago*Sees thumbnail* it's Mr. Klein Bottle

logiclrd4 days agoTry 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 Moeller4 days agoi love this guy

LeeJn4 days agokinda close to a powder bomb...stay safe

EDIT: not the colorful fun-fun powder bomb lol

Tsavorite Prince4 days agoYou could make a fractal out of this!

Agnes Ginardi4 days agoThat 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.

Amin4 days agoHEY! I'ts mr klein bottle !!

charlievane4 days agoyou should've continued shooting, he was getting interesting

Rafael Trevisan Lisboa4 days ago*Cocoa Explodes*

Rafael Trevisan Lisboa4 days agoI love this man so much!!!!!!!!!!! Such energy

DutchDread4 days agoBut they don't all get the same type, some get more crust, if you know kids, you know this solution is unaceptable

Erwin Lommer4 days agoWhat 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

NoriMori4 days agoThis was a triumph…

Luis Manuel Castro Moreno5 days agoDivide 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

mrBorkD5 days agoSince 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.

Nerobyrne5 days agoeasy:

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-two5 days agofigured this out in about 10s

rahul kumar5 days agoplease tell me if there's formula for calculating no of Latin cubes , I know there's one for latin squares , please reply

Harley Martin-Farrell5 days agoTechnically 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.

needforsuv5 days agoWHO measures a cake

also who gets the crumbs

Kori1145 days agoThat was pretty obvious.... I had figured out that solution before they got to it. I was expecting something more clever.

Hsterts Hertz5 days agoITS MY FAVOURITE MATHEMATICIAN :DDDDDDDDDDD

theorganguy5 days agomy 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 Krab5 days agoDivide it into a parker square

Jack Sainthill5 days agoOr slice the cake into four horizontally.

Pythonesque5 days ago1) 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 Dedede5 days agoCliff has a very nice garden.

Darius Duesentrieb5 days agoHe reminds me of Doctor Brown.

Devang Liya5 days agoIf 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 it5 days agohappy birthday

Rosie Fay5 days agoSomehow it doesn't look like a cake to me.

Oh, and let's divide that L-shape like this:

.

(scroll past the spoiler space)

.

.

.

.

AA

AB

CBBD

CCDD

SECK5 days agoDarn you exploding cocoa! When will technology ever advanced far enough to defeat you!!!

Neoares5 days ago1:52 :)

Jez5 days agoExploding 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!

Staudinka5 days agoCliff is the best!

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

Jebus Gaming5 days agoOr cut each of the 3 quarters into 4 pieces, giving you 12 tiny pieces, then each person gets 3 tiny pieces

GuanoLad5 days agoWhatever you do, don't watch any ignited dairy creamer videos.

Ganaelin5 days agocut 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?