# 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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**Runtime**: 3:38- numberphile cake cut

## Comments: 726

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Cliff Mohlomi Louw3 days agoplease assist on the conjecture

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

Where:

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 Rhines8 days agoI wonder if he made the bong he used before this video

Tristan Hollink9 days agoDoes this guy voice Ernie on Sesame street

The Owner9 days agoEasy. 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 Guzzler17 days agoI see where this is going if you have fractal umpa lumpa birthday guests.

Canaan Collier18 days agoLol I thought just to take the remaining cake, cut it half, then to cut both of those pieces in half

xXMinniNinJaXx20 days agoWooow I love cliff!

GrayEcho22 days agoTake 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 Morin22 days agowell 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.

Omnihil77723 days ago^{+1}Exploding Coco - extinguish it with Ice T

Henry Dickinson26 days agoCliff's laugh sounds like he might secretly be Santa Claus

andrewxc133528 days agoThe 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 Dhole28 days agoCut 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 WhyteMonth agoCake is for women and children!!!! Voila.

Alexander KalbachMonth 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 cashMaxMonth agowell 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.

BlytMonth agoI find this guy's accent to be grating :(

Christian FarinaMonth agocut 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 TeeceMonth agoI love how enthusiastic he is

RyungMonth agoOr 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 johnMonth agoMakes sense because your are cutting squares in quads

Marcus HellströmMonth agoCould 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))!!

Marcus HellströmMonth ago"Field of intergers" i got got by pseudoform

Chrstphre CampbellMonth agothat'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 MaroonMonth agoI 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.

TheTrogolizerMonth agoGreat. Now I want cake.

Thanks.

Analogy AcceptedMonth agoFor once, I solved a problem within 2 seconds...

LiamE69Month agoExploding custard HAS been this huge problem over the ages

Dara GroenMonth agoI won a chocolate bar solving this in highschool

Gyro ZeppeliMonth agoI'm a simple man

I see Cliff Stoll

I click

santiago gimenezMonth agono general unlike population test favor spouse crash.

Malek FantaziMonth agoI 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 JonesMonth agoThey 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.

MBA2804Month agobake me a cake. bake me a cake. bake, bake me a cake, bake me a cake, bake me

Jason AxfordMonth agoInvert 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.

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

ShroudedPandaMonth ago^{+1}IM IN LOVE WIT DA COCOA

Mojos BigstickMonth agoHappy Birthday Brady!

Broken WaveMonth agoyeah but 1 piece gets no edge/crust...

AeroscienceMonth agoWhere's the optics video from cliff?

Assist King Eriksen #TottenhamMonth agoMeasure three quarters of the two bits of the cake on the side and the remainder has to be equal to the other two

Patrick BatemanMonth agoCliff is a gift to the world

nick mMonth agoEasier to cut each third into quarters

Yua HMonth agoUsing 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 GigaMonth agodo a video about the number 42(0)

jawad mansoorMonth agoI love real life Doc BRown

njack1994Month 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.

Julia GarbeMonth agoThe cake looks like a piece of bread in the thumbnail.

Ashish UpadhyayMonth 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.

PhenanthrolineMonth agoThis might be my favourite video on the internet :D

Uriel FabregatMonth 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 DunbarMonth agohoe abou' fievh?

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

Rizon1985Month 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 TutorialsMonth agoSell it on eBay

M JasonMonth 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 RoyMonth ago^{+1}Stuff like this, thats not scripted, is whats amazing about people. Going off script produces some real gems

ChilledfishMonth 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?

OverkilliusMonth agoI love this guy

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

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

Conway79Month agoIn the thumbnail it looks like a mouldy piece of bread.

Yoav LevMonth agoplease do the Banach- tarski next!

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

Adam BernsteinMonth 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. :)

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

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

Mr. O'Connor: ScienceMonth 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.

NnO0WorriesMonth agoThe cocoa is from Droste (from the effect): en.wikipedia.org/wiki/Droste_effect

Tristan JohnsonMonth 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).

B1GB1RDB4G3LMonth agoAw I love Cliff :)

Ur Dank Ass Boi FigmentMonth agoe

Robert Van BodegonMonth agoStick to numbers. Baking not so much.

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

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

John ThimakisMonth agoExploding coco. 🍫😃

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

sahariel187Month 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 CriclesMonth 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.

ThyeggmanMonth 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 RamirezMonth 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 JohnsonMonth 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 FlanaganMonth agoREPTILES...

Bingo BaseMonth agoTHIS MAN IS A GENIUS

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

neodoc1976Month agoCAKE IS A LIE.

D. CMonth agoEverybody's favourite Mathematician!! 😃😃😃

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

Devin AllenMonth ago^{+1}Rep-tiles ♥️♥️♥️

Ryan RobersonMonth 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 AmosMonth 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 GaldinoMonth 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 AinMonth agoI have imagined the solution before it was revealed...

Jaleb JayMonth 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.

palmomkiMonth 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/BirdMonth agoHE DID IT THE ABSOLUTE MADMAN

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

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

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

Harry MichelsonMonth agoThe cake in the thumbnail looks moldy.