Math Riddle: Can You Cut the Cake in Half? Easy & Tricky Interview Riddle

Tricky Interview Riddle: Divide the cake into two equal portions with a single straight cut.
It's a beautiful tricky interview math riddle that tests your basic math concepts.
It's a hard riddle with a simple solution.
Jeremy and Jane would like to divide a rectangular cake in half, but their friend Bob (who can be very annoying sometimes) has already cut out a piece for himself. Bob’s slice is a rectangle of some arbitrary size and rotation. How can Jeremy and Jane divide the remaining cake into two equal portions with a single straight cut?
- The single straight cut can pass through the cut-out portion.
- Please note that they both need an equal amount cream and the toppings, so a cut along the height would not be accepted.
Pause the video and think mathematically.
You are most welcome to share puzzle, math problems or any topics for upcoming videos.
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[@cool-aquarian]

killer puzzle with such basic solution

[@jessicataylor7174]

Killer puzzle indeed...I'm going to kill Bob lol 😂

[@abhinavbhutada9b484]

Indeed man!

[@shameelsadaka]

I thought out of the box and got the same solution. Since the size or the rotation of the slice or cakes in not given, the only unique property the rectangles have is their midpoints. And there are two mid points, we need a stright line, two points is enough to draw a straight line.

[@Knitboy1997]

And here I thought that you would; -Measure the hole and cake "height" and lenght" itself. -Calculate their volume. -Substract hole from cake. -Divide it by "height" and cut at the corresponding "lenght"... But I guess this solution would be more appropriate if the shape of hole was more irregular...

[@mohsinimam2048]

Haha

[@stephenbochicchio9351]

Without measurements it is as arbitrary for you to know the exact center of the cake and the center of the missing rectangle as it is arbitrary for me to know the area of the cake and missing rectangle. So my solution of slicing the cake with equal amounts of surface area works perfectly well. : - )

[@donaldasayers]

2 dimensional analogue of the 3D "Ham Sandwich Theorem". There is always a plane cut that divides two arbitrary shaped pieces of bread and the piece of ham into equal portions. The solution is the same as this puzzle, just make sure the plane passes through the centroids of all the items.

[@donaldhobson8873]

The centeroid is the centre of gravity. It can balance a small area at a large distance on one side, with a large area at small distance at the other. If you take an arbitrary shape, and draw all the lines that cut it in half areawise, the lines don't all intersect at a point. If you take an equilateral triangle, and divide it into 9 smaller triangles. (in rows of 5,3,1) Then you can see that the line through the centre has 5/9 of the area below it. The halfing lines parrallel to the sides form a small triangle round the centre.

[@donaldasayers]

@@donaldhobson8873 Yeah you're right, silly me.

[@donaldhobson8873]

@@donaldasayers Its an easy mistake to make. My dad made the same mistake when I told him.

[@programaths]

That''s even a more degenerated case as it comes from a little theorem about shapes that are their own image under central symmetry. (or in other words, shapes fro which it is possible to find a central symmetry that applies the shape to itself) In that case, it comes that wherever is your cut going through the center of symmetry, it has to divide the shape in two equals. (by definition!) And when you have those center being collinear, then you can draw the cut between them. Two points are always collinear. So, no need to use the "Ham Sandwich Theorem", but only material you learn when you are 12. In a real interview, you give that final version. When the interviewee is stuck, you ask him how he would divide only the big rectangle. Then ask him other possibilities until he used diagonals and bisectors. At some point, it should click that he can draw any line going through the center. Then you go back to the one with the hole. The hard work is being able to abstract what was just learned and apply it. It's not really hard here, but enough to weed out people that will do their job poorly if it requires some thinking.

[@damaramohanareddy9220]

I think that's a wrong answer, because he said both need equal amount of creem and toppings but in this solution, it doesn't satisfy

[@namitagangrade2714]

Me after seeing the solution : Why couldn't I think this way, am I really too dumb ?

[@davidinark]

Not dumb. The education system doesn’t teach is to think this way. We are always taught the longest, most complicated solutions then later may or may not be taught the “shortcut.” So, we always expect a solution to be overly complex. Basically, education failed us.

[@rajatpathak6524]

Awesome awesome ❤️❤️.... learnt something today.... enjoyed it 🙌🙌🙌🙌

[@sabyasachirimpa]

I cut the cake in the middle and gave extra to the size of the rectangle.

[@sankarganesh2858]

Give half of the size of rectangle

[@tonyhaddad1394]

Its simple but very intersting !!! The fact that a straight lign pass the center of a rectangle always cut it into to equal area (you can proove it easly by similar triangles which scaled by 1 so congruent and ....) So if we make a straight lign pass the centers of the 2 rectangles we are done !!!!

[@hrayz]

I was going to cut a piece from the centre to fill Bob's cut out. Then cut through the middle making sure the missing part is halved ... Yours was easier.

[@jameskuyper]

That doesn't meet the requirement of using only a single straight cut it requires at least 5 straight cuts.

[@michaelcoll433]

LMAO. A friend of mine went on an interview with a largish tech company. Interview went well until they trotted out these dumbass puzzles. She walked out. Two days later they called her back in for a second interview, she said no because of the puzzles. The next day they called and apologized. Still a nope. These puzzles can be fun and are ok for entry level positions. After that, they're insulting. I've never used them when doing interviews.

[@albertbatfinder5240]

I cut out another piece of the same size, then cut the cake in half, then gave the cut-out piece to anyone who complained I wasn’t solving it with one cut.

[@sivateja2769]

Superb sir🙏, it is really simple but hard to think...

[@DarkVoidIII]

If Bob had really wanted to be annoying he could have cut a half-circle that wasn't aligned to any side of the cake or the centroid. :D

[@rickharriss]

Because I am an engineer I would cut off a thin slice from one end large enough to fill in the missing rectangle, then just cut directly down the middle.

[@sciencetube4574]

A rectangle is centrally symmetric, which means that any straight line through the centre of the rectangle will always split it exactly in half. This is easy to see because a straight line through the centre also possesses point symmetry in this point, and since all figures involved are point symmetric about the centre of the rectangle, the two halves are not just equal in size, they are the exact same shape and can be mapped onto each other via reflection through the centre. In this case, it is impossible to calculate how much cake was cut out and thereby fairly divide the cake, since the dimensions of the missing piece are not given. However, if both people get half the original cake (assuming the hole wasn't there) and also half the hole, then they will definitely end up with half the remaining cake. Since both the original cake and the hole are rectangles, they can be split in half by a line through their respective centre, so a line through both centres (which is always possible with two points) will evenly divide the remaining cake.

[@parikshitde3147]

all your riddles are all very simple to follow yet solid.

[@soujitd]

Wow ! Simple common sense but uncommon. Thank you Ammar ❤.

[@donaldhobson8873]

Pick any angle, slide the knife across the cake. The areas change continuously, exactly one position will half the cake.

[@u.v.s.5583]

That's an existence proof. It is correct but not constructive.

[@jc5318]

Cut in the middle of a cake with extra cake (half of rectangle ) to left portion.

[@littzy5576]

I would have worked out the square meter of the whole cake and the rectangle. The adjusted my cut line to allow for this.

[@geogreg1123]

Make a vertical cut at (ab-xy)/2*b from either of edge if xy is area of hole and ab is area of cake. b is breadth and a is length. Basically each half volume is (ab-xy)/2 and since breadth is b need to divide by b

[@elfboy745]

Me: you only get 1 cut... Wife: knife is to kill Bob and put back the slice he cut. Me: ... Wife: if he cuts cake like that he deserves to die. Me: yes dear. *goes hide the knives*

[@essayasnigussie5790]

Additional assumptions: Cake does not melt while cutting and the cutting has to be done perpendicular to the surface the cake is placed on.

[@skandpratap1619]

One loop hole is there. I sent this screenshot to my friends and everyone answered "divide the cake diagonally from bottom left corner to top right corner." And unfortunately they were telling the correct answer but not logically. Take a look at the first image "yellow rectangle with blue rectangle in it". Make diagonals of small rectangle, let's assume the intersection point of smaller rectangle is "P". Now draw diagonal of yellow rectangle from bottom left to top right, it will pass right through point "P". Logically this diagonal is passing through mid points of both the rectangles. If the blue rectangle was little above or below its current position it would have been more logical. Just a suggestion, no hard feelings.

[@LOGICALLYYOURS]

Yes bro, i realized it soon after posting the puzzle. But your comment about the screenshot thing also made me feel that I should have taken care of the screen very well. Thanks for the feedback, I'll certainly keep it in mind for upcoming puzzles.

[@skandpratap1619]

@@LOGICALLYYOURS Apart from this comment thing. I was searching for some website or some KZbin channel where I can read or watch truly logical questions and trust me, your channel ended my search. I've seen a number of images on social media claiming "90% will fail" but almost everybody knows the answer but when I visited your channel and when you say "90% will fail" then trust me, more than 90% people fail. Keep it up bro. Kudos.

[@jessicataylor7174]

@@LOGICALLYYOURS You do say 0:18 that Bob's slice is of arbitrary size and rotation. It was clear the image wasn't the only possibility for where Bob mutilated the delicious cake while no-one was watching because he is mentally disturbed...lock him up already, he's a danger to cakes! 😁 You may have noticed I'm somewhat disturbed by how Bob cut that cake lol 😲😭😬😂

[@GetMeThere1]

This is a trick question. You require "magical" information about the "center" of unknown shapes. On a rectangular piece, the only "answer" is a cut from one corner to the other -- for which you don't need to know the center point. In your example TWO center points are required, that you DON'T KNOW.

[@Guile21]

Shapes are not unknown, they're both rectangles. And you can pin point the center of a rectangle easily without requiring any measuring devices. It's simply where the two diagonals cross each other. Even in a practical way, you can trace/identify diagonals with the straight edge of the knife and use toothpicks to mark where the centers are. It's not that big of a deal.

[@GetMeThere1]

@@Guile21 First, they said the blank spot could be any shape -- so no, there is no way to find it's center. Secondly, in the practical sample they gave, there would be no good way to "draw two lines" to find the center of the big rectangle -- you are allowed ONE "cut" only.

[@manojsinghal1292]

What about cake and topping? Would both pieces have equal amount of these if the cake is cut this way?

[@deepakp927]

I come with another solution... For normal rectangle a vertical straight cut from center will divide it into two equal parts For this rectangle find area of small rectangular portion and shift vertical cut from center to add half of area of small rectangle. So, we can get two equal parts for remaining cake. Little bit more complex 😅

[@RamInChennai]

That's precisely what I did too. May be he should have specified that we should not use any measuring device.

[@LOGICALLYYOURS]

Still acceptable solution considering a practical case.

[@aronblanche]

Good Puzzle

[@adityakumarsingh6402]

They can take out the mid points of both the rectangles by the intersection of diagonals and then make a cut passing through both mid points.

[@amfulger]

This is in principle a nice idea. But how do you see the intersection of the diagonals in the missing small rectangle? And what if the center of the large rectangle is in the small rectangle? You won't see that either. This is a great interview question because in real life you get a lot of stupid questions and the expected correct answer is also stupid.

[@adityakumarsingh6402]

@@amfulger intersection of diagonals will give u the centre. We r not gonna draw that on cake 😂. In mathematics, we assume...

[@_Volt_gaming]

But the rule was that both wanted equal amounts of cream. Plz dont add those details if you dont intend to fulfill them.

[@tamirerez2547]

Beautiful puzzle, looks hard... Where to begin? And then, surprising solution!! Suddenly it became so simple...😀 Thank you Ammar for excellent question and brilliant answer!! The first big diagonal is passing through the center of the big rectangle, so it cut it to two pieces with equal area. But! there is a black hole in the cake. Since the line goes through the middle of the "black hole" it cut the black hole also into two equal areas. Each one get half of the big rectangle, minus half of the black hole rectangle. Brilliant Ammar!

[@notchmath9642]

Before I watch: I think any line drawn through the center of a rectangle cuts it in half. So if you draw a line through the center of both rectangles, it cuts the big cake in half minus the bits lost, but since the bits lost are equal the whole thing is cut in half

[@jessicataylor7174]

Yay! You included the 'value' of the cake topping! 💖 Also...where is Bob? I have a knife and know what he did...where is he? RUN BOB, RUN!!!! 😆

[@essayasnigussie5790]

Very funny!!

[@deadcatthinks6725]

Easy - give Bob a slap so he gives you back the piece he took, replace it in the cake then cut straight down the middle.

[@ABCXYZ-zt3dr]

My solution: First of all they will find it's center of mass, then no matter how they cut the cake (with a straight line), the cake will be divided into two equal parts( probably my solution is true).

[@jasdeepsinghgrover2470]

It gives the same result... The center of mass of rectangle is its center (where diagonals meet). Take the original rectangle and the cut out part as an anti-rectangle and you will get the same line of suspension as joining the centers.

[@jasdeepsinghgrover2470]

I am taking the initial rectangle without the cutout and the cutout part and treating it as a negative mass. Individually the center of masses are their respective centers

[@jasdeepsinghgrover2470]

You can find the new center of mass along the cut line by balancing their torques... Would love to know your ideas about proving the same. Maybe yours would be much simpler or I get something new to learn.

[@mohamedhusam8189]

Actually no because a line through the center of mass would divide the cake to two parts with equal torques about the line but not equal masses

[@ABCXYZ-zt3dr]

@@mohamedhusam8189 we can balance anything on the tip of a pin if we find it's center of mass. It means all mass is spread equally around the center of mass. Then it should divide into two equal masses if we cut it along a line passing through it center of mass.

[@parthsaxena160]

Amaar bhai always op . 👍👍

[@abs1426]

If we can make ourselves remember all the theorem of geometry, it is quite easy to solve such problems with little brain exercise. 👍🏽👍🏽

[@dalehall7138]

Nice, intuitive solution. Far better than the kludge I came up with.

[@JaredFrontman]

The fact, that we can take screenshot and share it is the best

[@qilunren3070]

so happy I solved it. I think it was because I been watching your vid so long

[@devendrabisht3615]

Cream and toppings are mostly on the upper part of the cake, so how come they will get equal cream and toppings..?

[@51_meehir_walkar80]

Same doubt ,anybody here to clear it?

[@devendrabisht3615]

@@51_meehir_walkar80 only possible if the shown image is the top part of the cake.

[@51_meehir_walkar80]

@@devendrabisht3615 ooh, so basically , it was top view . I was assuming it's a side view.

[@saikatkarmakar6633]

Excellent man.. i really love your videos..

[@FF7ATgood]

This problem is just a piece of cake No, two pieces of cake

[@rohanpawar1603]

Amazing puzzle

[@tanmayjain6837]

I was thinking about diagonal bt that was not cutting the bigger rectangle. Bt the solution was just simple and amazing

[@manshulgarg8399]

Cut plane from 1 corner of upper face to opposite corner of bottom face

[@stevena3244]

You didn't discuss the punishment Bob received when they caught up with him

[@hiyou7696]

I thought it was a riddle where you cut the cake in half from the side as it would be 3D.

[@KundanKumar-im1gs]

Really beauty

[@basheerlubssak4272]

Great. Really loved it.

[@gmchess7367]

Awesome puzzle 👍👍

[@kartikeyasatyarthi8665]

Good logic .. learned something today

[@arpyboi]

Really awesome puzzle... But I figured it out😊😉

[@LOGICALLYYOURS]

Perfect :)

[@pandiyanb4025]

Using maths 1. Calculate the whole area of rectangle. 2. Calculate the area of rectangular hole. 3. Subtract area 2 from area 1. 4. Divide the above result by 2 which results to equal area for both people. 5. Divide the above area by width of old rectangle. 6. Slice the cake at a distance obtained above from any of the edges of the cake so that it is not disturbing the hole in the cake. 7. If this solution is tedious, follow the video solution.😅

[@feelingzhakkaas]

Mind-blowing solution

[@maruthasalamoorthiviswanat153]

Really amazing solution

[@NikitaNair]

Very nice

[@asmitrai1035]

Brilliant

[@pedrosil77]

Very interesting. Thanks for the upload.

[@deltaphant_]

It always feels good to get one of these correct!

[@yemesvee]

Wow.. nice one..Thanks for sharing

[@visavou]

Enjoyed the solution more than the cake.

[@sanchit6107]

The real question is how tf BoB cut out the rectangular shape from a rectangular cake?

[@ciberiada01]

I think Bob was kinda stupid. The time it took him to cut it in the middle, he would have eaten half of the cake.

[@deepaksuriya8267]

What about the cream?? The green part doesn't have any cream. The 2nd rule is the cream should be equal.

[@ChandanKumar-rl6df]

Really it was awesome

[@mushfikaikfat]

That's really amazing 😎 Such a cool experience 👍👍 Thanks a Trillion 😊😊

[@AH17293]

Can we not just cut the cake in the centre of the big cube in relation to the z axis? That way the small cube cross section should be consistent for the depth of the cake.

[@pjmmccann]

But then the person receiving the bottom portion would receive no icing/toppings.

[@vikashKumar-ep1ce]

It was very nice and good concept ☺️ Thanks

[@BCS-IshtiyakAhmadKhan]

So jeremy and jame knows the centre of smaller rectangle

[@myash32]

The answer is, "as many times as you can". Thats what the mom told her

[@piyushborse]

That's clever

[@aquabestindian]

Solved this without using pen and paper (or actual cake) 😋 Center is the key!

[@amfulger]

How did you find the center?

[@MysticJabulon]

Pet peeve: "criteria" is plural. "The only criteriON is..."

[@sumitg1743]

superb👏👏👍

[@robertcitrus5974]

What if you cut the cake into the top half and bottom half? Like how the top half is where all the frosting is.

[@jessicataylor7174]

Bob has mutilated the cake enough, don't you start taking all the frosting or you'll both be banned from my parties in future...respect the cake! 😁

[@Prabakaran-k]

Here annoying is not bob, infact its jeremy and Jane who wants exactly half. Lol. Anyways it was a nice puzzle.

[@vivekanandachalladi207]

Cream not distributed equally🙄

[@belligerentapj3685]

Since I could do it.. I don't know whether I've improved or the puzzle was easy bcz after everything seems easy

[@ramaraobonagiri9365]

Good logic.

[@siddharthkale6339]

Its wrong. The cut from the middle horizontally should also be accepted here, as the toppings are not distributed evenly.

[@bm-ub6zc]

This one was unusually easy ...

[@rajivpokharel88]

Wow. So simple soln.

[@CapAnson12345]

Bah. Always gotta read the question carefully. The key being Bob cut a rectangular slice. I hate my brain. It just doesn't work well with these things.

[@vaishnavipalawar9717]

Also we cut it horizontally i.e parallel to the ground in the midway. That will also divide the cake into 2 equal parts.

[@jameskuyper]

No, that solution will give all of the toppings to whoever got the top half, when he explicitly said that the toppings must also be divided equally.

[@andreare7766]

That IS good!

[@TwinshuParmar]

If bob had cutted 2 rectangular cake then how to get the same result?

[@Deep23508]

LOL if I would have been there I would have put the topping in middle and then easily cut the cake into half

[@raushankumar-ug4zh]

Can i divide rectangle into equal halves and make a small rectangle in other half

[@jessicataylor7174]

Not in one straight cut though. 😊

[@raushankumar-ug4zh]

@@jessicataylor7174 but i can achieve result in 2 cuts

[@N8570E]

Logically Yours, that was awesome.

[@yashvardhangupta10]

What if we cut the diagonally so that both get equal topping as well as base portion

[@amarmkulkarni]

Cut the cake from above

[@dollcyjain2452]

It's a easy one. I just took 1 minute to solve it.

[@arnabpersonal6729]

pretty basic but can be tricky in an interview

[@angelodc1652]

Yes

[@dicksonrobert1492]

but...they do get equal amount of cream

[@anonymouslyfamous6102]

Just wow

[@sundusafreen4430]

What if the cut is done on the edge?

[@jerzylutoborski1330]

I had to take a shower to solve this.