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

[Knitboy]

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...

[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.

[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.

[stephenbochicchio]

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. : - )

[rajatpathak]

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

[parikshitde]

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

[sciencetube]

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.

[tonyhaddad]

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 !!!!

[namitagangrade]

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

[sivateja]

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

[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.

[sabyasachirimpa]

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

[geogreg]

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

[dalehall]

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

[soujitd]

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

[donaldhobson]

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

[notchmath]

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

[albertbatfinder]

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.

[michaelcoll]

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.