You invite all your friends to a birthday party.

At the party, you need to share your cake equally with everyone.
The friends that came aren't your best friends, so you don't give anyone an extra piece.
You can cut three times. No more, no less.

How do you share the cake with everyone?

The cake is a cylinder, it looks something like this:

• Are you taking a piece, also? Jan 26, 2015 at 1:58
• Yes, everyone that has a birthday would want cake. Jan 26, 2015 at 2:49
• All right; I made that assumption in my answer. Thanks for clarifying that :) Jan 26, 2015 at 2:50
• OK, your welcome. ☺ Jan 26, 2015 at 2:57
• isn't it very trivial that you can just make a cross? so you only need 2 cuts?
– Ivo
Jan 26, 2015 at 8:13

Can't you just do this? Surprised nobody thought of this.

• Cool! I never thought of that. Jan 26, 2015 at 3:07

Assuming you want 4 equal pieces and the cake is cylindrical shaped:

Cut the cake into fourths (perpendicular cuts through the center of the circular face), and then cut through the cake horizontally (half way between both circular faces) to make 8 equal pieces. Each person gets 2 pieces. (this idea from your profile pic)

If you meant each person can only get one piece, then there are still many ways to do it.

One way using parallel lines is to first cut the cake in half normally, then use the remaining two cuts to divide the semicircles in half. There are many ways to make these cuts and if you want them parallel, you will cut approximately $.407*R$ away from the center where $R$ is the radius of the cake's circular face. (This from http://www.mathopenref.com/segmentarea.html)

• That wasn't the answer I had in mind, but it works. ☺ Jan 25, 2015 at 23:16
• P.S. I don't have this profile pic just for this question. It's a Rubik's Cheese, a product similar to a Rubik's Cube. ☺ Jan 25, 2015 at 23:18
• Once you've cut the cake in half, can't you just separate the two halves and then cut each piece in half again? Not as much fun perhaps, but easier... Jan 25, 2015 at 23:45

1. First, cut into half (1)
2. Rotate the first half 90 degree and put on the other half.
3. Cut the edge. (2)
4. Flip
5. Cut the edge (3)

• Similar to what was suggested in this answer? Jan 26, 2015 at 3:51
• the answer not give you when we must stop in the middle to get exact same size Jan 26, 2015 at 3:55
• Fair enough, I guess. Jan 26, 2015 at 3:57

Take off the candles first; you don't want to eat those :)

I assume that you (as the birthday boy!) will take a piece also, so we're looking for four pieces.

Thus, you have to

tilt the cake sideways, and cut it three times horizontally, like this (picture not to scale):

These won't be traditionally shaped "wedge" cake pieces, but they'll still work :)

See this Wikipedia article for more info about why this question sounds so complicated to some people.

This answer was really a piece of cake :P

• Yes but usually all the layers of the cake aren't the same so I'm not sure how "equal" it would be. Some people get more frosting. Jan 26, 2015 at 16:53