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You invite all your friends to a birthday party.
Three of your friends came.

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:

pic

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closed as too broad by Len, dmg, xnor, mdc32, Tryth Jan 27 '15 at 1:42

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Are you taking a piece, also? $\endgroup$ – Shokhet Jan 26 '15 at 1:58
  • $\begingroup$ Yes, everyone that has a birthday would want cake. $\endgroup$ – ʇolɐǝz ǝɥʇ qoq Jan 26 '15 at 2:49
  • $\begingroup$ All right; I made that assumption in my answer. Thanks for clarifying that :) $\endgroup$ – Shokhet Jan 26 '15 at 2:50
  • $\begingroup$ OK, your welcome. ☺ $\endgroup$ – ʇolɐǝz ǝɥʇ qoq Jan 26 '15 at 2:57
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    $\begingroup$ isn't it very trivial that you can just make a cross? so you only need 2 cuts? $\endgroup$ – Ivo Beckers Jan 26 '15 at 8:13
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Can't you just do this? Surprised nobody thought of this.

Answer (Click me)

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    $\begingroup$ Cool! I never thought of that. $\endgroup$ – ʇolɐǝz ǝɥʇ qoq Jan 26 '15 at 3:07
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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)

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  • $\begingroup$ That wasn't the answer I had in mind, but it works. ☺ $\endgroup$ – ʇolɐǝz ǝɥʇ qoq Jan 25 '15 at 23:16
  • $\begingroup$ 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. ☺ $\endgroup$ – ʇolɐǝz ǝɥʇ qoq Jan 25 '15 at 23:18
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    $\begingroup$ 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... $\endgroup$ – Callidus Jan 25 '15 at 23:45
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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)
enter image description here

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  • $\begingroup$ Similar to what was suggested in this answer? $\endgroup$ – Shokhet Jan 26 '15 at 3:51
  • $\begingroup$ the answer not give you when we must stop in the middle to get exact same size $\endgroup$ – Septian Primadewa Jan 26 '15 at 3:55
  • $\begingroup$ Fair enough, I guess. $\endgroup$ – Shokhet Jan 26 '15 at 3:57
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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):

enter image description here
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

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  • $\begingroup$ 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. $\endgroup$ – CyanogenCX Jan 26 '15 at 16:53

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