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How could you cut a piece of dough into $3$ even pieces? Cutting it into $2$ is easy, but it's not that trivial for greater numbers.

If you can cut it into $n$ pieces, you could repeat the process on each piece, getting any multiplication of $n$, so to ask a more general question:

Let $p\in\mathbb{N}$ be a prime number. How can you cut a piece of dough into $p$ pieces?

P.S. I couldn't find a good tag, any bright idea?

maxuel
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    What's the shape of the dough ? For an arbitrary shape, cutting in 2 is equally difficult. For a ball or a rotationally symmetric shape, use a protractor or a pair of compasses. –  May 26 '14 at 09:58
  • If it's a square (or any sort of rectangle), just make $p-1$ cuts parallel to each other and to one pair of sides. – user2357112 May 26 '14 at 10:17

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It is straightforward to divide an arbitrary line segment into $n$ equal pieces if one has a unit measure and can construct parallels. Let the segment be $AB$ - take an arbitrary line through $A$ which is not the line $AB$ and mark off $n$ unit intervals so that $AC$ has length $n$ units. Construct $CB$ and parallels to $CB$ through the marked off points - they cut $AB$ evenly into $n$ equal pieces. Arrange your dough in a rectangle and use this construction.

Mark Bennet
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