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Fair division of sausages


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2 hours ago, Thalia said:

 

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12 cuts, 42 pieces? Unless you want to line up the sausages and do one giant cut...

 

You have the right idea with your comment. I an designing a cut as a swipe of the knife,  so lining them up and then cutting with one swipe would  count as one cut. 

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Simplify to dividing 5 sausages for 3 people

Denote a third of a sausage (whether cut or uncut) by [3].
Denote an uncut sausage by [3][3][3] and an intact 2/3 of a sausage by [3][3].

Three persons would be optimally served as follows:

  1. [3][3][3]  [3][3]
  2. [3][3][3]  [3]  [3]
  3. [3][3][3]  [3][3]

The black sausages were not cut.
Two sausages, the red one and the green one, were each cut once, creating four pieces.

Do this 6 times.

12 cuts will have created 24 pieces.

 

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