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# Fair division of sausages

## Question

I wish to share 30 identical individual sausages equally amongst 18 people. What is the minimum number of cuts I need to make? What is the minimum number of pieces I need to create?

## Recommended Posts

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The common number between 30 and 18 is 90.

So we bundle the sausages together and cut them into 3 equal parts, resulting 90 pieces.

90/18= 5 pieces for each person.

Spoiler

It looks simple

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

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Spoiler

18 sausages uncut

12 sausages bundled together and a single 1/3 cut off  (or 12 sausages with 1/3 cut off each individually) giving 24 pieces.

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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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So 1 cut then. Is a whole sausage considered a piece or just the partial ones? If whole sausages count, I stand by my original pieces count. If not, I think rocdocmac has it.

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Spoiler

Thalia, was your 42 a typo for 24 or the total of 24+18?

Edited by rocdocmac
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I was counting whole sausages as "pieces". So it was the sum.

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Appears to be ...

Spoiler

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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90x18/18

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