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# Divide the cake three ways fairly

## Question

Two persons can fairly divide a piece of cake if one person cuts it, and the other person chooses which piece to take.

Suppose there are three persons who want to fairly divide the cake?

Suppose there are N persons?

Person #1 cuts off a piece of the cake.

Person #2 can make the piece smaller or pass.

Person #3 can make the piece smaller or pass.

The last person who touched the piece takes it.

The other two divide the remaining cake the usual way - one cuts, the other chooses.

Explanation:

If Person #1 cuts off too small of a piece, the others will pass, and Person #1 will be stuck with it.

If Person #1 cuts off too big of a piece, Person #2 will want a shot at getting it and will make it a little smaller.

Depending on how small Person #2 makes the piece, Person #3 can either pass [so Person #2 will have to take it] or reduce it very slightly in order to keep it.Person #1 cuts off a piece of the cake.

Person #2 can make the piece smaller or pass.

Person #3 can make the piece smaller or pass.

...

Person #N can make the piece smaller or pass. The last person who touched the piece takes it and is removed from the process.

Repeat until everyone has a piece.

## 4 answers to this question

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I don't think this is true for N eaters. After about 5 or 6 I'd be grossed out by the little cuts and bits of cake everywhere and just pass on the whole thing.

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but what if you have like, a really BIG cake.

Then there wouldn't be very small pieces of cake.

I think people would rather have slightly uneven slices of cake than to have to cut cake for the next three hours though.

But that's just one opinion

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but what if you have like, a really BIG cake.
And, I assume, a large number of people among whom to divide.

Seems a fair point to consider.

Divide the people into two groups, and have each group elect a captain.

The captain of Group 1 cuts the really BIG cake in half.

The captain of Group 2 chooses one of the halves.

Optionally repeat the process - like if you have a really REALLY big cake.

Each Group then fairly divides the not-so-really-BIG cakes.

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sounds good to me.

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