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So when i was a kid we used to do this thing when we shared a snack. one kid would cut the snack in half and the other would pick which of the two halfs he wants. this way, even though the picker will always have a slight edge, the cut would be pretty fair.

I thought about generalizing this for cakes and for a lot of people. My intuition is:

  1. let the first two kids do the "cut and pick" routine.
  2. each kid will get a half of the cake.
  3. the two kids will repeat this routine with two new kids for their respective pieces.
  4. repeat this process until all kids have their own peice

I see two big problems with this method. One, is that this will only work for $2^n$ kids. The other is that because "pickers" have a slight edge, and one kid is guaranteed to "descend" from a line of pickers, this edge will become significant with a lot of kids and he will have a big advantage.

What would be a better way of doing this?

RobPratt
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DAcheese
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  • This question which treats the "3 kids" case contains a lot of discussion on this topic and may be worth looking at. – Carl Schildkraut Aug 07 '21 at 22:03
  • https://www.google.com/books/edition/For_All_Practical_Purposes/ehlk3RCQXg4C?hl=en&gbpv=1&printsec=frontcover I taught this book one semester, quite good. Later I viewed one or more of the videotapes that go with it, impressive. – Will Jagy Aug 07 '21 at 22:05
  • Cut the cake into $2\times 2=4$ pieces using the “cut and pick”method twice. Give each of the three kids $1/4$ of the cake and throw the remaining $1/4$ of the cake in the bin. – Adam Rubinson Aug 08 '21 at 00:34

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