3 people are dividing a cake. Each person wants as much cake as possible for himself, but each person thinks that the other two might be colluding. Lets call the three A, B, and C.

A suggests that he will cut the cake into 3 portions, and then C will pick his piece from the 3, and B then would pick his choice from the 2 remaining. and A takes the last piece. B objects to this scheme, saying that A can cut the cake into 1 large piece, and 2 smaller equal pieces. C then would have the largest piece, and B would have to take the smaller piece. In fact, B claims, If A and C were really colluding, this method would allowing them to get the entire cake to share among them two.

Given this distrusting atmosphere, is there a way to divide the cake so that each person is satisfied? Any proposed method would have to convince each person that he would get his fair share even if the other two were colluding.

I know of two solutions to this, but I wouldn't be surprised if the den can come up with a couple extra solutions.

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## bushindo 14

3 people are dividing a cake. Each person wants as much cake as possible for himself, but each person thinks that the other two might be colluding. Lets call the three A, B, and C.

A suggests that he will cut the cake into 3 portions, and then C will pick his piece from the 3, and B then would pick his choice from the 2 remaining. and A takes the last piece. B objects to this scheme, saying that A can cut the cake into 1 large piece, and 2 smaller equal pieces. C then would have the largest piece, and B would have to take the smaller piece. In fact, B claims, If A and C were really colluding, this method would allowing them to get the entire cake to share among them two.

Given this distrusting atmosphere, is there a way to divide the cake so that each person is satisfied? Any proposed method would have to convince each person that he would get his fair share even if the other two were colluding.

I know of two solutions to this, but I wouldn't be surprised if the den can come up with a couple extra solutions.

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