It is always possible to "fairly" divide a cake among n people using only vertical cuts. Furthermore, it is possible to cut and divide a cake such that each person believes that everyone has received 1/n of the cake according to his own measure. Finally, if there is some piece on which two people disagree, then there is a way of partitioning and dividing a cake such that each participant believes that he has obtained more than 1/n of the cake according to his own measure. There are also similar methods of dividing collections of individually indivisible objects among two or more people when cash payments are used to even up the final division.
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