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Excursions in Modern Mathematics: Pearson New International Edition | 8th Edition | ISBN: 9781292022048 | Authors: Peter Tannenbaum
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Solved: Five players are dividing a cake among themselves using the lone-divider method

Chapter 3, Problem 29

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QUESTION:

Five players are dividing a cake among themselves using the lone-divider method. After the divider D cuts the cake into five slices 1s1, s2, s3, s4, s52, the choosers C1, C2, C3, and C4 submit their bids for these shares. (a) Suppose that the choosers bids are C1: 5s2, s46; C2: 5s2, s46; C3: 5s2, s3, s56; C4: 5s2, s3, s46. Describe two different fair divisions of the cake. Explain why thats itwhy there are no others. (b) Suppose that the choosers bids are C1: 5s26; C2: 5s2, s46; C3: 5s2, s3, s56; C4: 5s2, s3, s46. Find a fair division of the cake. Explain why thats itthere are no others.

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QUESTION:

Five players are dividing a cake among themselves using the lone-divider method. After the divider D cuts the cake into five slices 1s1, s2, s3, s4, s52, the choosers C1, C2, C3, and C4 submit their bids for these shares. (a) Suppose that the choosers bids are C1: 5s2, s46; C2: 5s2, s46; C3: 5s2, s3, s56; C4: 5s2, s3, s46. Describe two different fair divisions of the cake. Explain why thats itwhy there are no others. (b) Suppose that the choosers bids are C1: 5s26; C2: 5s2, s46; C3: 5s2, s3, s56; C4: 5s2, s3, s46. Find a fair division of the cake. Explain why thats itthere are no others.

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Given:- Five players are dividing a cake among themselves using the lone-divider method. After the divider  cuts the cake into five slices , the choosers  and  submit their bids for these shares.

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