Four people (Alex, Betty, Carl, and Dan) are trying to split a cake evenly. They

Question

Four people (Alex, Betty, Carl, and Dan) are trying to split a cake evenly. They decide the "lone-divider" method is the best method to use. They randomly select Dan to be the divider. Dan proceeds to cut the cake into four pieces {p_1, p_2, p_3, and p_4}. Upon inspection of the pieces... Alex wants {p_2 or p_4} Betty wants {p_2} Carl wants {p_1 or p_2} Why are Dan's preferences not listed? Now that everyone has decided what pieces are acceptable, determine a fair division of the slices. Andrew and Bill are two complete strangers that happen upon a $12 sub that is 12 inches long. They agree to use the Divider-Chooser method to split the sub. Bill is chosen to be the divider. He values ham three times as much as turkey. How will he cut the sub? Andrew does not eat ham. If Andrew had been chosen to be the divider, how would he have cut the sub?

Explanation / Answer

(a) Here Dan`s preference is not included because he is the divider, so he will not be allowed to put his choice and remainging persons will put their preferences first as they put also. Dan`s will be allowed to take his remaining slice at the last .

(b) Here based on given preferences as Betty wants, p2 piece, it will be given to him in the beginning and thus Carl will only get piece p1. Further as piece p2 is already given to Betty, thus Alex will opt only piece p4. And thus lastly remaining piece p3 will be give to Dan, the divider.

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