Exam 3: The Mathematics of Sharing: Fair-Division Games

Four friends {Joe , Tim , Sam , and Ron } have decided to divide up a multi-flavored cake which was jointly purchased for $24 . The cake is divided into four pieces { s1 , s2 , s3 , and s4 } . The following table gives the dollar value of each of the slices according to e3ach of the four friends . Which of the four slices are considered fair shares according to Ron? -Based on the above scenario , find a fair division of the cake using as fair shares.

You have decided to live in a converted loft with eleven of your college friends. The loft is a large open room and as a group you have decided to divvy up the floor space using the Last-Diminisher Method. You label yourselves and the order in which the method is played has P₁ first, P₂ second, and so on. Here is how the method begins: Round 1: P₁ makes the first cut; P₂ passes; P₃ diminishes; diminishes; P₁₂ passes. Round 2: After the first claim is made, P₈ is the only diminisher. Round 3: After the first claim is made, all the remaining players pass. After the end of Round 3 , which three players have received what they consider a fair share of the loft space?

Five friends {Alice, Bob, Cathy, Dave, and Earl} have decided to divide up a multi-flavored cake which was jointly purchased for $30 using the Lone-Divider Method. The cake is divided into five pieces {s1 2 3 4 5 , , , , and s s s s } . The following table gives the dollar value of each of the slices according to each of the five friends Which of the five slices are considered fair shares according to Bob? -According to the scenario above , which of the following would be a fair division?

Which of the following items would best be divided among five people using a continuous method of division?

Jeff and Kyle jointly purchase the box of Neapolitan Ice-Cream ( 1 / 3 chocolate, 1 / 3 vanilla, and 1 / 3 strawberry) shown below. They will use the Divider-Chooser Method to divide the box. After flipping a coin it is determined that Kyle will divide the ice-cream into two pieces and Jeff will choose one. Kyle values chocolate five times as much as he values vanilla; however, he values strawberry four times as much as he values vanilla. As the divider, which of the divisions could Kyle make?

Alex, Bob and Cathy used the Lone-Chooser Method to divide up a cake. Alex and Bob are the Dividers for this method, and each of them cuts their portions into thirds allowing Cathy to make her selections. Based off of this chart, who (Alex or Bob) acted as the original Divider when performing the Divider-Chooser Method between the two players. Explain how you know this.

Horace and Pete jointly purchase a pizza which is half pepperoni and half sausage for $24. Suppose that Horace values pepperoni three times as much as he values sausage. According to Horace’s preference system, what is the dollar value of the slice shown below? -Based on the scenario above and knowing Pete values sausage seven times as much as he values pepperoni, what is the dollar value of the slice shown above according to Pete's preference system?

John and Sara have jointly purchased a half pepperoni and half sausage pizza. They use the DividerChooser Method to divide the pizza. John is the divider and cuts the pizza into the following two pieces. Based on John's division, he prefers pepperoni sausage. Fill in the blank.

Ron , Tim , Sam , and Joe are dividing an estate consisting of a house and a car using the method of fealed bides their bids on each of the items are given in the following table . how much dose each person gets in surplus money?

Four friends {Joe , Tim , Sam , and Ron } have decided to divide up a multi flavored cake which was jointly purchased for $24 using the lone-divider method . the cake is divided into four pieces {s₁ , s₂ , s₃ , and s₄} . the following table gives the dollar walue of each of the slices according to each of the four fiends . which of the four friends is the divider? -Based on the above scenario , find a fair division of the cake using s₁, s₂, s₃ , and s₄ as fair shares, and explain why this is the only possible fair division.

A group of friends is going to divide up a plot of land amongst themselves using the Lone-Divider Method. After the divider D divides the land into four parcels S1,S2,S3, AND S4, C1, C2, AND C3, submit their bids on what they consider a fair share. Suppose that the choosers' bids are . Give two different fair divisions of the land.

Four friends {Joe , Tim , Sam , and Ron } have decided to divide up a multi-flavored cake which was jointly purchased for $24 . The cake is divided into four pieces { s1 , s2 , s3 , and s4 } . The following table gives the dollar value of each of the slices according to e3ach of the four friends . Which of the four slices are considered fair shares according to Ron?

Horace and Pete jointly purchase a pizza which is half pepperoni and half sausage for $24. Suppose that Horace values pepperoni three times as much as he values sausage. According to Horace’s preference system, what is the dollar value of the slice shown below?

Jackson and Sherry jointly purchased a circular pizza which is half pepperoni and half sausage for $18. suppose that Jackson values pepperoni five times as much as he values sausage , while sherry values sausage two times as much as she values pepproni . which of the following statments is true ?

Four friends {Joe , Tim , Sam , and Ron } have decided to divide up a multi-flavored cake which was jointly purchased for $24 . The cake is divided into four pieces { s1 , s2 , s3 , and s4 } . The following table gives the dollar value of each of the slices according to e3ach of the four friends . Which of the four slices are considered fair shares according to Ron? -Based on the above scenario , find a different fair division (different from problem 4) of the cake using as fair shares. If no other fair division is possible, explain why.

A group of friends is going to divide up a plot of land amongst themselves using the Lone-Divider Method. After the divider D divides the land into four parcels submit their bids on what they consider a fair share. Suppose that the choosers' bids are and . Describe how a fair division would result.

Four people are going to fairly divide up a pareel of land worth $240,000.00 using the lone-divider method . the divider partitions the land into four different pieces s1 , s2 , s3 , and s4 . accourding to the divider what is the doolar value of s3?