 Consider a fair division problem involving 5 players. The phrase
"a player receives a fair share" describes the fact that
 the player receives a share that is at least as valuable as that
of any other player.
 the player receives a share that is more valuable than that of
any other player.
 the player receives a share that, in the player's opinion, has
value that is equal to 20% or more of the total.
 the player receives a share that, in the player's opinion, has
value that is exactly equal to 20% of the total.
 None of the above
 An estate consisting of a car, a boat a house and a diamond ring
must be divided fairly among five heirs. This type of problem is
called
 a continuous fair division problem.
 a discrete fair division problem.
 a mixed fair division problem.
 the method of sealed bids.
 None of the above
 Which of the following is a discrete fair division problem?
 dividing a gallon of ice cream
 dividing a tropical island
 dividing a cheese pizza
 dividing an antique car collection
 None of the above
Questions 4 through 6 refer to the following situation: Three players
(Tiffany, Paxton and Sandra; Paxton divider and
Tiffany and Sandra choosers) are going to divide a
cookie (a large one) fairly using the lone divider method.
Paxton cuts the cake into three slices (s1, s2, and s3).
 If the choosers declarations are Sandra: (s2) and Tiffany:
(s3}, which of the following is a fair division of the cookie?
 Sandra gets s1; Tiffany gets s2; Paxton gets s3.
 Sandra gets s3; Tiffany gets s2; Paxton gets s1.
 Sandra gets s2; Tiffany gets s3; Paxton gets s1.
 Sandra gets s2; Tiffany gets s1; Paxton gets s3.
 None of the above
 If the choosers declarations are Sandra: (S2, S3) and
Tiffany : (S1, S3), which of the following is not a fair division
of the cookie?
 Sandra gets S2; Tiffany gets S3; Paxton gets S1.
 Sandra gets S1; Tiffany gets S3; Paxton gets S2.
 Sandra gets S3; Tiffany gets S1; Paxton gets S2.
 Sandra gets S2; Tiffany gets S1; Paxton gets S3.
 None of the above
 If the choosers declarations are Sandra: (s2) and
Tiffany: (s1, s2), which of the following is a fair division
of the cookie?
 Sandra gets S2; Tiffany gets s1; Paxton gets S3.
 Sandra gets S2; Tiffany gets S3; Paxton gets s1.
 Sandra gets S3; Tiffany gets s1; Paxton gets S2.
 Sandra and Tiffany split s2; Paxton gets s1 and S3.
 None of the above
 Three players (Missy and Tiffany dividers and
Paxton chooser) are going to divide a cake fairly using the
lone chooser method. Using this method
 the first division consists of dividing the cake into 2 pieces,
the second division consists of dividing each of these pieces into 2
pieces.
 the first division consists of dividing the cake into 3 pieces,
the second division consists of dividing each of these pieces into 2
pieces.
 the first division consists of dividing the cake into 2 pieces,
the second division consists of dividing each of these pieces into 3
pieces.
 the first division consists of dividing the cake into 3 pieces,
the second division consists of dividing each of these pieces into 3
pieces.
 None of the above
 Paula and Ginger won a computer in a MAT 131 joint competition.
Except for the computer, they own very little of value. As a result
they have agreed to
divide the computer fairly using the method of sealed bids. Paula bids
3,000 and Ginger bids 2600. After all is said and done, the final
outcome is
 Paula gets the computer and pays Ginger 2600.
 Paula gets the computer and pays Ginger 1500.
 Paula gets the computer and pays Ginger 1400.
 Paula gets the computer and pays Ginger 1300.
 None of the above
Questions 9 through 12 refer to the following example: Three heirs
(Natasha, Taurus, and Ginger) must divide fairly an
estate consisting of two itemsa house and a paintingusing the
method of sealed bids. The players' bids (in dollars) are:
Natasha Taurus Ginger
House 180,000 200,000 210,000
Painting 30,000 40,000 33,000
 The original fair share of Ginger is worth
 $243,000.
 $81,000.
 $84,000.
 $33,000.
 None of the above
 After the initial allocation to each player is made there is a
surplus of
 $24,000.
 $32,000.
 $19,000.
 $129,000
 None of the above
 After all is said and done, the final allocation to
Natasha
is:
 $76,333 in cash.
 $70,000 in cash.
 the painting and $46,333 in cash.
 the house and Natasha must pay $70,000.
 None of the above
 After all is said and done, the final allocation to Ginger
is:
 $81,000 in cash.
 $129,000 in cash.
 the painting
and $40,000 in cash.
 the house and Ginger must pay
$122,667.
 None of the above
Questions 13 through 16 refer to the following: Four players
(Michelle, Jeniere, Melicent, Lolitta) agree to divide 15 items
using the method of markers. The items are numbered 1, 2, ..., 15.
Figure 1
Each of the player's three markers are placed as follows:
Michelle: immediately to the right of items 1, 6, 12
Jeniere: immediately to the right of items 3, 8, 14
Melicent: immediately to the right of items 2, 9, 13
Lolitta: immediately to the right of items 2, 7, 12.
 Item 5
 goes to Michelle.
 goes to Jeniere
 goes to
Melicent.
 goes to Lolitta.
 is left over.
 Item 9
 goes to Michelle.
 goes to Jeniere
 goes to
Melicent.
 goes to Lolitta.
 is left over.
 Item 11
 goes to Michelle.
 goes to Jeniere
 goes to
Melicent.
 goes to Lolitta.
 is left over.
 Item 15
 goes to Michelle.
 goes to Jeniere.
 goes
to Melicent.
 goes to Lolitta.
 is left over.
Questions 17 through 20 refer to the following situation:
Missy and Sandra want to divide fairly the
chocolatestrawberry cake shown below using the dividerchooser
method. The upper half is chocolate the lower half strawberry.
The total cost of the cake was $12.00. Missy values strawberry
three
times as much as she values chocolate, while Sandra values chocolate
twice as much as she values strawberry.
Figure 2
 In Sandra's eyes, the piece in Figure 3 is worth
Figure 3
 $8.00
 $10.00
 $9.50
 $9.00
 None of the above
 In Missy's eyes, the piece in Figure 4 is worth
Figure 4
 $4.50
 $7.50
 $10.50
 $10.00
 None of the above
 In Sandra's eyes, the piece in Figure 5 is worth
Figure 5
 $8.00
 $6.00
 $7.00
 $5.00
 None of the above
 In Missy's eyes, the piece in Figure 6 is worth
Figure 6
 $4.50
 $6.00
 $7.00
 $7.50
 None of
the above
Questions 21 through 24 refer to the following situation: Five
players agree to divide a cake fairly using the last diminisher
method. The players play in the following order: Amber first,
Demetrius second, Shanni third, Sherri fourth,
and Stacee last. Suppose that there are no diminishers in
round 1 and Shanni and Sherri are the only diminishers in round 2.
 Which player gets her fair share at the end of round 1?
 Amber
 Demetrius
 Shanni
 Sherrie
 Stacee
 Which player is the first to cut the cake at the beginning of
round 2?
 Amber
 Demetrius
 Shanni
 Sherrie
 Stacee
 Which player gets her fair share at the end of round 2?
 Amber
 Demetrius
 Shanni
 Sherrie
 Stacee
 Which player is the first to cut the cake at the beginning of
round 3?
 Amber
 Demetrius
 Shanni
 Sherrie

Stacee
ADDITIONAL EXERCISES
 If John bids $50.00 and Joan bids $65.00 for
a math 131 book, how would you reach a fair division of this object?
 Almaz, Eden, and Hiwet inherit a house by the Red Sea. Assume that their
evaluations of the house are $305,000, $360,000, and $380,000
respectively. Describe a fair division.
 Hiwet and Lydia inherited a plot of land. If their monetary bids
on the house are $205, 000 and $214,000, respectively,
 Describe a fair division for the two heirs when they receive equal
shares.
 Describe a fair division for the two heirs if their shares are 2/5
and 3/5, respectively.
 Two people inherit a painting. Assume that their evaluations of the
painting are $10,680 and $8,880, respectively.
 Describe a fair division for the two heirs when they receive equal
shares.
 Describe a fair division for the two heirs if their shares are 1/5
and 4/5, respectively.
 Stacee, Paxton, and Ginger inherit a painting. Assume that their
evaluations of the painting are $28,800, $22,600, and $20,000,
respectively.
 Describe a fair division for the three heirs when they receive
equal shares.
 Describe a fair division for the heirs if their shares are 1/2,
1/3, and 1/6, respectively.
 A parent leaves a house, a grand piano, and plot of land to be
divided equally among four children who submit dollar bids on
these objects as follows. Describe a fair division for the four heirs.
Children

Objects  First Second Third Fourth

House  $240,000 $225,000 $200,000 $290,000

Piano  $30,000 $20,000 $25,000 $10,000

Land  $100,000 $140,000 $125,000 $145,000

 In Exercise 30 describe a fair division for the four heirs when
their shares are 2/10, 3/10, 1/10, and 4/10, respectively.
Three indivisible objects X, Y, and Z are to be shared equally
among four people. Assume that these three objects have dollar
values to the four as follows:
Objects

People  X Y Z

First  $3,600 $4,500 $5,100

Second  $3,900 $4,800 $5,100

Third  $2,700 $5,700 $4,500

Fourth  $4,200 $3,900 $2,400

 Describe a fair division for the four people when they receive equal
shares.
 In Exercise 32 describe a fair division for the four people when
their shares are 2/5, 1/5, 1/5, and 1/5, respectively.
 Describe an envyfree method of dividing a cake among four people.
 Is the dividerchooser method an envyfree method? If yes why, if
not, why not?