Name: ___________________
Block: ______
Fair Division Test
Discrete Math
Form A
Answer each of the questions below to the best of your ability. SHOW ALL WORK! No partial
credit will be given for incomplete work.
1) Explain the difference between discrete and continuous goods. Give examples of each.
2) Listed below are all the methods of fair division which we learned about in this unit. Which
methods can be used to divide continuous goods? You may circle more than one answer.
a) Divider-Chooser
b) Lone-Divider
c) Lone-Chooser
d) Marker
e) Sealed Bids
f) Adjusted winner
3) Sam has cheesecake which is equal parts strawberry, chocolate, original, and pumpkin. Sam
likes strawberry three times as much as pumpkin; he likes chocolate twice as much as pumpkin;
and he likes original and pumpkin equally. The cheesecake is worth $14. What is the value of
each section of the cheesecake to Sam?
Value of: Strawberry = ________
Chocolate = _______
Original = __________
Pumpkin = ________
4) April, Brian, and Chan have a pie which is half citrus and half chocolate mousse. The cake is
worth $27. To April both sections are worth $13.50. To Brian, the citrus section is worth $0 and
the chocolate mousse is worth $27. To Chan, the citrus section is worth $18 and the chocolate
mousse is worth $9. Describe a fair division of the pie using the Lone-Chooser Method with
April and Brian as the dividers and April making the first cut.
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5) Wesley, Xavier, Yogi, and Zack are dividing a piece of land using the Lone-Divider Method.
Wesley divided the land into sections and labeled them s1, s2, s3, and s4. The remaining players
then submitted bid lists, which are listed below. Using the bid lists, describe a fair division of
the land.
Xavier: {s1, s2}, Yogi: {s1, s4}, Zack: {s3}
6) In problem 5, how do the choosers decide which items to bid on?
7) Charlotte and David have a pizza which is half veggie lovers and half meat lovers. Charlotte
likes both equally, while David does not eat vegetables. They will use the Divider-Chooser
method to divide the pizza. If David is the divider, describe a fair division of the pizza.
8) Abigail, Bart, Cierra, and Dude must divide their great grandmother’s estate using the
Method of Sealed Bids. The items to be divided are: an apartment in New York City, a brand
new Cadillac, and a painting. Their bids are given in the chart below. Describe a fair division of
their great grandmother’s estate.
Apartment
Cadillac
Painting
Abigail
120,000
40,000
28,000
Bart
150,000
30,000
20,000
Cierra
111,000
47,000
24,000
Dude
198,000
52,000
19,000
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9) Three children (A, B, and C) are dividing the array of 12 candy pieces using the Method of
Markers. The player’s bids are given in the figure below. Hint: First number your candies.
C1
A1
A2
B1
C2
B2
a) Describe the allocation of candy to each child.
b) Which items are left over?
11) True or False. If the statement is false, change the sentence to make it true. In the Method
of Sealed Bids (Estate Division), players bid on the actual value of the goods.
12) At the end of the lease on their apartment, Toni and Terry decide to rent separate places and
so must make a fair division of the property they purchased together. The items to be divided
and the point values each person places on them are given below. If Toni and Terry use the
Adjusted Winner Method to divide the property, what will Terry end up with?
Item
CD player
Sofa
Microwave
TV
Toni
15
30
20
35
Terry
20
25
25
30
Bonus: At the beginning of this unit we read one of Aesop’s fable. Write your own fable which
involves fair division.
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