Queenie, Roxy, and Sophie are dividing a set of 15 CDs − 3 Beach Boys CDs, 6 Grateful Dead CDs, and 6 opera CDs using the method of markers. Queenie loves the Beach Boys equally well but hates opera. Sophie loves the Grateful Dead and opera equally well but hates the Beach Boys. The CDs are lined up in an array as follows: O O O GD GD GD BB BB BB GD GD GD O O O (O represents opera CDs, GD the Grateful Dead CDs, and BB the Beach Boys CDs.) a. Describe the placement of each player’s markers. ( Use Q 1 , Q 2 for Queenie’s markers, R 1 , R 2 for Roxy’s markers, etc.) b. Describe the allocation of CDs to each player and describe what CDs are left over. c. Suppose that the players agree that each one gets to pick and extra CD from the leftover CDs. Suppose that Queenie picks first, Sophie picks second, and Roxy picks third. Describe which leftover CDs each one would pick.
Queenie, Roxy, and Sophie are dividing a set of 15 CDs − 3 Beach Boys CDs, 6 Grateful Dead CDs, and 6 opera CDs using the method of markers. Queenie loves the Beach Boys equally well but hates opera. Sophie loves the Grateful Dead and opera equally well but hates the Beach Boys. The CDs are lined up in an array as follows: O O O GD GD GD BB BB BB GD GD GD O O O (O represents opera CDs, GD the Grateful Dead CDs, and BB the Beach Boys CDs.) a. Describe the placement of each player’s markers. ( Use Q 1 , Q 2 for Queenie’s markers, R 1 , R 2 for Roxy’s markers, etc.) b. Describe the allocation of CDs to each player and describe what CDs are left over. c. Suppose that the players agree that each one gets to pick and extra CD from the leftover CDs. Suppose that Queenie picks first, Sophie picks second, and Roxy picks third. Describe which leftover CDs each one would pick.
Solution Summary: The author explains the method of markers, which is a discrete fair-division method.
Queenie, Roxy, and Sophie are dividing a set of
15
CDs
−
3 Beach Boys CDs, 6 Grateful Dead CDs, and 6 opera CDs using the method of markers. Queenie loves the Beach Boys equally well but hates opera. Sophie loves the Grateful Dead and opera equally well but hates the Beach Boys. The CDs are lined up in an array as follows:
O O O GD GD GD BB BB BB GD GD GD O O O
(O represents opera CDs, GD the Grateful Dead CDs, and BB the Beach Boys CDs.)
a. Describe the placement of each player’s markers. ( Use
Q
1
,
Q
2
for Queenie’s markers,
R
1
,
R
2
for Roxy’s markers, etc.)
b. Describe the allocation of CDs to each player and describe what CDs are left over.
c. Suppose that the players agree that each one gets to pick and extra CD from the leftover CDs. Suppose that Queenie picks first, Sophie picks second, and Roxy picks third. Describe which leftover CDs each one would pick.
Jen collects toy sports cars. She has
800800
yellowyellow
cars and
320320
blackblack
cars. She wants to line up the cars in groups so that each group has the same number of cars and contains only
yellowyellow
cars or only
blackblack
cars. What is the largest number of cars that she can have in a group?
The average A of three numbers a1, a2, a3.
On a varsity baseball team
of the players are
2
1
seniors,
of the players are juniors, and the re-
4
maining 5 players are sophomores. How many play-
ers are on the team?
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