Chapter 3, Problem 58E

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.