58. Queenie, Roxy, and Sophie are dividing a set of 15 CDs-3 Beach Boys CDs, 6 G

Question

58. 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 but hates the Grateful Dead and opera. Roxy loves the Grateful Dead and 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: OO O GD GD GD BB BB BB GD GD GDOO O (O represents the opera CDs, GD the Grateful Dead CDs, and BB the Beach Boys CDs.) (a) Describe the placement of each player's markers. (Use 01 and Q2 for Queenie's markers, Ri and R2 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 an 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.

Explanation / Answer

O O O GD GD GD BB BB BB GD GD GD O O O

S4 S5 S6 R7 R8 R9 Q1 Q2 Q3 R4 R5 R6 S1 S2 S3  

R DENOTES ROXIE

S DENOTES SOPHIE

Q DENOTES QUEENIE

WE JUST ENUMERATE THE POPSSIBIILITYS BUT THE TOTAL NUMBER OF CDS PICKED BY EACH IIS REQUIRED

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