Mathville puzzles: the advertising executive

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Aliquot Part is an advertising executive with Abelian Group Advertising, located at 31416 Adams Circle in Mathville. Mr. Part is in charge of scheduling the commercial breaks for the show Chain Rule, a top rated TV show in Mathville.

For the first commercial break there are seven slots available for advertisements. These slots are numbered 1 through 7, in the order in which they will be aired.

Mr. Part has lined up the following commercials to air during the first commercial break:

Bary Center Housewares
Cantor's Point Realty
Data Structure Computers
Fibonacci's Italian Restaurant
Hypercube Builders
Joachimstahl's Notations Office Store
Keith Numbers, Attorney at Law

Mr. Part must schedule only one commercial per time slot, and the arrangement of the spots is subject to the following rules:

(1)The Bary Center Housewares and Data Structure Computers commercials must occupy consecutive time slots.

(2)The Bary Center Housewares commercial must be aired during an earlier time slot than the commercial for Keith Numbers, Attorney at Law.

(3)The commercial for Data Structure Computers must be aired during a later time slot than the one for Hypercube Builders.

(4)If the commercial for Hypercube Builders is not in the fourth time slot, then the ocmmercial for Fibonacci's Italian Restaurant must be in the fourth time slot.

(5)The commercials for Keith Numbers, Attorney at Law, and for Joachimsthal's Notations Office Store cannot occupy consecutive time slots.

Keeping in mind the rules, answer this question:

If Joachimsthal's Notations Office is assigned to the seventh slot, then which of the following MUST be assigned to the fifth slot?

(A) Bary Center Housewares
(B) Cantor's Point Realty
(C) Data Structure Computers
(D) Fibonacci's Italian Restaurant
(E) Keith Numbers, Attorney at Law


Contest Rules

  • You must send the solution via email to Laura Skinner at lskinner@pvcc.edu.
    Solution due by Saturday, December 6th, at 11:59 p.m. Solutions sent after the deadline will not be considered.
  • You must email the solution from your PVCC email address.
  • You must explain how you arrived at the solution -- that is, you must show your work and/or explain your reasoning.
  • Only correct solutions with explanations of the reasoning used to arrive at the solution will be considered.
  • From the pool of qualifying entries, nine winners will be randomly selected: two first place winners, three second place winners, and four third place winners.
  • The first place winners will each be awarded a $30 gift certificate to the PVCC Bookstore.
  • The second place winners will each be awarded a $15 gift certificate to the Mermaid Express coffee cart.
  • The third prize winners will each be awarded a big Hershey’s milk chocolate bar.
  • Drawing will be conducted on Monday, December 8th, 2014. Winners will be notified by email, and their names will be published on a blog post.
  • The solution to the puzzle will be published on the blog after winners have been announced.
  • Winners must pick up their prizes by Friday, December 12th at 4 p.m., or they forfeit their prizes. Prizes must be picked up in person. Please present your student I.D.