Mathville puzzles: The hoop earrings

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Area Baseten is the CEO of Positive Integers, an ad agency in Mathville. As an ad exec, she always dresses very professionally, and likes to wear hoop earrings. She has a jewelry box on her dresser that has 30 pairs of hoop earrings.Fifteen pairs are gold hoop earrings, and fifteen pairs are silver hoop earrings. Other than that, all the earrings are exactly alike.

One evening, when Area was getting dressed to go to a business reception, the lights went out, and she was left in complete darkness. She wanted to wear matching earrings, of course. She thought for a moment, and then opened her jewelry box and removed some earrings, putting them in her pocket before heading out.

What is the smallest number of earrings that Area would have to pull out of the jewelry box to ensure she had a matching pair?


Contest Rules


  • You must send the solution via email to Laura Skinner at lskinner@pvcc.edu.
  • Solution due by Thursday, October 16th 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, explain your reasoning. 
  • Only correct solutions with explanations of the reasoning used to arrive at the solution will be considered.
  • Six entries will be drawn from all the correct solutions, to determine two first places, two second places, and two third places.
  • 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 Friday, October 17th. 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, October 24th at 4 p.m., or they forfeit their prizes. Prizes must be picked up in person. Please present your student I.D.