Mathematics Problem Of the Week

Fall 2005

POW #1

Phone a Friend

Erik is off at college and separated from his good friend Donna for the first time. But they agree to talk by phone at least once every day, sometimes more often. Knowing that they must each attend to their own studies, Erik and Donna agree that their average number of phone conversations per day over any week long (7 day) period must be less than two.

Prove or disprove: If Erik and Donna stick to their plan, there must be a sequence of consecutive days in the month of September where they talk by phone exactly 20 times.

Due Friday, September 2^nd at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.

Presentation counts! The prize-winning entry will be selected from all correct submissions, based on the clarity, creativity and elegance of the solution.

The SLU POW is a FY Cup eligible event.

Look for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/