Mathematics Problem of the Week
Fall 2004
POW 7: S & P 100
A mathematics
professor picks two positive integers, both less than or equal to 10, not
necessarily different. The professor
tells the sum of the integers to Sam, and tells the product of the integers to Prue (and tells them both what has happened).
Sam, a bright math
student, calls up Prue and says, “There is no way
that you can possibly figure out my sum.”
Prue, also a bright math student, thinks it
over, calls back, and says, “You are right – and even after you’ve told me
that, I still can’t figure out your
sum.” Sam pauses for a moment and then
says, “Ah, in that case, now I know your product.”
What is Prue’s product?
Solutions
should be submitted to Dr. Maegan Bos’ mailbox in the Math office or sent via
e-mail to mbos@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.
Look
for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/