Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s). Each week’s entries are scored by a faculty judge, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button. The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.
Solutions Due: Saturday, March 9, 5:00 p.m.
Send solutions to bkennedy@gettysburg.edu.
The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited. Weekly winners will receive a POW victory button, and the best-performing students of the semester will receive the Paul Mugabi problem-solving award.
An Enclosed-Minded Problem
You have four sections of fencing, each five meters long. You break each piece into two smaller pieces; each smaller piece is a positive whole number of meters in length. You then arrange the eight pieces of fencing to enclose an area in your garden according to the following rule: any two distinct pieces of fencing must meet at right angles.
What is the largest area you can enclose this way? What is the smallest area you can enclose this way? Submit a picture of the fences you think enclose the largest and smallest possible areas. If you can, explain why you think (or how you know!) that your answers are the best possible.
