Problem of the Week: Cutting Up, Naturally
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.
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. Send solutions to firstname.lastname@example.org. Weekly winners will receive a POW victory button, and the best-performing students of the semester will receive the Paul Mugabi problem-solving award. This problem was posted on Friday, September 3 and solutions are due on Friday, September 10 by 5:00 p.m.
Suppose we have a square. We pick a point inside the square and use that point to make four triangles like this:
Suppose that the four triangles each have different areas, and that the areas of all four triangles are positive whole numbers.
QUESTION: What is the smallest that the area of the original square can possibly be? Give the answer, and explain how you know.