# Problem of the Week: Fall 2023, Number 1

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: Friday, September 1, 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.

It’s just a flipping (and adding) game!

You and your friend are playing a game. Here’s how it works: start with a fraction of two positive whole numbers. You and your friend take turns changing the number. You are allowed to change the number in one of two ways: you may flip the fraction over, or you may add 1 to the denominator. So, for example, 3/5 can be turned into 5/3 or into 3/6 = 1/2. (The fraction is always reduced at the end of a turn).

The first person whose move results in a number that has already occurred loses. The other player receives a dollar amount equal to the total number of moves they made during the game.

Suppose the starting number is 2/3, and you’re going first. What do you do and why?

Author: Gettysburgian Staff