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, November 10, 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.
Now we’re rolling!
We start rolling a coin with radius 1 in a straight line, along a level surface, at speed 1 inch per second. After t seconds, the center of the coin will have traveled t inches.
Choose a point p on the edge of the coin, and write d(t) for the total distance through space that point p has traveled after t seconds. After a long enough time, it is guaranteed that the point p will have traveled further than the center of the coin; but for some choices of p, d(t) is less than t for small t.
QUESTION: What is the largest possible value of t for which it is possible that d(t) = t? (Computer-approximated answers OK; just explain how you got them.)
