Hampden-Sydney students **Matthew Carrington**, **Avery Moncure**, **Ke Shang**, **Tian Shihao**, and **Alex Smith** participated in the Virginia Tech Regional Mathematics Competition (VTRMC) on Saturday, October 24. More than 130 colleges and universities throughout Virginia, DC, Georgia, Illinois, Maryland, New Jersey, New York, Ohio, North Carolina, Pennsylvania, South Carolina, Tennessee, West Virginia and other states are invited to participate each year. Now approaching its 31st year, the contest began in 1979 and has grown to the point where over 50 schools with over 300 contestants participate in a typical year. Contestants at each participating school take the two and one-half hour exam on their own campus under the supervision of one of their own faculty members.

The VTRMC problems are typically quite challenging. Here’s a problem from this year’s competition:

A walker and a jogger travel along the same straight line in the same direction. The walker walks at one meter per second, while the jogger runs at two meters per second. The jogger starts one meter in front of the walker. A dog starts with the walker, and then runs back and forth between the walker and the jogger with constant speed of three meters per second. Let

f(n) meters denote the total distance traveled by the dog when it has returned to the walker for thenth time (sof(0) = 0). Find a formula forf(n).

Our Hampden-Sydney “mathletes” are to be commended for their participation in this contest!