Presented by Cold Stone Creamery(R)

The Department of Mathematics Challenge of the Week

A solution and a new problem is posted every Monday during fall and spring semesters at www.cs.colostate.edu/~rmm

Email your solutions to solution@math.colostate.edu

One winner each week is eligible for a free ice cream and topping, courtesy of Cold Stone Creamery.

Challenge 3, Fall '03

The problem: An inchworm is at one end of a mile-long rubber band, and would like to reach the other side.

After he walks one inch, the rubber band stretches to two miles in length. Though this is a discouraging development for the inchworm, he can take some solace in the fact that the rubber band stretches evenly along its length. The inch of rubber band he's already covered has doubled to two inches, boosting him along by an inch.

He now walks another inch, and is now three inches from the beginning. The rubber band now stretches to three miles in length, which has the side effect of stretching the part he has already covered to 4 1/2 inches.

Each time he walks an inch, the rubber band stretches by another mile.

Question: Will the poor caterpillar ever reach the other end? Explain how you arrived at your answer.

Solution

Bonus question: The mother is twenty-one years older than the child. Six years from now, the mother will be five times as old as the child. Question: Where's the father?

Solution

For questions, comments or suggestions for future challenge problems: please e-mail Ross McConnell, rmm@cs.colostate.edu.