Presented by Cold Stone Creamery(R)

The Department of Mathematics Challenge of the Week

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

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

Email your solutions to solution@math.colostate.edu. Indicate your status (undergrad/grad/faculty/other) and school affiliation or city of residence if you are not affiliated with a school.

Email ideas for future challenges to Ross McConnell (rmm@cs.colostate.edu)



Challenge 12, Fall '04

Let us revisit the problem about the inchworm from Challenge 3.

For this week's problem, there are now 1000 inchworms distributed randomly along the mile-long rubber band, some facing forward and some facing backward. They all walk an inch and the rubber band stretches by a mile; they walk another inch and the rubber band stretches by another mile, etc. If an inchworm reaches either end of the rubber band, he leaves. If an inchworm meets another, he turns around and starts inching in the opposite direction.

In Challenge 3, we showed that one inchworm starting at one end will get off the rubber band after a finite number k of iterations. How much longer does it take the 1000 inchworms? That is, how large must j be to guarantee that all 1000 inchworms are off the rubber band after jk iterations?

Hint: The problem is quite easy once you get the right insight.

Solution

People who solved this week's puzzle were Ben Joeris (student at Fort Collins High), Monica Chawathe and Saravana Sellappa (CSU Grad students), Andrew Johnson (Colorado School of Mines grad student), Nicolae Popescu (Fort Collins), Rocke Verser (Loveland), Byung-Soo Kim (South Korea). The ice cream goes to Monica.


Previous Challenges, Fall '04

Challenge 1

Challenge 2

Challenge 3

Challenge 4

Challenge 5

Challenge 6

Challenge 7

Challenge 8

Challenge 9

Challenge 10

Challenge 11

If you would like to receive a weekly email reminder about the Challenge Problem, send an email to solution@math.colostate.edu

The Department of Mathematics Challenge Problem is sponsored by the Cold Stone Creamery, which is providing all the prizes.

If more than one correct solution is submitted, one prize winner will be chosen from among the correct solutions. Submissions from CSU faculty and people not affiliated with CSU are encouraged, but they are ineligible for the prizes.

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