Math Challenge of the Week

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 9, Fall '04 A game-show host shows you two boxes and tells you that one of them contains x dollars the other contains 2x dollars. He won't tell you the value of x, but he allows you to draw one of the boxes randomly. You have drawn the box containing x dollars with a probability of 1/2.

After opening it, you discover that it has $200 in it. The host now gives you a chance to pocket the money, or give it up in exchange for whatever money is in the other box, which you now know is either $100 or $400. You want to maximize the expected value of your winnings. Should you take him up on the deal? If so, what is your expected gain in doing so?

A solution is given with Challenge 10

Previous Challenges, Fall '04

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.