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 11, Fall '04

Contributed by Carol Andreyev, Estes Park

One hundred passengers are in line to board a plane that has 100 seats. All the passengers have seat assignments. However, the first passenger is crazy, and, instead of sitting in his assigned seat, he picks one of the 100 seats randomly. All seats, including the one he is assigned to, have equal probability. After that, each passenger sits in his own seat unless he finds it occupied, in which case, he picks one of the remaining seats randomly and with equal probability.

What is the probability that the last passenger on the plane will get his assigned seat?

Solution



Previous Challenges, Fall '04

Challenge 1

Challenge 2

Challenge 3

Challenge 4

Challenge 5

Challenge 6

Challenge 7

Challenge 8

Challenge 9

Challenge 10

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.