PROBLEM OF THE MONTH

September 2006




Congratulations to this month's winners Roman Kogan, Say Cheong and Thomas Riedel! Here is the solution by Roman Kogan: [pdf]

There are 100 seats on a plane. All seats are assigned to passengers. Passengers enter the plane one at a time. First, enters a crazy old lady, who takes any seat with uniform probability (by chance, this may happen to be her own seat). Each subsequent passenger acts as follows: if his/her seat is vacant, then he/she takes this seat; but if his/her seat is already taken, he/she takes any of the remaining seats with uniform probability.

What is the probability that the last passenger takes his/her own seat?

This month's prize will be awarded to the best explained, correct solution.


Submit your solution to the Mathematics Undergraduate Office (Math P-142) or electronically to problem@math.sunysb.edu by the due date. Acceptable electronic formats are: PDF, Postscript, DVI, (La)TeX, or just plain text. Please include your name and phone number, or preferably your email address.

Closing date: October 1st at 12 pm.