"A point is selected at random from the region inside of a regular n-gon. What is the probability that the point is closer to the center of the n-gon than it is to the n-gon itself?”
For the last nine years, the Missouri State University Problem Solving Group has been finding the solutions to problems like this. The group consisting of both students and faculty gets together once a week to work on these problems which come from a variety of mathematical journals (for example, the American Mathematical Monthly, Mathematics Magazine, the College Mathematics Journal, and Crux Mathematicorum). When a solution is obtained, it is written up and submitted to the appropriate journal. The group has submitted over 100 solutions, a number of which have been published. Over the years, more than 30 students have participated in the group. The faculty members of the group are Richard Belshoff, Shelby Kilmer, Les Reid, Cameron Wickham, and Matt Wright.
The latest set of problems is here.