Problem of the Month
Aha! The Mathematics Department's Problem of the Month has returned after a long rest on a sunny beach somewhere. It has been busily proving theorems using sticks to draw in the sand, but alas, such vacations must eventually come to an end.
First, the rules: You must work alone or with a single partner. You may not use any external resources such as the internet, Maple, Mathematica, your computer, etc. You may, however, use books that physically exist on paper. (Computers may be used to type solutions if you wish, but handwritten solutions are welcome.) Submit solutions (including a careful justification of your answer) to Prof. Mitch Keller in Robinson Hall 206 or Beedle Hinely in Robinson Hall 113A. Write your name(s) and the date and time of submission on your paper before turning it in. Each month's problem list has a designated deadline (generally noon on the last day of classes in the month).
Second, the prizes: You are encouraged to turn in problems one-by-one as you solve them. The first five correctly solved problems will receive a prize of $1. The grand prize winner is the first person/team to submit correct solutions to all three problems. The grand prize is a $25 Main Street Lexington gift certificate usable at most of the fine eateries and shops in Downtown Lexington.