Challenging Challege of the Week
It is that time of year that mathematics teachers search for new and interesting problems to share with their students (to help keep their attention) or to do themselves (to help renew your own attention). If you aren't searching for new problems for either of these reasons, then you probably should be!
One interesting problem resource site is Challenge of the Week, a website challenge with a prize--a gift certificate to Baskins-Robbins. The challenge is coordinated by the Mathematics Department at the University of Washington.
First, Challenge of the Week offers its "latest" problems on a weekly basis...every Tuesday to be specific. Anyone can submit a solution via e-mail, with a deadline of the next Monday at noon. If multiple correct solutions are submitetd, the "winner" of the Ice Cream Certificate is "randomly" drawn from the pool of correct solutions. However, "random" only in the sense that preference is given according to a heirarchy: "to solutions that are better than others (for instance, an exact result over a floating point result, etc.); to undergraduate students over graduate students over faculty; and to people who have not won a prize."
The problems are neither necessarily difficult nor do they require advanced mathematical knowledge; but, most of the problems will require both careful and creative thoughts. They will challenge high school students and college students alike....as well as teachers of mathematics!
You also can browse the web site's extensive archive that includes about three year's worth of problems. The archive includes solutions to past problems as well.