Here's a fun puzzle I found out about recently. It's called Ancient Greek Geometry. The challenge is to create different shapes (like triangles, and circle patterns) using only a straight-edge and a compass. For example, here's a solution for a hexagon:
Hexagon Created Using a Straightedge and Compass
The program runs right in your browser and is easy to learn. Just point your students to the website (http://sciencevsmagic.net/geo/) and they'll figure out the rest.
There's also a number of other neat features from the same people at their website.