Naomi has a triangle which is blue on one side and yellow on the other. It has a dot in one corner on each side.

How many ways are there of posting this triangle through a triangular shaped slot?

http://nrich.maths.org/public/viewer.php?obj_id=2644

This flash program could be used to introduce simple transformations to the littlies, or an an application of group theory to senior high school students. How cool is that!
http://nrich.maths.org/public/viewer.php?obj_id=5560