*Problem #2*

In the "Brain Bogglers" section of the November 1998 issue of
*Discover* the reader was asked to find a way of overlaying three 2x1
rectangles so that the number of regions created was as large as possible.
For example, in the figure below, there are 13 regions.

In the magazine's solution, there were 23 regions.

- Improve on the magazine's solution.
- Does the answer depend on the dimensions of the rectangle?
- More generally, what is the maximum number of regions that can be
created with
*n* rectangles?