This was my submission to athenahealth for a job interview in May 2012. I found the puzzle interesting enough to share!
The answer it produces for the number of 48x10 panels that can be built within the parameters of the puzzle is 806844323190414 (806.8 trillion), computed in about 100 milliseconds when I measured it.
It was simple enough to come up with a brute force solution that worked for inputs up to 27x5, but far too slow for 48x10 - so I had to find a more creative approach.
javac GarberBlockCalc.java
java GarberBlockCalc 48 10