Answer to Puzzle Contest:

12 patterns. There are 32 total permutations (2 colors with 5 variable sides, which is 2 to the 5th power, or 32), but 20 of those simply duplicate the 12 unique patterns.

I solved the problem by using a die as a visual aid, numbering all the sides on a diagram I drew, listing all 32 permutations in numeric order (assigning a '1' for a red side, '2' for a green, and then counting them out from 11111 to 22222), and marking each off that duplicated a pattern I had already counted as unique/distinct.

Unless you enjoy logical and mathematical puzzles like this (I personally am lukewarm as puzzles go), and have a little experience at them, this was likely very tough for you.

Statistics:
# of Answers: 6
# of Correct Answers: 2
Percentage for Attempts: 33%

Winner: Andy Muenz, Glenolden, PA