The "official" answer to the puzzle currently stands at 29. (To view the 29 configurations, click here.) However, we will pay $20 in cash to the first person who can either:
Update: [2002 May 23] Gene #317 and I have each independently written separate computer programs to solve for the number of unique configurations, and we both verified that 29 is indeed the correct answer. Furthermore, we both found that the number of unique configurations that can be made with six cubes is 166. With seven cubes, my program found 1023 unique configurations in about 8 minutes.