Thanks for the feedback. I was debating whether or not to post the solution or some kind of hint along with the answer. I'll try some different things in the future and see what seems to be the most helpful to people. For this one, I plan on posting the answer tomorrow.
I think if people can immediately check the answer and see that their first instinct was wrong, this will tend to get them involved more and make them curious...I think they'll start wondering where they went wrong and figure it out for themselves.
Why the black box? Just for aesthetic reasons...makes it a little more fun, I think.