Obviously we were thinking the same thing as far as the strategy went for picking numbers, and I saw through the same possibilities you did.  One reason that I posted with so much time to spare was because I knew I would be out and offline when the deadline came.  You made the right move at the right time, so congrats.

As for your new system, conceptually it is good but it is mathematically flawed.  I'll go into further detail in response to the appropriate comment.