Binary Control

Today I offer you a challenge of the mind. The game I present to you now is a window in to my sanity. Should you succumb to the madness .... Well lets just say it's very dark in here. The objective is not simply to find an answer although that is part of it. I challenge you to come up with the solution (Yes, high school mathematics, (Show your work)). Should you discover the method to my madness I ask that you do not expose your answers/solutions to the rest of us here. Although you are free to do as you please.

I originally made this as a challenge for the suck-o.com forums hacking community.