Okay, I admit it. I cheated.

After two or three tries, I could not think of the pattern. Even thinking about the title of the game... That led me into a few other possibilities, none of which worked.

After viewing the source (yeah, I know - I am a computer engineer by training and by trade - solve the problem quickly before the users find out, then figure out what happened...), it took me a moment or two to understand how they derived the algorithm. Then, in a blinding flash (think Magicubes!) it all made sense.