We played this game in our math class, okay, I'll explain how it's played. There are 21 squares in a straight line across, the first person shades in 2 adjacent squares. The next player shades in 2 more adjacent squares. They continue taking turns until there are no more adjacent squares to shade in. The last player to play wins. That's how you play, but the question we got after was how many possible combinations of shaded and unshaded squares are there? He then introduced what he calls "function building" which is basically taking a more simple problem and keep adding onto it until you can find a function for it. I really would appreciate any help, and I hope I can learn from this!
Edit: I guess I forgot to include that for a solution to be considered a solution, it has to be a finished game, so no two adjacent squares are left unshaded.