Each grid has nine squares. Starting with an empty grid, we have two choices for coloring the first square. After we have colored the first square, we have two choices for coloring the second square. If we continue this process, we see that the total number of colorings doubles every time we color the next square.
Since there are nine squares, how many colorings will we end up with?
How does this method of counting help us make sure that we count every possible combination? How does it help prevent us from creating duplicates?