The third level of the game tree is the first point at which transpositional symmetry can make a difference. Let us imagine that you have completely filled out the left $($corner first$)$ and middle $($center first$)$ branches of the game tree, and you are about to complete the right branch. How many NEW game states $($nodes or vertices not already in one of the other branches$)$ will there then be in the third level of the right branch. Remember, most of the possibilities are transpositions of vertices in the other branches, but don't neglect symmetry!