Question 134
You and I play the following game on an $8 \times 8$ square grid of boxes: Initially, every box is empty. On your turn, you choose an empty box and draw an $X$ in it; if any of the four adjacent boxes are empty, you mark them with an $X$ as well. (Two boxes are adjacent if they share an edge.) We alternate turns, with you moving first, and whoever draws the last $X$ wins. How many choices do you have for a first move that will enable you to guarantee a win no matter how I play?