Problem 2 (13 points) Suppose we have an S x S board divided into S2 equal-sized squares colored in a checker-board pattern. We then modify the board by removing two diagonally opposite corner squares (the removed squares are X'd out in red). Here's what it would look like when S = 6: Original board (for S=6) Modified board (for S=6) Dominoes are then placed on the modified board one at a time in such a way that they cover exactly two squares (and don't overlap any other dominoes): X X X Dominoes placed correctly Dominoes placed incorrectly