 Out of the 10 basic strategies for problem solving, let us look now at adopting a different point of view. Let us consider the following problem. Suppose we cut out two opposite corners of a chessboard. If one domino can cover exactly two squares of a chessboard, can we cover the chessboard with 31 dominoes? If this is the first time you encounter this problem, you may wish to pause the video and think about it for a few minutes. The initial reaction is for students to say, well of course I have 31 dominoes, and 31 times still is 62, and since I cut out two opposite corners I have 62 squares, so of course I can cover it. So show me how to do it, and they start trying to come up with a way of arranging the domino tiles so that it works, and they try and try and try, and nothing seems to work. And they realize that something is missing, something is wrong, and then they might consider the coloring of the chessboard. So this is a change of viewpoint, and they will realize that it doesn't matter whether you place a domino horizontally or vertically, it always covers exactly one dark square and one light square, and when we cut out two opposite corners, notice what happens. You cut out two opposite corners, and they have the same color. In this particular case, we have cut out two dark corners, so we have 32 light squares and 30 dark squares. So with 31 dominoes, each of which must cover a dark and a light square, with 31 we want to cover 32 light squares, which is impossible.