Suppose we have this odd-shaped piece of wood bearing a checkered pattern. We want to make it into an 8x8 checkerboard. We could cut off the top two rows of squares, cut off the eight squares sticking out to the right, and then stack the two smaller pieces to form the missing corner. (See the smaller diagram.) However, you are only allowed to make one straight-line cut and then arrange the resulting pieces into a square checkerboard. There is a further complication: The pattern only appears on the top of the board, so you can't turn any piece face down and maintain the checkerboard pattern.