Bonus: some old games had a "wrap around" effect. if you move past the right side of the screen you appear at the left side, and if you move past the top you appear at the bottom. we can model this in the following way. identify the screen with the the unit square [0, 1] x [0, 1] (rescale things to points of the form (a, 1) and points of the form (0, y) equal to points of the form (1, y) so the aspect ratio is 1: 1). now set points of the form (x, 0) equal (a) show that in this environment, it's possible to solve the utility puzzle without crossing any edges (b) show that it's possible to draw k3 in this environment without dividing it into two disconnected regions