nimnam

choose two integers x and y. These represent the first point on a plain. Only adjacent points can be added i.e. any point can only be 1 integer away from this origin point otherwise there will exist an integer point between the origin point the chosen point. so now we have (x, y), (x+1, y), (x, y+1), and (x+1, y+1). Adding a fifth point anywhere on the graph will make it such that an integer point will exists between two of the selected points.