I'm not sure if this is right, it's been a while but it's not possible for a fifth coordinate to exist by the rules because only four coordinates can be plotted with numbers being (odd,odd) (even,even) (odd,even) and (even,odd) and not create an integer coordinate. A fifth one would always create a full integer coordinate plot because there's only odd and even sets of numbers and finding the midpoint of any two coordinates involves dividing by two. Further, since there can only be four combinations of odd and even, one set combination would be repeated resulting in two integers. I don't remember if there's an exception so this'll be my final answer until I see otherwise.