A square parking lot has exactly eight lights numbered 1 through 8 situated along its perimeter as diagrammed below.
The lot must always be illuminated in such a way that the following specifications are met:
At least one of any three consecutively numbered lights is off.
Light 8 is on.
Neither light 2 nor light 7 is on when light 1 is on.
At least one of the three lights on each side is on.
If any side has exactly one of its three lights on, then that light is its center light.
Two of the lights on the north side are on.
Which one of the following statements must be true?