* Arrange 7 points and 7 lines on a plane.
* For each pair of points, there must be a line that goes through both points.
* A line can go through multiple points, if they're collinear. It'll then satisfy the above item for all pairs of points on that line.
* No line can go through all 7 points.
Good luck and have fun.
Edit:Removed incorrect rule.
Edit2: I changed the spoiler to contain what I believe are the only 2 families of solutions. All other solutions that I can see are spinoffs of these two branches of thinking. Also copied phlip's explanation of the rules. He was much more elegant in explaining than I was.
3 points on each line "Fano Plane"