A few days ago, I was told the following problem:
Let E a finite set of points in the plane with the property that any line containing two points of E contains at least a third one. Show that E is included in a line.
I find this problem particularly interesting because the problem a priori reflects an affine property of the plane, however the only solution I know is very tricky and uses an additional structure of the plane…
Can you find the solution of this problem ?