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Drawing the Line
Submitted by Sam Northshield, 01/1999. This article by Allen Stenger.
Show that given any finite set of points P1, P1, ..., Pn in the plane (with n>1), either all the points lie on the same line, or there is a pair Pi, Pj such that the line through Pi and Pj meets no other point of the set.
This problem seems intuitively obvious and you probably think it's easy to solve, but....
Need a hint? Click here.
Click here for the complete solution.