Third Week, January 24. Points and Lines.Suppose you are given finitely many points in the plane, not all of which lie on a single straight line. Prove that you can always find some straight line that has exactly two of the given points on it (no more, no less).
(This was an open problem for a while. It has a simple and elegant solution, due (I believe) to Paul Erdös. I heard of this problem from M. Kegelmann.)
Note: I am not giving out solutions to "Problems of the Week". But I am very happy to discuss these problems with you, including any partial or attempted solutions that you might have. I am always interested in hearing about interesting or creative solutions, so let me know if you have any!
See previous Problems of the Week.
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