Problem of the Week

In this space, I will try to post an interesting and challenging puzzle or short problem every week. I am giving these problems to my classes for their mathematical entertainment. Some of the weekly puzzles I invented myself, but many are scavenged from other sources. If you would like to contribute a problem, please email me. Enjoy!

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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Peter Selinger / Department of Mathematics and Statistics / Dalhousie University
selinger@mathstat.dal.ca / PGP key
Updated Jan 24, 2000