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Problem of the Week 881

Minimize the Slopes

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Find 881 points in the plane so that the lines between them determine as few different slopes as possible. Of course, they must not all be on a straight line.

For example: 3 points determine 3 slopes. Four points forming a square determine 6 segments, but only 4 distinct slopes. (Proof of optimality not requried -- though it is known.)

Source: A beautiful new book titled: "Problems from the Book" by Aigner & Ziegler (Springer-Verlag). The "book" refers to Erdos's mythical book that contains the BEST proofs of everything.


A report, with photo, of our mathematical entry at the 1999 Breckenridge Snow Sculpture Championships appeared in the Feb. 5 issue of SCIENCE.


I am leaving town for several weeks. The PoW program will be administered by my colleague Rob Leduc ( in my absence.

© Copyright 1999 Stan Wagon. Reproduced with permission.

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23 February 1999