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Problem of the Week 817

Celebrating Erdös

Paul Erdös died on Friday September 20 in Warsaw at the age of 83. [Jerry Grossman's Erdös number page has a brief announcement. -Jeff] Here is a Problem of the Week in his honor.

Suppose n = 3, 4, 5, ... . Find n points in the plane such that

  1. no three points lie on the same line,
  2. no four points lie on a circle,
  3. of the Binomial[n,2] distances between the points, one distance is realized once, another distance twice, another distance three times, and so on up to the last distance being realized n-1 times.
Award goes to the student with the highest n.

Source: In 1983 Erdös asked: For which n do these sets exist? [He also offered $500 for arbitrarily large examples, or $50 for a proof that there is a largest example. -Jeff]

There will be a total lunar eclipse on Thursday night (September 26), the last one this century in the U.S.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998