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approximating the diameter of a set of points

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November 15, 2009
geometrycircumcircleMath Prize for Girls

Problem Statement

Let S S be a set of 100 100 points in the plane. The distance between every pair of points in S S is different, with the largest distance being 30 30. Let A A be one of the points in S S, let B B be the point in S S farthest from A A, and let C C be the point in S S farthest from B B. Let d d be the distance between B B and C C rounded to the nearest integer. What is the smallest possible value of d d?
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