Solution to Problem 268

Correct solutions came from Aaron Kahn; Jean Moreau de Saint-Martin, France; Dan Dima, Romania; Jerome Cherry, Canada; Farid Lian, Colombia; Lou Cairoli, USA; John Snyder, USA. 

Placing one point in the center of the cube and the other points at (or arbitrarily close to) its vertices shows that r must be at least √3/2.  To see that this is large enough, bisect each edge and look at the eight smaller cubes inside the large one.  Since we have nine points, two of them must be in one of the small cubes and the diagonal of the small cube is √3/2.

You are visitor number  3186   to this page.
ã2007 Alberto L. Delgado