Eight points are placed on the surface of a sphere with a radius of 1. The shortest distance between any two points is greater than 1.2. How can the points be arranged?

Hint: They are not arranged as a cube. The cube would have an edge length of only 2/sqrt(3) = 1.1547.

(In reply to re(3): Solution by brianjn)

The program took perhaps 15-20 minutes to write; further refinements could have been made, such as having the program automatically decrease the interval and try again, thereby coming up with the answer directly, rather than have me go in and change the parameters of the for-loop and rerun to home in on the answer. But the way it was does show the steps, so it was good enough.

Posted by Charlie on 2008-02-02 10:40:29