Question 24
(POL 5) For points $A_1,\ldots,A_5$ on the sphere of radius 1, what is the maximum value that $\min_{1\le i,j\le5}A_iA_j$ can take? Determine all configurations for which this maximum is attained. (Or: determine the diameter of any set $\{A_1,\ldots,A_5\}$ for which this maximum is attained.)