[math-fun] n-dimensional geometry puzzle

Puzzle: ------- In n-dimensional space R^n, find the radius R = R(n) of the smallest sphere containing (whether inside or on the surface) the standard basis vectors {e_k} = {(1,0,...,0), ..., (0,...,0,1)} and the origin 0 = (0,...,0). I.e., R(n) = inf {r > 0 | for some c in R^n ||p - c|| <= r for p = 0 and all p = e_k} Apologies if this has been asked already; I don't recall. —Dan