RIOPLATENSE 2000 Problem 3

Let $n>1$ be an integer. For each numbers $(x_1, x_2,\dots, x_n)$ with $x_1^2+x_2^2+x_3^2+\dots +x_n^2=1$ , denote $m=\min\{|x_i-x_j|, 0<i<j<n+1\}$ Find the maximum value of $m$ .