我直接把矩陣硬爆出來 看大家有沒有更好的方法

Before we start, let’s show that $x_i\not=\mu_x$ for some $i$. We’re given that $x_1, \dots, x_n$ is not totally equal i.e. $x_p\not=x_q$ for some $p$, $q$ in $\{1, \dots, n\}$. Therefore, $\mu_x\not= x_p$ or $\mu_x\not= x_q$ because the relation of equality is transitive. Hence, either $i=p$ or $i=q$, or both, satisfy $x_i \not= \mu_x$