Question 90
Let $a,b,c,d$ be real numbers. Suppose that some permutation $(x,y,z,t)$ of $a,b,c,d$ satisfies
$$x\le2a-b,\quad y\le2b-c,\quad z\le2c-d,\quad t\le2d-a.$$
Prove that $a=b=c=d$.
$$x\le2a-b,\quad y\le2b-c,\quad z\le2c-d,\quad t\le2d-a.$$
Prove that $a=b=c=d$.