MathNet 2019-part-05 — 184 problems (EN–VI) Question 101

Let $x$, $y$, $z$, $t$ be a permutation of the real numbers $a$, $b$, $c$, $d$. It is known that $x \le 2a - b$, $y \le 2b - c$, $z \le 2c - d$, $t \le 2d - a$. Prove that $a = b = c = d$.