Question 14
Given $1400$ real numbers, prove that among them there are at least three numbers $x$, $y$, $z$ such that
$$
\left| \frac{(x-y)(y-z)(z-x)}{1+x^4+y^4+z^4} \right| \lt \frac{9}{1000} .
$$
$$
\left| \frac{(x-y)(y-z)(z-x)}{1+x^4+y^4+z^4} \right| \lt \frac{9}{1000} .
$$