Problem

Source: South African Mathematics Olympiad 2020, Problem 3

Tags: algebra, polynomial, system of equations



If $x$, $y$, $z$ are real numbers satisfying \begin{align*} (x + 1)(y + 1)(z + 1) & = 3 \\ (x + 2)(y + 2)(z + 2) & = -2 \\ (x + 3)(y + 3)(z + 3) & = -1, \end{align*}find the value of $$ (x + 20)(y + 20)(z + 20). $$