Let $x_i$ be nonnegative integer variables in $\mathbb{N}$. The system is to find $x_i$ in
$$\sum_{i=1}^nx_i=3n,\\\quad \quad \quad \quad \;\;\,x_i\leqslant3,\,\forall\, i\in\{1,\ldots,n\}.$$
I find the solution to be $x_i=3$ for all $i$ but I cannot prove that it is the unique solution.