[2 points]
Suppose we have a general CSP with variables $X = (X_1, \dots, X_n)$ and constraints $f_1, \dots, f_m$.
Assume that each variable $X_i$ can only take on only integer values $1, \dots, M$ (that is, $\text{Domain}_i = \{1, \dots, M\}$).
Assume that the first constraint function is $f_1(x) = [\sum_{i=1}^n x_i = T]$, which says
that the sum of the integer values must equal some known target integer value
$T$. Recall that it's generally good to have constraint functions that depend on few variables.
Since $f_1$ depends on all the variables, this is not desirable.
Your job is to define a new CSP with $O(n)$ additional integer-valued auxiliary variables,
where the original constraint $f_1$ is represented by $O(n)$ ternary constraints (those that depend on three variables).