Question 144
For a given positive integer $n$, find the greatest positive integer $k$, such that there exist three sets of $k$ distinct nonnegative integers, $A = \{x_1, x_2, \dots, x_k\}$, $B = \{y_1, y_2, \dots, y_k\}$ and $C = \{z_1, z_2, \dots, z_k\}$ with $x_j + y_j + z_j = n$ for any $1 \leq j \leq k$.