$31 \cdot 15$ The number of different integer solutions for the equation $|x|+|y|-3=0$ is
(A) 16.
(B) 14.
(C) 12.
(D) 10.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991)
[Solution] Given $|x|+|y|=3$, then its integer solutions are
$$
\begin{array}{l}
( \pm 3,0), \quad( \pm 2,1), \quad( \pm 2,-1), \\
( \pm 1,2),( \pm 1,-2),(0, \pm 3) \text {. } \\
\end{array}
$$

There are a total of 12 sets.
Therefore, the answer is $(C)$.