2. In a Cartesian coordinate system, a point whose both vertical and horizontal coordinates are integers is called an integer point. Therefore, the number of integer points $(x, y)$ that satisfy the inequality $(|x|-1)^{2}$ $+(|y|-1)^{2}<2$ is
(A) 16
(B) 17
(C) 18
(D) 25
(A)
2.【Analysis and Solution】From $(|x|-1)^{2}+(|y|-1)^{2}<2$, we know that $(|x|-1,|y|-1)$ is $(0,0),(0,1),(0,-1),(1,0)$ or $(-1,0)$. Therefore, the possible values of $(x, y)$ are a total of 16.