1. The number of elements in the set $\left\{(x, y) \mid x^{2}+y^{2} \leq 100\right.$, and $\left.x, y \in \mathbf{Z}\right\}$ is
Answer 317.
Explanation: We can first calculate the number in the first quadrant, then add the number on the coordinate axes. There are 69 in each quadrant, $69 \times 4 + 41 = 317$.