14.18 Indicate all points $(x, y)$ in the $(x, y)$ plane that satisfy $[x]^{2}+[y]^{2}=4$.
(7th Canadian Mathematics Competition, 1975)
[Solution] Since $[x]$ and $[y]$ are both integers, there are the following four possibilities:
(1) $[x]=2, [y]=0$, i.e.,
$$
2 \leqslant x<3, \quad 0 \leqslant y<1 ;
$$
(2) $[x]=0, \quad [y]=2$, i.e.,
$$
0 \leqslant x<1, \quad 2 \leqslant y<3 ;
$$
(3) $[x]=-2, \quad [y]=0$, i.e.,
$$
-2 \leqslant x<-1, \quad 0 \leqslant y<1 ;
$$
(4) $[x]=0, \quad [y]=-2$, i.e.,
$$
0 \leqslant x<1, \quad -2 \leqslant y<-1 .
$$

From this, we can obtain the shaded regions as shown in the figure on the right.