AMC 12 2009b Problem 25

The set $G$ is defined by the points $(x,y)$ with integer coordinates, $3\le|x|\le7$, $3\le|y|\le7$. How many squares of side length at least $6$ have their four vertices in $G$?

defaultpen(black+0.75bp+fontsize(8pt));
size(5cm);
path p = scale(.15)*unitcircle;
draw((-8,0)--(8.5,0),Arrow(HookHead,1mm));
draw((0,-8)--(0,8.5),Arrow(HookHead,1mm));
int i,j;
for (i=-7;i<8;++i) {
for (j=-7;j<8;++j) {
if (((-7 <= i) && (i <= -3)) || ((3 <= i) && (i<= 7))) { if (((-7 <= j) && (j <= -3)) || ((3 <= j) && (j<= 7))) { fill(shift(i,j)*p,black); }}}} draw((-7,-.2)--(-7,.2),black+0.5bp);
draw((-3,-.2)--(-3,.2),black+0.5bp);
draw((3,-.2)--(3,.2),black+0.5bp);
draw((7,-.2)--(7,.2),black+0.5bp);
draw((-.2,-7)--(.2,-7),black+0.5bp);
draw((-.2,-3)--(.2,-3),black+0.5bp);
draw((-.2,3)--(.2,3),black+0.5bp);
draw((-.2,7)--(.2,7),black+0.5bp);
label("$-7$",(-7,0),S);
label("$-3$",(-3,0),S);
label("$3$",(3,0),S);
label("$7$",(7,0),S);
label("$-7$",(0,-7),W);
label("$-3$",(0,-3),W);
label("$3$",(0,3),W);
label("$7$",(0,7),W);

\textbf{(A)}\ 125 \textbf{(B)}\ 150 \textbf{(C)}\ 175 \textbf{(D)}\ 200 \textbf{(E)}\ 225