Problems(1)
A △ or ◯ is placed in each of the nine squares in a 3-by-3 grid. Shown below is a sample configuration with three △s in a line.[asy]
//diagram by kante314
size(3.3cm);
defaultpen(linewidth(1));
real r = 0.37;
path equi = r * dir(-30) -- (r+0.03) * dir(90) -- r * dir(210) -- cycle;
draw((0,0)--(0,3)--(3,3)--(3,0)--cycle);
draw((0,1)--(3,1)--(3,2)--(0,2)--cycle);
draw((1,0)--(1,3)--(2,3)--(2,0)--cycle);
draw(circle((3/2,5/2),1/3));
draw(circle((5/2,1/2),1/3));
draw(circle((3/2,3/2),1/3));
draw(shift(0.5,0.38) * equi);
draw(shift(1.5,0.38) * equi);
draw(shift(0.5,1.38) * equi);
draw(shift(2.5,1.38) * equi);
draw(shift(0.5,2.38) * equi);
draw(shift(2.5,2.38) * equi);
[/asy]How many configurations will have three △s in a line and three ◯s in a line?<spanclass=′latex−bold′>(A)</span>39<spanclass=′latex−bold′>(B)</span>42<spanclass=′latex−bold′>(C)</span>78<spanclass=′latex−bold′>(D)</span>84<spanclass=′latex−bold′>(E)</span>96 AMC 82022 AMC 8