2000 PMWC Problems/Problem I8


A circle and a triangle are placed on intersections of the grid. The circle and the triangle are not allowed to lie on the same vertical and horizontal line. How many total possible ways are there of placing the circle and the triangle? (the following is an example).

[asy] for(int i = 0; i < 4; ++i){ if(i < 2){ draw((i,0)--(i,3)); }else{ draw((i,0)--(i,2)); } } for(int i = 0; i < 4; ++i){ if(i < 3) draw((0,i)--(3,i)); else draw((0,i)--(1,i)); } filldraw(Circle((0,3),0.3),white); filldraw((2-0.3*cos(pi/2),1+0.3*sin(pi/2))--(2-0.3*cos(7pi/6),1+0.3*sin(7pi/6))--(2-0.3*cos(11pi/6),1+0.3*sin(11pi/6))--cycle,white); //Credit to chezbgone2 for the diagram[/asy]


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