Cube Stacking
Source: AMC 12 2008A Problem 11
February 17, 2008
geometry3D geometryAMC
Problem Statement
Three cubes are each formed from the pattern shown. They are then stacked on a table one on top of another so that the visible numbers have the greatest possible sum. What is that sum?
[asy]unitsize(.8cm);pen p = linewidth(.8pt);
draw(shift(-2,0)*unitsquare,p);
label("1",(-1.5,0.5));
draw(shift(-1,0)*unitsquare,p);
label("2",(-0.5,0.5));
label("32",(0.5,0.5));
draw(shift(1,0)*unitsquare,p);
label("16",(1.5,0.5));
draw(shift(0,1)*unitsquare,p);
label("4",(0.5,1.5));
draw(shift(0,-1)*unitsquare,p);
label("8",(0.5,-0.5));[/asy]