MathDB
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 13 13 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]<spanclass=latexbold>(A)</span> 154<spanclass=latexbold>(B)</span> 159<spanclass=latexbold>(C)</span> 164<spanclass=latexbold>(D)</span> 167<spanclass=latexbold>(E)</span> 189 <span class='latex-bold'>(A)</span>\ 154 \qquad <span class='latex-bold'>(B)</span>\ 159 \qquad <span class='latex-bold'>(C)</span>\ 164 \qquad <span class='latex-bold'>(D)</span>\ 167 \qquad <span class='latex-bold'>(E)</span>\ 189