<p>Three cubes are each formed from the pattern shown. They are then stacked on a table one on top of another so that the <img alt="$13$" height="13" src="https://latex.artofproblemsolving.com/0/3/0/030e19e4e2f1c074127cb50581e8496470c5419f.png" width="17" /> visible numbers have the greatest possible sum. What is that sum?</p> <p><img alt="[asy] unitsize(.8cm); pen p = linewidth(1); draw(shift(-2,0)*unitsquare,p); label("1",(-1.5,0.5)); draw(shift(-1,0)*unitsquare,p); label("2",(-0.5,0.5)); draw(unitsquare,p); 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]" height="118" src="https://latex.artofproblemsolving.com/a/3/2/a32f7c9839807c1cb204fd5a2f87f33747244a18.png" width="155" /></p>

Question No: 286

Three cubes are each formed from the pattern shown. They are then stacked on a table one on top of another so that the $13$ visible numbers have the greatest possible sum. What is that sum?

$[asy] unitsize(.8cm); pen p = linewidth(1); draw(shift(-2,0)*unitsquare,p); label("1",(-1.5,0.5)); draw(shift(-1,0)*unitsquare,p); label("2",(-0.5,0.5)); draw(unitsquare,p); label("32",(0.5,0.5)); draw(shift(1,0)*unitsquare,p); label("16",(1.5,0.5)); draw(shift(0,1)*unitsquare,p); label("4",(0.5,1.5)); draw(shift(0,-1)*unitsquare,p); label("8",(0.5,-0.5)); [/asy]$

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Tags: Algebra Geometry Probability

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