Problem:
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?
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Solution:
The sum of the six numbers on each cube is 63. The three pairs of opposite faces have numbers with sums , , and . On the two lower cubes, the numbers on the four visible faces have the greatest sum when the 4 and the 8 are hidden. On the top cube, the numbers on the five visible faces have the greatest sum when the 1 is hidden. Thus the greatest possible sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions