Problem:
The numbers from to are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same. What is this common sum?
Answer Choices:
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Solution:
Each vertex appears on exactly three faces, so the sum of the numbers on all the faces is
There are six faces for the cube, so the common sum must be . A possible numbering is shown in the figure.
The problems on this page are the property of the MAA's American Mathematics Competitions