### Brain Teasers

# Cube Edges

A cube has six faces and twelve edges. Arrange the numbers 1 through 12, placing one number at each edge, such that the sum of the four edges of each face is the same for all six faces. There are many possible solutions (80, to be exact). Find one of them.

### Answer

Each of the numbers 1 through 12 is used one time. The summation of those numbers is 78. Each of the numbers appears on two faces, meaning that the sum of all faces is 78*2, or 156. There are six faces, so each face has a sum of 156/6, or 26. The sum of the four edges of each face is 26. One solution: the four numbers on one face are 1 (top), 8 (right), 6 (bottom), and 11 (left); on the opposite side, directly behind those four numbers, are 10, 2, 9, and 5; the remaining four numbers, located on the edges that connect the front and back faces, are 3 (upper left), 12 (upper right), 4 (lower right), and 7 (lower left).Hide Answer Show Answer

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