Brain Teasers
Cube Corners
A cube has six faces (sides) and eight vertices (corners). Arrange the numbers 1 through 8, placing one number at each corner, such that the sum of the four corners of each side is the same for all six sides.
Answer
The sum of the four corners of each side is 18. The four numbers on one side are 8 (upper left), 1 (upper right), 6 (lower right), and 3 (lower left). On the opposite side, directly behind those four numbers, are 2, 7, 4, and 5. There are seemingly other arrangements, but they are all due to the orientation of the cube.Hide Answer Show Answer
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Comments
Terrific teaser! Simply stated, fun to work through. Accessible to a wide audience. Good work!
I was initially surprised that such a solution would exist, but sure enough...
I was initially surprised that such a solution would exist, but sure enough...
There are two other solutions (following the same order as above): 8, 1, 7, 2, 5, 4, 6, 3 and 8, 1, 4, 5, 3, 6, 7, 2.
Great math puzzle! However, the answer should be displayed as an unfolded cube in the shape of a cross.
@MarcM1098
Using scip to solve this teaser revealed that, due to symmetry, there are 144 possible solutions.
Using scip to solve this teaser revealed that, due to symmetry, there are 144 possible solutions.
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