AMC 10 Step by Step
2016 AMC 10AProblem 18P16-20~10 minPrint

Each vertex of a cube is to be labeled with an integer 11 through 88 , with each integer being used once, in such a way that the sum of the four numbers on the vertices of a face is the same for each face. Arrangements that can be obtained from each other through rotations of the cube are considered to be the same. How many different arrangements are possible?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.