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2016 AMC 10A Problem 18

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2016 AMC 10A Problem 18AMC 10 Step by Step
Name:                             Date: September 13, 2026
Arrangements with Restrictions · difficulty 5 of 5 · about 10 min · position P16-20

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?

  1. A)

    11

  2. B)

    33

  3. C)

    66

  4. D)

    1212

  5. E)

    2424

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