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# Each vertex of a cube is to be labeled with an integer 1 through 8

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Senior Manager
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Joined: 02 Nov 2018
Posts: 280
Each vertex of a cube is to be labeled with an integer 1 through 8  [#permalink]

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12 Mar 2019, 09:01
4
00:00

Difficulty:

95% (hard)

Question Stats:

21% (02:49) correct 79% (02:17) wrong based on 24 sessions

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Each vertex of a cube is to be labeled with an integer 1 through 8, 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?

(A) 1

(B) 3

(C) 6

(D) 12

(E) 24

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Re: Each vertex of a cube is to be labeled with an integer 1 through 8  [#permalink]

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26 Mar 2019, 10:56
Each vertex of a cube is to be labeled with an integer 1 through 8, 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?

(A) 1

(B) 3

(C) 6

(D) 12

(E) 24

make a cube
label top face ; with no 3,4,5,6 and bottom face ; 7,2,8,1 ; the right hand side of the cube must have 5,4,8,1 and left hand side 6,3,7,2
total faces of cube 6 ; so in toal 6 such arrangements can be made where the sum of vertices are same
IMO C
Re: Each vertex of a cube is to be labeled with an integer 1 through 8   [#permalink] 26 Mar 2019, 10:56
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