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. Find all the arrangements


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Question Number 90122 by M±th+et£s last updated on 21/Apr/20

$e a c h v e r t e x o f a c u b e i s t o b e l a b e l e d$ $w i t h a n i n t e g e r 1 t h r o u g h 8, w i t h$ $e a c h i n t e g e r b e i n g u s e d o n c e, i n s u c h$ $a w a y t h a t t h e s u m o f t h e f o u r n u m b e r s$ $o n t h e v e r t i c e s o f a f a c e i s t h e s a m e$ $f o r e a c h f a c e . A r r a n g e m e n t s t h a t c a n$ $b e o b t a i n e d f r o m e a c h o t h e r t h r o u g h$ $r o t a t i o n s o f t h e c u b e a r e c o n s i d e r e d$ $t o b e t h e s a m e .$ $F i n d a l l t h e a r r a n g e m e n t s$
Commented by M±th+et£s last updated on 21/Apr/20

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