I've got a problem that I don't know how to solve. On every side of a regular octahedron is written one of these numbers: $1,2,3,4,5,6,7,8.$ On every side there is a different number. We take one side and add to its number the numbers of its neighbooring sides. Then we take these sums and add them together. What numbers can this sum be? Is there any way to generalize? Because I don't want to do every side separatedly and remember all the sums. Thanks dor your help
Regular octahedron with numbers
0
$\begingroup$
geometry
arithmetic
1 Answers
2
HINT.
Each face enters the sum four times: one as the center face, and three as a neighbour face.