You want to label the vertices (corners) of a regular octahedron (see Figure 3) with whole numbers bigger than one so that the labels of two vertices have a common factor (bigger than one) if and only if they are adjacent on the octahedron (connected by an edge). Is it possible? If so, what is the minimum possible sum of the labels?

### D23. Factor Network

*Contributed by Gordon Hamilton, MathPickle*

*This problem originally appeared in the* Prisoner’s Dilemma *in the 2024 Fall issue of the PMP Newsletter. Solutions will be accepted through 2024 Dec 31.*