Draft:Bpow1997-15

Is it possible to label each of the edges of a regular cube (see figure below) with distinct positive integers (i.e. > 0) in such a way that:

(a) the sum of the integers assigned to the three edges at any corner is the same for each of the eight corners; and

(b) the sum of the integers assigned to the four edges of any face is the same for each of the six faces.

If so, give a labeling with the smallest possible labels.

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.