Is it possible to number the edges of a cube using each of the numbers -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, and 6 once, so that for every vertex, the sum of the numbers on the edges that meet there is zero? (See figure 1 for a diagram of the cube with a space on each edge to fill in — the labels on the three red lines that meet at any corner should add up to zero.) What about if instead you use the 12 consecutive integers from -5 to 6, inclusive?

### D3. Zero Sum Game

*Contributed by Ian Stewart, University of Warwick*

*This problem originally appeared in the* Prisoner’s Dilemma *in the 2022 Winter issue of the PMP Newsletter. Solutions are no longer being accepted for this Dilemma.*