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 GameContributed 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.