Question 91
Each vertex of a regular $2n$-gon, where $n\geq3$, is to be labeled with a number from $\{1,2,\ldots,2n\}$, so that the sum at any two adjacent vertices equals the sum at the two diametrically opposite vertices. All $2n$ labels must be distinct. Prove that this is possible if and only if $n$ is odd.