Question 62
A circle divided into $2n$ arcs, we intend to write $0, 1, \dots, n-1$ on these arcs such that each number is used exactly two times and for $0 \le i \le n-1$ from one direction there are exactly $i$ arcs between two arcs such that $i$ is written on them. Prove that this is impossible for $n = 1399$.