Question 107
Vertices of a regular $n$-gon are marked on a circumference. Integer numbers are placed at the vertices such that the difference of any two adjacent numbers equals $\pm 1$ or $0$. At a moment, simultaneously, the half-sums of each pair of the adjacent numbers are placed at the midpoints of the arcs subtending the corresponding sides of the $n$-gon.
Find all possible values of $n$ for which after some such moves there exist a pair of opposite points, among $2n$ points thus obtained, with the same numbers at them.
(M. Karpuk)
Find all possible values of $n$ for which after some such moves there exist a pair of opposite points, among $2n$ points thus obtained, with the same numbers at them.
(M. Karpuk)