Question 103
We have to place natural numbers $a_1, a_2, \dots, a_n$ that are not all equal at the vertices of a regular $n$-sided polygon $A_1A_2\dots A_n$, $n \ge 6$ with center at $O$ in such a way that for every vertex $A_i$ there exist two vertices $A_k$ and $A_l$, that are symmetrical with respect to the line $OA_i$ and the equation $a_i = \frac{1}{2}(a_k + a_l)$ holds. For which $n \ge 6$ can we do this?
(Bogdan Rublyov)
(Bogdan Rublyov)