Baltic Way 1995 · Problem 15

Solution:

First, label the midpoints of the sides of the polygon with the numbers $1, 2, \ldots, 2n+1$, in clockwise order. Then, beginning with the vertex between the sides labelled by $1$ and $2$, label every second vertex in clockwise order with the numbers $4n+2, 4n+1, \ldots, 2n+2$.