MathDB

A_0A_1\ldots A_n

is a regular polygon with

n+1

vertices (n>2). Initially

n

stones are placed at vertex

A_0

. In each allowed operation,

2

stones are moved simultaneously, at the player's choice: each stone is moved from the vertex where it is located to one of the adjacent

2

vertices. Find all the values of

n

for which it is possible to have, after a succession of permitted operations, a stone at each of the vertices

A_1,A_2,\ldots ,A_n

.
Clarification: The two stones that move in an allowed operation can be at the same vertex or at different vertices.

Problem Statement