MathDB

Points

A_1, A_2,\ldots, A_n

are found on a circle in this order. Each point

A_i

has exactly

i

coins. A move consists in taking two coins from two points (may be the same point) and moving them to adjacent points (one move clockwise and another counter-clockwise). Find all possible values of

n

for which it is possible after a finite number of moves to obtain a configuration with each point

A_i

having

n+1-i

coins.

Problem Statement