MathDB

Let

n > 3

be a positive integer. Suppose that

n

children are arranged in a circle, and

n

coins are distributed between them (some children may have no coins). At every step, a child with at least 2 coins may give 1 coin to each of their immediate neighbors on the right and left. Determine all initial distributions of the coins from which it is possible that, after a finite number of steps, each child has exactly one coin.

Problem Statement