CZ-SK-MO 2013 Problem 2

Each of the thieves in the $n$ -member party ( $n \ge 3$ ) charged a certain number of coins. All the coins were $100n$ . Thieves decided to share their prey as follows: at each step, one of the bandits puts one coin to the other two. Find them all natural numbers $n \ge 3$ for which after a finite number of steps each outlaw can have $100$ coins no matter how many coins each thug has charged.