Macedonian Junior Mathematical Olympiad

At the beginning, let the first pile contain $2010$ coins. After every step, we consider the value $S$, denoting the sum of the number of piles and the number of coins in them. We have $$S_0=1+2010=2011,S_1=2+(2010-1)=2011,S_2=3+(2009-1)=2011$$ i.e. $S$ is invariant (it does not change), at any step. Suppose that the required state is attainable i.e. let's have, after a finite number of steps, $n$ piles with $3$ coins in every one of them. Then, from the above stated, we get $S=n+3n=4n$, i.e $2011=4n$, which is not possible. According to this, the required state is not attainable.