Question 31
A pile of $2010$ coins is given. We take one coin from the pile, and we arbitrarily divide the rest in two piles. Then, we choose an arbitrary pile from the two, we take one coin, and we divide the rest in two arbitrary piles, and so on. Is it possible after a finite number of repetitions of this procedure to get a number of piles such that in every one of them there are $3$ coins?