Find the solution for the following: There are 3 hats with 11, 6, and 4 marbles, respectively. On a single move we can remove one marble from one of the hats, one marble from some other hat, and place both removed marbles to the third hat. Can we reach a situation where there are 7 marbles in each hat after some number of moves? If so, show the way. If not, provide some argument why not?