A right hexagon with side length $n$ is divided into tiles of three types, which are shown in the image, which are rhombuses with side length $1$ each and the acute angle $60$. In one move you can choose three tiles, arranged as shown in the image on the left, and rearrange them, as shown in the image on the right Moves are made until it is impossible to make a move. a) Prove that for the fixed initial arrangement of tiles the same amount of moves would be made independent of the moves. b) For each positive integer $n$ find the maximum number of moves among all possible initial arrangements M. Zorka