inactive objects impact on memory

Hey guys, I am working on my game, and I had an idea. Right now the game has 6 puzzle object types. Depending on what type of puzzle piece it is, I instantiate it and parent it to the main puzzle piece (they all have the same main puzzle piece type). If there are no more of those puzzle pieces on the board and there are some in the que, I destroy the child piece and instantiate a new piece that does exist on the board.

Would it be better to have all 6 pieces as a child of the main puzzle piece all the time, and just activate the one piece that is available? If the other 5 pieces are set to inactive, how much does that affect memory on a mobile platform?

I guess simply, do inactive gameobjects take up as much memory as when they are active?