A different kind of Limit

2048 is game where the player has to move tiles of numbers in order to create a 2048 tile. The board is a 4x4 square with 16 places.

Supossing that for every move, a number 2 tile is added on the board, find the maximum number a player can create.

Hint: If you don't know the game rules, take a look here: http://en.wikipedia.org/wiki/2048%28videogame%29

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