Science of Apps! - Part 3: 2048

20482048 is an insanely addictive game. The objective is simple, bring the same powers of two together to add them together, and keep increasing the powers of 22 until you reach 20482048 and beyond.

The game starts with 22 and 44 tiles, popping up in different places of the 4×44\times 4 grid.

To get to the 20482048 tile requires finesse, and a slight bit of luck. In the best scenario, what is the least number of moves required to get the 20482048 tile?

This problem is part of the Science of Apps! series

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