Science of Apps! - Part 3: 2048

\(2048\) 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 \(2\) until you reach \(2048\) and beyond.

The game starts with \(2\) and \(4\) tiles, popping up in different places of the \(4\times 4\) grid.

To get to the \(2048\) tile requires finesse, and a slight bit of luck. In the best scenario, what is the least number of moves required to get the \(2048\) tile?

This problem is part of the Science of Apps! series

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