Minimum Moves to 2048

In the game 2048, a player needs to slide numbered tiles on a grid to combine them and create a tile with the number 2048. Write a Python function, min_moves_to_n, that calculates the minimum number of moves required to reach a tile with a given value n. $x$.

You can make the following assumptions:

• The game always starts with two 2 tiles randomly placed in the grid.
• In each turn, a new 2 tile appears on the grid.
• The lowest value for n is 4.
• Every move successfully merges the highest possible tiles.

This problem deals with an ideal scenario. Don’t worry about the tiles’ positions on the board. Actual gameplay may require more moves.

The function should take an integer n as input and return an integer representing the minimum number of moves required to reach the n tile.

Example:

Input:

n = 8

Output:

def min_moves_to_n(n) -> 4

Explanation:

In the first move, the two 2 tiles combine to create a 4 tile, while a new 2 tile appears. In the second move, there is a 4 and a 2 tile, so there are no tile merges. A new 2 tile appears after making the move. In the third move, we merge the 2 tiles, obtaining a new 4 tile. A new 2 tile appears after making the move. We’re left with tiles 4, 4, 2. In the fourth move, we merge the 4 tiles, obtaining the 8 tile we were looking for. After a new 2 tile appears, we’re left with tiles 8, 2, 2.