MathDB

Sir Alex plays the following game on a row of 9 cells. Initially, all cells are empty. In each move, Sir Alex is allowed to perform exactly one of the following two operations:
[*] Choose any number of the form

2^j

, where

j

is a non-negative integer, and put it into an empty cell. [*] Choose two (not necessarily adjacent) cells with the same number in them; denote that number by

2^j

. Replace the number in one of the cells with

2^{j+1}

and erase the number in the other cell.
At the end of the game, one cell contains

2^n

, where

n

is a given positive integer, while the other cells are empty. Determine the maximum number of moves that Sir Alex could have made, in terms of

n

.
Proposed by Warut Suksompong, Thailand

Problem Statement