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 2j, 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 2j. Replace the number in one of the cells with 2j+1 and erase the number in the other cell.At the end of the game, one cell contains 2n, 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 IMO Shortlistcombinatorics