Question 4
Tom and Jerry play a game. They alternately take some marble(s) out of a box containing 2024 marbles, starting with Tom. In each turn, each player must take $2^m$ marble(s) from the box, where $m$ is a non-negative integer, i.e., $m=0,1,2,3,\ldots$. For example, a player may take 1 marble, 4 marbles or 32 marbles, but cannot take 10 marbles, because 10 is not a power of 2. The player who takes the last marble(s) from the box wins the game. Determine who has a winning strategy and explain the winning strategy.