Question 15
Anne and Bob will play a number game, where they use one piece of paper with only the number 2024 written on it. Starting with Anne, each player takes turns writing down a positive integer that is at least one-third of the previous number but less than the previous number. For the first step, Anne should write a number less than 2024 but no less than $\dfrac{2024}{3}$. The player who writes down the number 1 wins the game. Determine, with complete proof, which player has a winning strategy? What is the strategy?
Section B instruction: Show your detailed solution.
Section B instruction: Show your detailed solution.