Question 5
Alice and Bob play a number game. Starting with a positive integer $n$, they take turns changing the numvber with Alice going first. Each player may change the current number $k$ to either $k-1$ or $\lceil k/2\rceil$. The person who changes 1 to 0 wins. Determine all $n$ such that Alice has a winnin strategy. (For each real number $x$, its ceiling $\lceil x\rceil$ is the smallest intger $\ge x$.