Question 11
There are 17 empty boxes and an infinite supply of balls. In each step, we choose some number of boxes, then put in each chosen box a different number of balls, where each number must be a power of 2 (including 2 to the power of 0). After $k$ steps, it's possible that all boxes have the same non-zero number of balls inside. What is the smallest positive integer $k$ to achieve this?