$13 \cdot 60$ water is poured into $n$ cups of sufficiently large capacity, with each cup receiving an equal amount of water. Water can be poured from any cup to any other cup, but the amount of water poured must be equal to the amount of water already in the receiving cup. It is known that after a finite number of pourings, all the water can be collected into one cup. Find all possible natural numbers $n$.


[Solution] Suppose the amount of water in each cup at the beginning is 1. Since after a finite number of water transfers, all the water ends up in one cup, we will examine the situation of this one cup being filled. According to the given information, each time this cup is filled with water, the amount of water in the cup doubles. If water is poured into this cup a total of $k$ times, then the amount of water in the cup is $2^{k}$. Since the amount of water in each cup at the beginning is 1, it follows that there are $2^{k}$ cups in total, meaning that all $n$ that meet the requirement are $\{1,2$, $\left.\cdots, 2^{k}, \cdots\right\}$.