4- 2117 elves are sitting around a round table, and in front of each elf is a glass of milk. One elf pours all his milk evenly into the other glasses. Then his first neighbor to the right does the same, followed by the next one, and so on. After the 7th elf has poured his milk into the other glasses, there is still the same amount of milk in each glass as there was initially, and there are a total of 3 liters of milk in all the glasses. How much milk was there in each glass initially?
[Solution] Initially, each cup contains milk of $\frac{6}{7}, \frac{5}{7}, \frac{4}{7}, \frac{3}{7}, \frac{2}{7}, \frac{1}{7}, 0$ liters.
In fact, after each elf pours milk to the others (giving each elf $\frac{1}{7}$), they still end up with the original distribution, just shifted by one position. The total amount of milk $\frac{1+2+3+\cdots+6}{7}$ is exactly 3, which meets the conditions of the problem.

The solution to this problem is unique.
In fact, we can assume that during the milk pouring process, when it is a certain elf $A$'s turn to pour milk, $A$ has the most milk, $x$ liters. Since the pouring process can be repeated indefinitely, we can assume $A$ is the first to pour milk. After the 7 elves take turns pouring milk, since the other 6 elves pour no more than $\frac{x}{6}$ liters to $A$, but the total amount of milk poured to $A$ is $x$ liters, therefore, the other 6 elves each pour exactly $\frac{x}{6}$ liters to $A$. Thus, by the given conditions, each elf has $x$ liters of milk when it is their turn to pour, and after receiving $k$ portions, they have $\frac{k x}{6}$ liters $(k=1,2, \cdots, 6)$. Since the total amount is 3 liters, we have $\frac{x}{6}+\frac{2 x}{6}+\cdots+\frac{6 x}{6}=3$.

Thus, $x=\frac{6}{7}$.
This leads to the solution mentioned above.
The uniqueness is proven.