13 -59 7 dwarfs are sitting around a round table, and in front of each dwarf is a cup of milk. A dwarf pours all his milk into the other cups evenly. Then his right neighbor does the same, and the next one, and so on. After the 7th dwarf has poured his milk into the other cups, the amount of milk in each cup is exactly the same as it was at the beginning. It is known that there are a total of 3 liters of milk in all the cups. How much milk was there in each cup at the beginning?
[Solution] Since the 7 dwarfs pour milk in a cycle and return to the original state after a full round, the process will continue to cycle with a period of 7. Suppose after a certain pour, a dwarf $A$ has the maximum amount of milk, which is $x$ liters. Of course, the next one to pour milk will be $A$. He pours $\frac{x}{6}$ liters to each of the others. Then, the other 6 dwarfs pour milk into $A$'s cup in turn, each pouring at most $\frac{x}{6}$ liters. After the 6 dwarfs have each poured once, the amount of milk in $A$'s cup should return to $x$ liters. Therefore, each of them must have poured $\frac{x}{6}$ liters. This means that when it is each person's turn to pour, they all have $x$ liters in their cups. Therefore, the 7 dwarfs' cups should contain $\frac{k}{6} x$ liters of milk, where $k=0,1, \cdots, 6$. Since there is a total of 3 liters of milk, we get $x=\frac{6}{7}$. Thus, the amount of milk in the 7 dwarfs' cups is sequentially $\frac{6}{7}, \frac{5}{7}, \frac{4}{7}, \frac{3}{7}, \frac{2}{7}, \frac{1}{7}, 0$.