13.327. A total of 24 liters of liquid is distributed among three vessels. First, from the first vessel, as much liquid was poured into the other two as was already in each of them. Then, from the second vessel, as much liquid was poured into the other two as was in each of them after the first pouring. Finally, from the third vessel, as much liquid was poured into the other two as was in each of them after the second pouring. As a result, each vessel ended up with the same amount of liquid. How much liquid was in each vessel initially?
Solution.

Let's fill in the table:

| Vessel | Initially | After the  first transfer | After the  second transfer | After the  third transfer |
| :--- | :---: | :---: | :---: | :---: |
| First | $x$ | $x-y-z$ | $2(x-y-z)$ | $4(x-y-z)$ |
| Second | $y$ | $2 y$ | $3 y-x-z$ | $6 y-2 x-2 z$ |
| Third | $z$ | $2 z$ | $4 z$ | $7 z-y-x$ |

According to the condition, we have the system $\left\{\begin{array}{l}x+y+z=24, \\ 4(x-y-z)=6 y-2 x-2 z, \\ 4(x-y-z)=7 z-y-x,\end{array}\right.$ $x=13, y=7, z=4$.

Answer: 13, 7, and 4 liters.