Useful Cups

By using the formula: $3x+9y+20z=A, 1 \le A \le 20: x, y, z \le 0 \| x, y, z \ge 0$ So it is easy to try to get answer: $Ans = \boxed{20}$

1L can be produced by filling the 20L container with 3L container until there is 1L left in the 3L container.This 1L can be stored in the 9L container and since we can produce 1L now we can produce any volume just by producing 1L numerous times. Volumes greater than 1L can be produced in a reversed way that is by adding some volume from the 20L container to the partially filled 9L/3Lcontainer. For example. 19 L can be produced by adding 1L to the 8L filled 9L container from the 20L one.