To show our solution more clearly, we’ll substitute clear containers with liter markings for the red pails.

We’ll start by filling the 11-L container from the pond.

Next we pour from the 11-L container into the 6-L container until it is full, leaving 5 L (5.3 qt) in the larger container.

Now we dump the contents of the small container into the pond . . .

. . . and pour the 5 L from the large container into the smaller one.

Next, we fill the large container from the pond.

Now we pour as much as we can from the large container into the smaller one. That fills the small container and leaves 10 L (10.6 qt)  in the large one.

Now we dump the contents of the small container back into the pond . . .

. . . and pour as much as possible from the large container into the smaller one. This leaves 4 L (4.2 qt) in the large container.

Next we dump the contents of the 6-liter container back into the pond . . .

. . . and pour the contents of the large container into the smaller one.

Now we again fill the 11-L container from the pond . . .

. . . and pour as much as possible from the large container into the smaller one.

We dump the contents of the 6-L container back into the pond . . .

. . . and pour as much as possible from the large container into the smaller one.

Again we dump the contents of the 6-L container into the pond . . .

. . . and transfer the contents of the large container into the small one.

We fill the 11-L container from the pond.

Finally, we pour as much as we can from the 11-L container into the 6-L container. This leaves 8 L in the large container.

We’re done. It’s time to go home.

This process is repetitious. On the way to getting 8 L, we also had 10 L and 9 L (9.5 qt). And, we could continue and end up with 7 L. We also isolated 5, 4, and 3 L along the way.

In fact, we can measure out any whole number of liters from 1 through 11 using the method described above. This will work for other combinations of containers, not just 6 and 11 L. The trick is that the quantities must be mutually prime: Two numbers are said to be mutually prime if there is no other whole number, except 1, that can be evenly divided into both of them. For example, 7 and 12 are mutually prime. So are 4 and 9.

For more details about this puzzle visit Cut the Knot.