[dsvick]

Here is my effort

Spoiler:

Fill both the 3 and the 7 pint containers, discard what is left in the bucket.
Pour the two containers back into the bucket for a total of 10 pints.

Fill the 3 pint to the top and pour it into the 7 pint, do this twice.
There is now 6 pints in the 7 pint container and 4 pints in the bucket

Fill the three pint container again, pour from there into the 7 pint container until it is full, this will leave 2 pints in the 3 pint container.

Dump those 2 pints, pour the 7 pints from the large container into the bucket that had 1 pint left - it now has 8 pints in it.