Have Your Cake and Eat It Too

Classic puzzles are fun to revisit now and then, especially if there's a new twist.

In this puzzle, see if you can be as successful as John in retrieving water for his mother. The new twist? The buckets are different sizes.

John's mother told him to go to the river and bring back exactly 9 gallons of water in one trip. She gave him a six-gallon bucket and a five-gallon bucket to complete his task. Of course, John's mother told him she'd bake his favorite cake if he came back with the 9 gallons.

John had his cake and ate it, too. Can you?

(Source: The Big Book of Mind-Bending Puzzles by Terry Stickels)

John took the following steps:

1. He filled the five-gallon bucket.
2. He emptied the five-gallon bucket into the six-gallon bucket.
3. He filled the five-gallon bucket again.
4. He topped off the six-gallon bucket with the five-gallon bucket, leaving four gallons in the latter.
5. He emptied the six-gallon bucket back into the river (or on the ground, whatever you like).
6. He emptied the five-gallon bucket into the six-gallon bucket which, per step four, left four gallons of water in the latter.
7. He filled the five-gallon bucket.
8. Then he went home with exactly nine gallons.

Given that, at this point, the six- and five-gallon bucket respectively weighed about 33 and 42 lbs., he may have worked up quite an appetite by the time he got home.