More Brain Busting

At a rural cabin, you get water from a well using only a 4-gallon bucket and a 9-gallon bucket. In a single trips from the well to the cabin, describe how it is possible to get all of the whole number gallon amounts 1-13.

There are no markings on the pails.  And, you can’t do any estimating or add any markings!

Explain each trip for each gallon amount.

For example

1 gallon-  Fill the 9 gallon bucket.  Pour 4 gallons into the 4 gallon bucket and pour it out.  You now have 5 gallons in the 9 gallon bucket.  Pour 4 gallons into the 4 gallon bucket and pour it out.  You now have 1 gallon in the 9 gallon bucket.