Activity For Math Class: Waterbucket Puzzle

At a rural cabin, you get water from a well using only a 4-gallon bucket and a 9-gallon bucket. In a single trip from the well to the cabin, what whole number gallon amounts of water could you bring back to the cabin?

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

The easy ones are 4, 9, and 13.

It turns out that you can bring any number up to 13 by successive pourings. E.g., get 5 by filling the 9-gallon bucket and then pouring into the 4-gallon bucket. Then, pour out the 4-gallon bucket.

Have your students try the rest.. I'llpost the answers if anyone wants me to!