The Water Jug Puzzle (Thursday, July 10, 2008)

While reviewing for my PhD qualifying exams, I came across the following puzzle:

In the water-jug puzzle we are given a 4-liter jug, and a 7-liter jug. Initially, both jugs are empty. Either jug can be filled with water from a tap, and we can discard water from either jug down a drain. Water may be poured from one jug into the other. There is no additional measuring device. Explain how to measure out precisely 1, 2, 3, 4, 5, 6, and 7 liters of water.

Obviously, measuring out 4 liters is as easy as filling the 4-liter jug, and measuring out 7 liters is as easy as filling the 7-liter jug. But see if you can figure out how to end up with the other amounts in one of the two jugs. Remember, there is no "half a jug" nor any other place to store water. Leave a comment with your solution!

Comments

Thanks Matt, but it doesn't count if we've already been over the answers!! -- editor