Water Jug Problem

Water Jug Problem

 

Water Jug Problems[107]

  1. A mother sends her boy to the river in order to measure out 3 quarts of water. The mother gives her son a 7-quart bucket and a 4-quart bucket. How can the son measure out exactly 3 quarts of water using nothing but thee two buckets and not guessing as to the amount of water that he brings home?
  2. A circus owner sends one of his clowns to bring back from a nearby river 7 gallons of water to give to the elephants. He gives the clown a 5-gallon bucket and a 3-gallon bucket and tells him to bring back exactly 7 gallons of water. How can the clown measure out exactly 7 gallons of water using nothing but these two buckets and not guessing the amount?
  3. A cook needs 1 gram of salt to season a special meat he is cooking. When he opens the drawing to get a measuring spoon, he finds out that he has only an 11-gram measuring spoon and a 4-gram measuring spoon. How can the cook measure out exactly 1 gram of salt using nothing but these two spoons and not guessing at the amount?
  4. With a 5-minute hourglass and a 9-minute hourglass, what is the quickest way to time a 13-minute steak?
  5. * You have three jugs — A, B, and C. Jug A has a capacity of 8 quarts. Jug B has a capacity of 5 quarts and Jug C has a capacity of 3 quarts. Initially, Jug A is full, but the two smaller jugs are empty. How can you divide the contents of the largest jug evenly between the largest and middle-sized jugs — that is, between Jugs A and B?

 

A Solution to Water Jug Problem #5e
There are many possible sequences of moves to end with the 8 quarts of water divided evenly between the largest and middle-sized jug.

This is the solution using the fewest number of moves for the water. The numbers in the parentheses indicate the number of quarts of water in the first, second, and third jugs.

Quarts in each jug move # Description of move (pour)
( 8, 0, 0 ) 0 Beginning
( 3, 5, 0 ) 1 5 quarts from #1 into #2.
( 3, 2, 3 ) 2 3 quarts from #2 into #3.
( 6, 2, 0 ) 3 3 quarts from #3 into #1.
( 6, 0, 2 ) 4 2 quarts from #2 into #3.
( 1, 5, 2 ) 5 5 quarts from #1 into #2.
( 1, 4, 3 ) 6 1 quart from #2 into #3.
( 4, 4, 0 ) 7 3 quarts from #3 into #1.
DONE!