The Right Amount of Water

Can you measure out exactly 4 L of water?

You have three large jugs with capacities of 3, 5, and 8 L (3.2, 5.3, and 8.5 qt). The 8-L jug is filled with water. Your task is to measure out exactly 4 L of water. You have no other containers to work with, and there are no markings indicating fractions of each container.

You may pour the water from one container to another as many times as you want. You may discard the extra water.

You will find this and many other great math puzzles at Interactive Mathematics Miscellany and Puzzles [1].

Make up some puzzles like these and send them in with your solutions. We’ll post them in the SEED Science Center.

Course:

Math [2]

Result/Solution(s)

Solution: The Right Amount of Water Math Puzzle

Patrick Huseneau's Solution

Let's name the jugs:

A = 3 L
B = 5 L
C = 8 L

We begin with 8 L in C while A and B are each empty:

A = 0
B = 0
C = 8

To solve the puzzle, proceed as follows:

Pour from C into A.
Status: A = 3, B = 0, C = 5
Pour from A into B.
Status: A = 0, B = 3, C = 5
Pour from C into A,
so A = 3, B = 3, C = 2. Already half of the job is done and there is no waste of the precious liquid so far.
Pour from A into B and use 1 L for something else.
Status: A = 0, B = 5, C = 2
Pour from B into A.
Status: A = 3, B = 2, C = 2
Pour from B into C or C into B to have 4 L.
Status: A = 3, B = 4, C = 0

That’s it!

math [3]
Math Puzzle [4]