CHALLENGE

GRADE  4 - 6 / Age 9-11

The Decanting Puzzle...This puzzle dates back to the fifteenth or sixteenth century 

There are three pitchers for 8, 5, and 3 liters (see Figure A).  

3 pitchers

Figure A

The largest pitcher is entirely filled with milk.  The other two pitchers are empty.  Your job is to divide the milk into two equal parts (leaving the smallest pitcher empty).  The pitchers are not marked in any way so you can do nothing but pour milk from one pitcher to another until the first pitcher is entirely empty or the second pitcher entirely full.  Assume no milk is spilled.  Find the least number of pours to achieve this goal.

Another decanting puzzle with three pitchers...

We have three new pitchers holding 12, 7, and 5 liters (figure B).

Larger pitchers

Figure B

Again, your job is to divide the milk in the largest pitcher into two equal parts, leaving the smallest pitcher empty.  Except for the different size containers, the problem is exactly the same as above.  What is the least amount of pours that must be made to achieve this?

Be sure to use your MathWorld Interactive six problem-solving steps. Have fun!

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