You have 10 cups of water in a 10 cup vessel. Pour exactly 5 cups into one vessel with only the 10 cup, a 7 cup and 3 cup vessel available.

Question

This is one of those brain puzzles. The puzzle will only allow for you to pour water into one of the 3 vessels. You cannot empty water from any of them. If you pour water from one to the other, it will fill up the entire vessel. (there are no partial pours). How do you get exactly 5 cups of water in one of the vessels?

Answer 1

Whew!  This was a toughie.  Maybe someone can do it more quickly.  I'm going to write up my solutions as fractions.  For example, 3/7 means 3 cups are in the 7 cup vessel.  Each step reflects the new conditions, and I think you'll easily see where the water was coming from and going to with each step.  Notice the total always adds up to the 10 cups, and that the only way to have less than a full cup, is by emptying another full cup into a bigger vessel (all cup pours are the full cup).

 

1.  10/10  0/7  0/3  (starting conditions)

2.  7/10  0/7  3/3 (poured into the 3 cup vessel....I'm not going to include this for the next steps)

3.  7/10  3/7  0/3

4.  4/10  3/7  3/3

5.  4/10  6/7  0/3

6.  1/10  6/7  3/3

7.  1/10  7/7  2/3

8.  8/10  0/7  2/3

9.  8/10  2/7  0/3

10. 5/10  2/7 3/3