Fill and Pour Problem

D

darndt1

New member
Joined
Aug 19, 2010
Messages
2
Jim has five containers:
1. A full 20 oz container
2. A full 20 oz container
3. An empty 20 oz container
4. An empty 9 oz container
5. An empty 3 oz container

He needs to fill and pour until there are:
- 10 oz in container #1
- 10 oz in container #2
- 10 oz in container #3
- 10 oz combined in containers 4 and 5

So far, I have made the following moves:
1. 2 to 4
2. 4 to 3
3. 2 to 4
4. 4 to 3
5. 1 to 4
6. 4 to 3
7. 1 to 5
8. 1 to 2
9. 4 and 5 to 1
10. 1 to 4
11. 1 to 5

This leaves me with 0 oz in container 1, 10 oz in container 2, 20 oz in container 3, 9 oz in container 4 and 1 oz in container 5. I am so stuck! I need help please!!! :?
 


If you pour half the contents of #1 into #3, there will be:

#1 10
#2 20
#3 10
#4 0
#5 0

At this point, it looks like you simply need to pour off 10 ounces from #2 and split it between #4 and #5.

Am I missing something ?

 
However, you cannot do that, because the containers are not marked. You do not know what half is. You have to use the smaller containers to fill and pour back and forth until you get the desired 10, 10, 10, 10.
 
Hello, darndt1!

I've made some progress, but haven't solved it yet.

Jim has five containers:
. . 1. A full 20-oz jar
. . 2. A full 20-oz jar
. . 3. An empty 20-oz jar
. . 4. An empty 9-oz jar
. . 5. An empty 3-oz jar

He needs to fill and pour until there are:
. . 10 oz in jar #1
. . 10 oz in jar #2
. . 10 oz in jar #3
. . 10 oz combined in jars 4 and 5
Click to expand...


We start with this set up:

Code: 
    *:::::*   *:::::*   *     *
    |:::::|   |:::::|   |     |
    |:::::|   |:::::|   |     |
    |:::::|   |:::::|   |     |   *     *  
    |: 20 |   |: 20 |   |     |   |     |
    |:::::|   |:::::|   |     |   |     |   *     *
    |:::::|   |:::::|   |     |   |     |   |     |
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pur 1 into 4 and 5:

Code: 
    *     *   *:::::*   *     *
    |     |   |:::::|   |     |
    |     |   |:::::|   |     |
    |     |   |:::::|   |     |   *:::::*  
    |:::::|   |: 20 |   |     |   |:::::|
    |: 8 :|   |:::::|   |     |   |: 9 :|   *:::::*
    |:::::|   |:::::|   |     |   |:::::|   |: 3 :|
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pour 4 into 3:

Code: 
    *     *   *:::::*   *     *
    |     |   |:::::|   |     |
    |     |   |:::::|   |     |
    |     |   |:::::|   |:::::|   *     *  
    |:::::|   |: 20 |   |:::::|   |     |
    |: 8 :|   |:::::|   |: 9 :|   |     |   *:::::*
    |:::::|   |:::::|   |:::::|   |     |   |: 3 :|
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pour 1 into 4

Code: 
    *     *   *:::::*   *     *
    |     |   |:::::|   |     |
    |     |   |:::::|   |     |
    |     |   |:::::|   |:::::|   *     *  
    |     |   |: 20 |   |:::::|   |:::::|
    |     |   |:::::|   |: 9 :|   |: 8 :|   *:::::*
    |     |   |:::::|   |:::::|   |:::::|   |: 3 :|
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pour 5 into 4

Code: 
    *     *   *:::::*   *     *
    |     |   |:::::|   |     |
    |     |   |:::::|   |     |
    |     |   |:::::|   |:::::|   *:::::*  
    |     |   |: 20 |   |:::::|   |:::::|
    |     |   |:::::|   |: 9 :|   |: 9 :|   *     *
    |     |   |:::::|   |:::::|   |:::::|   |: 2 :|
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pour 5 into 1

Code: 
    *     *   *:::::*   *     *
    |     |   |:::::|   |     |
    |     |   |:::::|   |     |
    |     |   |:::::|   |:::::|   *:::::*  
    |     |   |: 20 |   |:::::|   |:::::|
    |     |   |:::::|   |: 9 :|   |: 9 :|   *     *
    |: 2 :|   |:::::|   |:::::|   |:::::|   |     |
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pour 4 into 3

Code: 
    *     *   *:::::*   *     *
    |     |   |:::::|   |:::::|
    |     |   |:::::|   |:::::|
    |     |   |:::::|   |: 18 |   *     *  
    |     |   |: 20 |   |:::::|   |     |
    |     |   |:::::|   |:::::|   |     |   *     *
    |: 2 :|   |:::::|   |:::::|   |     |   |     |
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pour 2 into 4 and 5.

Code: 
    *     *   *     *   *     *
    |     |   |     |   |:::::|
    |     |   |     |   |:::::|
    |     |   |     |   |: 18 |   *:::::*  
    |     |   |:::::|   |:::::|   |:::::|
    |     |   |: 8 :|   |:::::|   |: 9 :|   *:::::*
    |: 2 :|   |:::::|   |:::::|   |:::::|   |: 3 :|
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pour 2 into 1

Code: 
    *     *   *     *   *     *
    |     |   |     |   |:::::|
    |     |   |     |   |:::::|
    |:::::|   |     |   |: 18 |   *:::::*  
    |: 10 |   |     |   |:::::|   |:::::|
    |:::::|   |     |   |:::::|   |: 9 :|   *:::::*
    |:::::|   |     |   |:::::|   |:::::|   |: 3 :|
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pour 4 into 3

Code: 
    *     *   *     *   *:::::*
    |     |   |     |   |:::::|
    |     |   |     |   |:::::|
    |:::::|   |     |   |: 20 |   *     *  
    |: 10 |   |     |   |:::::|   |:::::|
    |:::::|   |     |   |:::::|   |: 7 :|   *:::::*
    |:::::|   |     |   |:::::|   |:::::|   |: 3 :|
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Pour 4 and 5 into 2

Code: 
    *     *   *     *   *:::::*
    |     |   |     |   |:::::|
    |     |   |     |   |:::::|
    |:::::|   |:::::|   |: 20 |   *     *  
    |: 10 |   |: 10 |   |:::::|   |     |
    |:::::|   |:::::|   |:::::|   |     |   *     *
    |:::::|   |:::::|   |:::::|   |     |   |     |
    *-----*   *-----*   *-----*   *-----*   *-----*
       20       20        20         9         3


Now what?

 
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