Thread: Pour me another one

You got a 4gallon and a 9gallon container, an unmarked container, and a huge water supply.

You want to end up with exactly 6 gallons in the unmarked container.
YES: the unmarked container > 6 gallons!

You mission is to do it in exactly 9 moves, and using the MINIMUM
number of gallons of water from the water supply.

A "move" is any pouring and/or filling; as example, filling the
9gal from the water supply, then pouring to fill the 4gal container,
then emptying it out is 3 moves: fill-pour-empty.

How do you do it?

I shall refer to the 9 gallon, 4 gallon, and unmarked container as A, B, and C respectively. When I say A = 4, it means there are 4 gallons of water in container A.

1. Fill A
A = 9 B = 0 C = 0

2. Pour water from A to B until B is full
A = 5 B = 4 C = 0

3. Pour the remaining water from A into C.
A = 0 B = 4 C = 5

4. Pour water from B into A
A = 4 B = 0 C = 5

5. Pour water from C into B until B is full
A = 4 B = 4 C =1

6. Empty B
A = 4 B = 0 C = 1

7. Top up the water in A
A = 9 B = 0 C = 1

8. Pour water from A to B until B is full
A = 5 B = 4 C = 1

9. Pour the remaining water from A to C
A = 0 B = 4 C = 6

Total gallons of water used = 9 + 5 = 14

I made that up along the way, but I'm not sure if it used the minimum number of water.

Hello, Wilmer!

I think I got it . . .

You have a 4-gallon and a 9-gallon container, an unmarked container, and a huge water supply.

You want to end up with exactly 6 gallons in the unmarked container.
(YES: the unmarked container > 6 gallons!)

Your mission is to do it in exactly 9 moves, and using the MINIMUM number of gallons of water
from the water supply.

A "move" is any pouring, filling or emptying.
For example, filling the 9-gal from the water supply,
then pouring it to fill the 4-gal container,
then emptying it is 3 moves: fill - pour - empty.

How do you do it?

Spoiler:

(1) Fill the "9".

Code:

                  *     *
                  |/////|
                  |/////|     *     *
                  |/////|     |     |
                  |/////|     |     |
      *     *     |//9//|     |  0  |
      |     |     |/////|     |     |
      |  0  |     |/////|     |     |
      *-----*     *-----*     *-----*
         4           9           U

(2) Pour "9" into "4".

Code:

                  *     *
                  |     |
                  |     |     *     *
                  |     |     |     |
                  |/////|     |     |
      *     *     |/////|     |  0  |
      |/////|     |//5//|     |     |
      |//4//|     |/////|     |     |
      *-----*     *-----*     *-----*
         4           9           U

(3) Empty "4",

Code:

                  *     *
                  |     |
                  |     |     *     *
                  |     |     |     |
                  |/////|     |     |
      *     *     |/////|     |  0  |
      |     |     |//5//|     |     |
      |  0  |     |/////|     |     |
      *-----*     *-----*     *-----*
         4           9           U

(4) Pour "9" into "4".

Code:

                  *     *
                  |     |
                  |     |     *     *
                  |     |     |     |
                  |     |     |     |
      *     *     |     |     |  0  |
      |/////|     |     |     |     |
      |//4//|     |//1//|     |     |
      * - - *     * - - *     * - - *
         4           9           U

(5) Pour "9" into "U".

Code:

                  *     *
                  |     |
                  |     |     *     *
                  |     |     |     |
                  |     |     |     |
      *     *     |     |     |     |
      |/////|     |  0  |     |     |
      |//4//|     |     |     |//1//|
      *-----*     *-----*     * - - *
         4           9           U

(6) Empty "4".

Code:

                  *     *
                  |     |
                  |     |     *     *
                  |     |     |     |
                  |     |     |     |
      *     *     |     |     |     |
      |     |     |  0  |     |     |
      |  0  |     |     |     |//1//|
      *-----*     *-----*     *-----*
         4           9           U

(7) Fill "9".

Code:

                  *     *
                  |/////|
                  |/////|     *     *
                  |/////|     |     |
                  |/////|     |     |
      *     *     |//9//|     |     |
      |     |     |/////|     |     |
      |  0  |     |/////|     |//1//|
      *-----*     *-----*     *-----*
         4           9           U

(8) Pour "9" into "4".

Code:

                  *     *
                  |     |
                  |     |     *     *
                  |     |     |     |
                  |/////|     |     |
      *     *     |/////|     |     |
      |/////|     |//5//|     |     |
      |//4//|     |/////|     |//1//|
      *-----*     *-----*     *-----*
         4           9           U

(9) Pour "9" into "U".

Code:

                  *     *
                  |     |
                  |     |     *     *
                  |     |     |     |
                  |     |     |/////|
      *     *     |     |     |/////|
      |/////|     |  0  |     |//6//|
      |//4//|     |     |     |/////|
      *-----*     *-----*     *-----*
         4           9           U

. . ta-DAA!

I used 18 gallons from the water supply
. . and discarded 8 gallons.
But I don't know if that's the optimal solution.

Edit: Gusbob, brilliant solution!
. . . You beat me by four gallons!
. . . Nice work!
.

Originally Posted by Gusbob

5. Pour water from C into B until B is full
A = 4 B = 4 C =1

6. Empty B
A = 4 B = 0 C = 1

7. Top up the water in A
A = 9 B = 0 C = 1

Good stuff....BUT only 10 gallons need be taken from supply:
At step#6, empty B into A: then you only need 1 gallon to fill A.

I'm assuming the 9 steps have to be defined and have meaning? So you don't pour into one barrel, then pour back, and repeat this to fill up a few steps? Because if such redundancy were permitted, this could be solved losing 6 gallons.

Total gallons of water used = 9 + 5 = 14

Hahaha very good answer, how did you get that so easily the question?

_________________________________
I love numbers
Treatment centers in georgia click here

Hey buddy, you made your first 9 posts today: clearly to expose that link of yours.
Why don't you return to that treatment center and ask them to lock you up!

Maybe it goes something like this Total gallons of water used = 9 + 5 = 14.... nice!


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