My challenge problem -- Pouring water from buckets into...

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lookagain

Elite Member
Joined
Aug 22, 2010
Messages
3,222
each other to end up with a certain number of gallons of water in a bucket.

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Problem:
-----------

You need to measure six gallons of water, but you have only a
7-gallon bucket (bucket A) and a 5-gallon bucket (bucket B).
Each bucket is in the shape of a right circular cylinder.
There is an unlimited supply of water, and each bucket starts
out empty.

Describe a way to do this.
 
Re: My challenge problem -- Pouring water from buckets into.

Code: 
              *
             *
            *
           *........*
            *      *
              *   *
                 *
[spoiler:pgkr4z8z]1: fill the 7gallon container; tip carefully until water level line horizontal as shown in diagram;
leaves 3.5 gallons in container.
2: repeat with 5gallon container: this time, let the water falling out fall in the 7gallon container;
leaves 3.5 + 2.5 = 6 gallons in 7gallon container.

NOTE: do not attempt if you have a hangover!
Nice puzzle, Sir.[/spoiler:pgkr4z8z]
 
Re: My challenge problem -- Pouring water from buckets into.

lookagain said:
each other to end up with a certain number of gallons of water in a bucket.

-----------------------------------------------------------------------------------------
-----------------------------------------------------------------------------------------


Problem:
-----------

You need to measure six gallons of water, but you have only a
7-gallon bucket (bucket A) and a 5-gallon bucket (bucket B).
Each bucket is in the shape of a right circular cylinder.
There is an unlimited supply of water, and each bucket starts
out empty.

Describe a way to do this.
Click to expand...

fill up 7 and and pour into 5 --- 2 left in 7

empty out 5 and pour 2 from 7 (3 left)

fill up 7 and pour 3 into five --- 4 left in 7.

empty out 5 and pour 4 from 7 --- 1 left (to be filled) in five.

Fill 7 and pour 1 into 5 ---- 6 left in 7.

You must do this with hangover - so that you can take a cold shower in the process.......
 
Re: My challenge problem -- Pouring water from buckets into.

Hello, lookagain!

You have a 7-gallon bucket (bucket A) and a 5-gallon bucket (bucket B).
Each bucket is in the shape of a right circular cylinder. .Is this relevant?
There is an unlimited supply of water.

Describe a way to measure exactly 6 gallons of water.
Click to expand...

1. Fill bucket A.

Code: 
      * - - - *
      |:::::::|
      |:::::::|     *       *
      |:::::::|     |       |
      |:: 7 ::|     |       |
      |:::::::|     |       |
      |:::::::|     |       |
      |:::::::|     |       |
      *-------*     *-------*
          A             B


2. Pour bucket A into bucket B.

Code: 
      *       *
      |       |
      |       |     * - - - *
      |       |     |:::::::|
      |       |     |:::::::|
      | - - - |     |:: 5 ::|
      |:::::::|     |:::::::|
      |:: 2 ::|     |:::::::|
      *-------*     *-------*
          A             B


3. Empty bucket B.

Code: 
      *       *
      |       |
      |       |     *       *
      |       |     |       |
      |       |     |       |
      | - - - |     |       |
      |:::::::|     |       |
      |:: 2 ::|     |       |
      *-------*     *-------*
          A             B


4. Pour bucket A into bucket B.

Code: 
      *       *
      |       |
      |       |     *       *
      |       |     |       |
      |       |     |       |
      |       |     | - - - |
      |       |     |:::::::|
      |       |     |:: 2 ::|
      *-------*     *-------*
          A             B


5. Fill bucket A.

Code: 
      * - - - *
      |:::::::|
      |:::::::|     *       *
      |:::::::|     |       |
      |:: 7 ::|     |       |
      |:::::::|     | - - - |
      |:::::::|     |:::::::|
      |:::::::|     |:: 2 ::|
      *-------*     *-------*
          A             B


6. Pour bucket A into bucket B.

Code: 
      *       *
      |       |
      |       |     * - - - *
      |       |     |:::::::|
      |:::::::|     |:::::::|
      |:::::::|     |:: 5 ::|
      |:: 4 ::|     |:::::::|
      |:::::::|     |:::::::|
      *-------*     *-------*
          A             B


7. Empty bucket B.

Code: 
      *       *
      |       |
      |       |     *       *
      |       |     |       |
      |:::::::|     |       |
      |:::::::|     |       |
      |:: 4 ::|     |       |
      |:::::::|     |       |
      *-------*     *-------*
          A             B


8. Pour bucket A into bucket B.

Code: 
      *       *
      |       |
      |       |     *       *
      |       |     | - - - |
      |       |     |:::::::|
      |       |     |:::::::|
      |       |     |:: 4 ::|
      |       |     |:::::::|
      *-------*     *-------*
          A             B


9. Fill bucket A.

Code: 
      * - - - *
      |:::::::|
      |:::::::|     *       *
      |:::::::|     | - - - |
      |:: 7 ::|     |:::::::|
      |:::::::|     |:::::::|
      |:::::::|     |:: 4 ::|
      |:::::::|     |:::::::|
      *-------*     *-------*
          A             B


10. Pour bucket A into bucket B.

Code: 
      *       *
      | - - - |
      |:::::::|     * - - - *
      |:::::::|     |:::::::|
      |:::::::|     |:::::::|
      |:: 6 ::|     |:: 5 ::|
      |:::::::|     |:::::::|
      |:::::::|     |:::::::|
      *-------*     *-------*
          A             B


Bucket A has exactly 6 gallons of water.

Edit: Subhotosh beat me to it . . . *sigh*
.
 
Re: My challenge problem -- Pouring water from buckets into.

soroban said:
Each bucket is in the shape of a right circular cylinder. .Is this relevant?
Click to expand...

soroban,

it *is* relevant if you want to do it by the method (in hidden form) by Denis.


It is not relevant for the method shown by Subhotosh Khan (which is also the method shown by you).


To all, if you have spent much time typing your text and your diagrams for this,
I thank you for your work and time in so doing.
 
Re: My challenge problem -- Pouring water from buckets into.

I did some googling to see if I could find a solution like mine done before;
unfortunately(!) I'm not the first one :(

It is mentionned here (scroll down a bit):
http://brainden.com/forum/index.php?/to ... g-water-v/

Of course, the containers need to be "symmetrical"....
 
Re: My challenge problem -- Pouring water from buckets into.

Denis said:
I did some googling to see if I could find a solution like mine done before;
unfortunately(!) I'm not the first one :(

It is mentionned here (scroll down a bit):
http://brainden.com/forum/index.php?/to ... g-water-v/

Of course, \(\displaystyle the \ containers \ need \ to \ be \ "symmetrical"....\)
Click to expand...


From the other forum:
--------------------------------------------------------------------------------------------------------------------------
#10 hoopshank

Newbie

Group: Members Posts: 4 Joined: 22-September 07 Posted 23 September 2007 - 01:25 AM

"Martini":2984f said:

"skbrown":2984f said:

"geekygirl":2984f said:

Both cases have a 4 litre bucket. If you fill the bucket and then slowly empty it until the water is touch just touching one side of the top and is just barely touching all of the bottom, you have the bucket half filled and therefore 2 litres. Basically, picture cutting the bucket diagonally.

Er, most buckets are tapered, aren't they?, and so this would not work at all. Or have I misunderstood your suggestion?

You haven't misunderstood; you're just under the assumption that skbrown's solution won't work with a tapered bucket. It will, as long as it's symmetrical.


This is not true! If it were a cylinder it would work. If it's tapered, it will not. Consider the extreme example of a bucket tapered to a point - you get a cone. How do you know when to stop pouring? Besides, we have BOWLS not buckets, which suggests an entirely different shape to me. Symmetrical or not, this method does not work with standard bowl or bucket shapes.

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Denis, I want to be clear to all readers. It is not only that they are "symmetrical," but the buckets
must also be right circular cylinders in shape for each to measure half-bucket amounts.

That is why your solution works. Otherwise, if instead they would have been "symmetrical,"
but not right circular cylinders in shape, then your method would not have worked.
 
Re: My challenge problem -- Pouring water from buckets into.

True; my bad.
 
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