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### Using 3C and 5C Pails to get 4 Cups

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Date: 6/19/96 at 23:30:59
From: Anonymous
Subject: Using 3 and 5 cup pails to get 4 cups

Jim has to get 4 cups of water into one of the cups. He must have it
right on and all he can use is water, a 5 cup pail, and a 3 cup pail.
Hint: he is outside.

Help!
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Date: 6/20/96 at 8:0:50
From: Doctor Anthony
Subject: Re: Using 3 and 5 cup pails to get 4 cups

Start with the 5-cup pail empty, and the 3-cup pail full.  Pour the
3-cup pail into the 5-cup pail.  We now have the larger pail 3/5ths
full, leaving 2/5ths space.

Now refill the 3-cup pail and pour 2 cups worth of this into the 5-cup
pail to fill it completely.  This leaves 1 cup at the bottom of the
3-cup pail.

Empty out the 5-cup pail and pour the 1 cup from 3-cup pail into the
5-cup pail.

Now refill the 3-cup pail and pour a further 3 cups into the 5-cup
pail to bring the total in the 5-cup pail to 4 cups.

We now have exactly 4 cups of water in the 5-cup pail.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Date: 09/04/2002 at 12:55:58
From: Natalie
Subject: Mathematics for elementary school teachers

You are given a 5 gallon and a 3 gallon pail, both of which are
unmarked.  You are asked to fetch 4 gallons of water from the well
in one trip.  You must have both completely filled and completely
emptied. How?
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Date: 09/04/2002 at 13:52:00
From: Doctor Schwa
Subject: Re: Mathematics for elementary school teachers

Hi Natalie,

You can try to understand this question by trying to make 4 by adding
or subtracting full containers of 5 and 3.

For instance, you could make it by

5 - 3 + 5 - 3

That is, first fill the 5 container. Then pour 3 of it into the 3
container, and dump out the 3 container (that's the -3 part; now you
have 5 - 3 = 2 in the 5 container).

Now you want to add 5, but there's no room in the 5 container, so move
the 2 to the 3 container. Then fill the 5, and now you have

5 - 3 + 5 = 7.

Now pour from the 5 container to fill the 3 container the rest of the
way, and dump out the 3 container, so finally you have

5 - 3 + 5 - 3.

To check that you understand it, you can try: solving it based on
3 + 3 - 5 + 3, explaining why 3 + 3 + 3 - 5 doesn't work and
5 + 5 - 3 - 3 doesn't work.

Enjoy,

- Doctor Schwa, The Math Forum

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