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### Farmer, Goat, Wolf, and Cabbage Cross a River

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Date: 03/13/98 at 21:00:33
From: Anthony
Subject: Logic Puzzle

A farmer, a goat, a wolf, and a cabbage have to cross a river. A boat
nearby only has enough room for the farmer and one other thing. What
is the fewest number of trips he must take so that the goat does not
eat the cabbage, and so the wolf does not eat the goat?

Name another problem like this with four things and a farmer getting
across with a boat that holds three things.
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Date: 03/16/98 at 09:54:42
From: Doctor Timothy
Subject: Re: Logic Puzzle

Hi Anthony,

Logic problems are so cool! I love thinking about them. This one
actually isn't as bad as you might think, because the answer is really
forced on you by the rules of the problem. I'll get you started, then
you can try to finish it on your own.

So at the beginning, you have all three things on one side of the
river.

Farmer   |
Wolf     |
Goat     |
Cabbage  |

Now, the second you (the farmer) leave to go to the other side of the
river, the animals can start eating each other, right? OK, so let's
list which things you absolutely CAN'T leave alone:

wolf + goat (the problem says that the wolf will eat the goat)
goat + cabbage (the problem says that the goat will eat the cabbage)

So what are the ONLY two things that you can leave alone together at
any given time?

Once you've figured that out, just start writing down lists of farmer
trips to get everything over to the other side. As long as you bring
something across the river every time you possibly can, and as long
as you don't duplicate any moves, you should end up with the fewest
possible trips.

Just so you know you're on the right track -- when you solve it with
the fewest number of trips, the farmer takes _nothing_ across the
river (in either direction) only twice.

(P.S. Remember that the farmer might need to take things _back_ across
the river in order to keep things from eating each other!)

As for your second question, I have one big hint: what if there were a
big, huge, hungry lion prowling around that particularly enjoyed
eating wolves?

Good luck, and feel free to write again if you have another question!

-Doctor Timothy, The Math Forum
Check out our web site http://mathforum.org/dr.math/
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Associated Topics:
Middle School Logic
Middle School Puzzles
Middle School Word Problems

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