Farmer, Goat, Wolf, and Cabbage Cross a RiverDate: 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. 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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