Crossing a River: Cannibals and Missionaries
Date: 10/15/2001 at 21:40:32 From: A.J. Subject: Extended Word Prblem Three missionaries and three cannibals wish to cross a river using a single boat that will hold only two people. If at any time the cannibals outnumber the missionaries, those missionaries will be eaten. How can the crossing be safely made? I tried to solve this problem by drawing pictures and trying to make the cross, but couldn't come up with an answer. I keep getting stuck with the fact that the person in the boat counts too. It is obvious that two people go over and one has to bring the boat back. If a missionary and a cannibal go first and the missionary goes back and picks up a cannibal and takes him over (remember there is already one cannibal already there), then there will be two cannibals and one missionary. No matter what I try missionaries always get eaten. Please help!
Date: 10/16/2001 at 13:06:54 From: Doctor Rob Subject: Re: Extended Word Prblem I like to draw a diagram like those below. There are two ways to start, either with a missionary and a cannibal in the boat, or with two cannibals in the boat. At each step after the first, without undoing what you have just done, there are either just one or just two possible things that can happen without any eating, so you can work your way through the process. Once you have two cannibals, two missionaries, and the boat on the far side, send one missionary and one cannibal back, then reverse the order of the previous steps. Here is one way to start: CCCMMM -- CM-> CCMM CM <-M CCMMM C CC-> MMM CCC <-... ... ... - Doctor Rob, The Math Forum http://mathforum.org/dr.math/
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