Concept of Farmer Crossing a RiverDate: 04/30/2002 at 19:32:04 From: Mikel Schlotterback Subject: Urgent logic behind the farmer Dr. Math, I have seen many interpretations of the problem about the farmer and three other objects. I would like to know the history or mathematical concept behind it or solving it. How does the concept relate to the sheriffs and outlaws problem, husband and wives problem, and missionaries and cannibals problem? Is there a simple method they all follow? They are all similar and are solved in a certain method, but I don't know the name of that method. Could you help? Mikel Date: 05/01/2002 at 14:53:03 From: Doctor Ian Subject: Re: Urgent logic behind the farmer Hi Mikel, Are you talking about problems like this? Farmer Crossing a River http://mathforum.org/library/drmath/view/57914.html The general term that covers solutions to problems like this is, simply, 'search'. The problem defines a 'space' made up of 'states', and a set of 'transformations' that determine which states can be reached from which other states. A 'search' is an algorithm or heuristic method for examining a path through this 'state space' that leads from the initial state to one or more 'goal states'. A large fraction of the literature in the field of artificial intelligence (AI) deals with efficient ways to transform problems into state spaces, and then search those spaces efficiently. Any introductory textbook on AI will give you a decent introduction to the subject. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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