Concept of Farmer Crossing a River

Date: 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/