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### 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/
```
Associated Topics:
High School Logic
High School Puzzles
Middle School Logic
Middle School Puzzles
Middle School Word Problems

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