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missionaries and cannibals problem
The missionaries and cannibals problem, and the closely related jealous husbands problem, are classic river-crossing problems.〔("The Jealous Husbands" and "The Missionaries and Cannibals" ), Ian Pressman and David Singmaster, ''The Mathematical Gazette'', 73, #464 (June 1989), pp. 73–81.〕 The missionaries and cannibals problem is a well-known toy problem in artificial intelligence, where it was used by Saul Amarel as an example of problem representation.〔(On representations of problems of reasoning about actions ), Saul Amarel, pp. 131–171, ''Machine Intelligence 3'', edited by Donald Michie, Amsterdam, London, New York: Elsevier/North-Holland, 1968.〕〔p. 9, (Searching in a Maze, in Search of Knowledge: Issues in Early Artificial Intelligence ), Roberto Cordeschi, pp. 1–23, ''Reasoning, Action andj Interaction in AI Theories and Systems: essays dedicated to Luigia Carlucci Aiello'', edited by Oliviero Stock and Marco Schaerf, Lecture Notes in Computer Science #4155, Berlin/Heidelberg: Springer, 2006, ISBN 978-3-540-37901-0.〕
==The problem==
In the missionaries and cannibals problem, three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, if there are missionaries present on the bank, they cannot be outnumbered by cannibals (if they were, the cannibals would eat the missionaries). The boat cannot cross the river by itself with no people on board. And, in some variations, one of the cannibals has only one arm and cannot row.〔
In the jealous husbands problem, the missionaries and cannibals become three married couples, with the constraint that no woman can be in the presence of another man unless her husband is also present. Under this constraint, there cannot be both women and men present on a bank with women outnumbering men, since if there were, some woman would be husbandless. Therefore, upon changing men to missionaries and women to cannibals, any solution to the jealous husbands problem will also become a solution to the missionaries and cannibals problem.〔
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