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The jealous husbands and The missionaries and cannibals

Published online by Cambridge University Press:  01 August 2016

Ian Pressman
Affiliation:
Department of Mathematics and Computing, Polytechnic of the South Bank, London SE1 0AA
David Singmaster
Affiliation:
Department of Mathematics and Computing, Polytechnic of the South Bank, London SE1 0AA

Extract

The classical river crossing problem of the jealous husbands involves three couples who have to cross a river using a boat that holds just two people. The jealousy of the husbands requires that no wife can be in the presence of another man without her husband being present. This can be accomplished in 11 crossings (i.e. one-way trips). Tartaglia gave a sketchy solution for four couples but Bachet pointed out that this was erroneous and that four couples could not get across the river. In 1879, De Fontenay pointed out that four or more couples could cross the river if there was an island in the river and gave a solution for n couples in 8n – 8 crossings. Dudeney improved the solution for n = 4 and Ball noted that this gives 6n – 7 crossings for n couples.

Type
Research Article
Copyright
Copyright © The Mathematical Association 1989

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