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Problem of the Week 1079

Dinnertime Dilemma

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Suppose eight characters from a Jane Austen novel are having dinner at a round table. Following the rules of etiquette of the period, each can converse with only their immediate neighbors. Thus they decide that, several times during dinner, they will all rise and switch seats. How many times must they do this so that everyone has a chance to speak to everyone else?

Note: The problem can be asked, and answered, with 8 replaced by general n.

Suggested by Paul Cantrell, Macalester graduate. It appears that a similar problem is in a graph theory text, but I do not yet know which one.

© Copyright 2007 Stan Wagon. Reproduced with permission.

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10 September 2007