Tarrying at An Inn

Nine gentlemen met at an inn, and were so pleased by their host, and with each other, that in a frolic they agreed to carry on so long as they, together with their host, could sit in a different position at dinner. Pray how long, had they kept their agreement, would their frolic have lasted ?

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Source: A New and Complete System of Arithmetic, Composed for the use of the citizens of the United States, Nicolas Pike, Worcester Massachusetts, 2nd edition, 1797